{"id":25754,"date":"2019-09-27T11:29:49","date_gmt":"2019-09-27T16:29:49","guid":{"rendered":"https:\/\/www.physicsforums.com\/insights\/?page_id=25754"},"modified":"2025-07-20T07:04:29","modified_gmt":"2025-07-20T12:04:29","slug":"new-home","status":"publish","type":"page","link":"https:\/\/www.physicsforums.com\/insights\/","title":{"rendered":"New Home"},"content":{"rendered":"\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-4vj50a-9128c539f73de6e396a5629f5b783829\">\n.flex_column.av-4vj50a-9128c539f73de6e396a5629f5b783829{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-4vj50a-9128c539f73de6e396a5629f5b783829 av_one_full  avia-builder-el-0  el_before_av_one_half  avia-builder-el-first  first flex_column_div av-zero-column-padding  '     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k3qfpza8-7346e15cbebe0e91fa1dfff94673ce3e\">\n#top .av-special-heading.av-k3qfpza8-7346e15cbebe0e91fa1dfff94673ce3e{\nmargin:0 0 0 0;\npadding-bottom:0;\n}\nbody .av-special-heading.av-k3qfpza8-7346e15cbebe0e91fa1dfff94673ce3e .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-k3qfpza8-7346e15cbebe0e91fa1dfff94673ce3e .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-k3qfpza8-7346e15cbebe0e91fa1dfff94673ce3e av-special-heading-h1 blockquote modern-quote  avia-builder-el-1  avia-builder-el-no-sibling  av-linked-heading'><h1 class='av-special-heading-tag '  itemprop=\"headline\"  >Physics, Math and Science Articles<\/h1><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mwb6wq-f42f8b65270e9e758397899dfd7544fc\">\n.flex_column.av-mwb6wq-f42f8b65270e9e758397899dfd7544fc{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-mwb6wq-f42f8b65270e9e758397899dfd7544fc av_one_half  avia-builder-el-2  el_after_av_one_full  el_before_av_one_half  first flex_column_div av-zero-column-padding  column-top-margin'     ><p><section  class='av_textblock_section av-k3qfn7qj-30245ff09c1fceecd439a6055e034b6d '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><\/div><\/section><br \/>\n<div  class='av-alb-blogposts template-blog  av-blog-meta-html-info-disabled '  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Blog\" ><article class=\"post-entry post-entry-type-standard post-entry-50705 post-loop-1 post-parity-odd post-entry-last single-big with-slider post-50705 post type-post status-publish format-standard has-post-thumbnail hentry category-math-tutorials\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" ><div class=\"big-preview single-big\"  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><a href=\"https:\/\/www.physicsforums.com\/insights\/ai-enriched-problem-solving\/\"  title=\"ai-problem-solving\" ><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2026\/02\/ai-problem-solving.png\" class=\"wp-image-51650 avia-img-lazy-loading-51650 attachment-entry_with_sidebar size-entry_with_sidebar wp-post-image\" alt=\"ai problem solving\" \/><\/a><\/div><div class=\"blog-meta\"><\/div><div class='entry-content-wrapper clearfix standard-content'><header class=\"entry-content-header\" aria-label=\"Post: AI Enriched Problem Solving\"><h2 class='post-title entry-title '  itemprop=\"headline\" ><a href=\"https:\/\/www.physicsforums.com\/insights\/ai-enriched-problem-solving\/\" rel=\"bookmark\" title=\"Permanent Link: AI Enriched Problem Solving\">AI Enriched Problem Solving<span class=\"post-format-icon minor-meta\"><\/span><\/a><\/h2><span class=\"post-meta-infos\"><time class=\"date-container minor-meta updated\"  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >February 28, 2026<\/time><span class=\"text-sep\">\/<\/span><span class=\"comment-container minor-meta\"><a href=\"https:\/\/www.physicsforums.com\/insights\/ai-enriched-problem-solving\/#comments\" class=\"comments-link\" >1 Comment<\/a><\/span><span class=\"text-sep\">\/<\/span><span class=\"blog-categories minor-meta\">in <a href=\"https:\/\/www.physicsforums.com\/insights\/science-math-tutorials\/math-tutorials\/\" rel=\"tag\">Mathematics Tutorials<\/a><\/span><span class=\"text-sep\">\/<\/span><span class=\"blog-author minor-meta\">by <span class=\"entry-author-link\"  itemprop=\"author\" ><span class=\"author\"><span class=\"fn\"><a href=\"https:\/\/www.physicsforums.com\/insights\/author\/neilparker62\/\" title=\"Posts by Neil Parker\" rel=\"author\">Neil Parker<\/a><\/span><\/span><\/span><\/span><\/span><\/header><div class=\"entry-content\"  itemprop=\"text\" ><p>Introduction This article is written by way of a reference for my longstanding PF colleague and prolific poster of challenging Maths\/geometry problems @chwala . The particular post this article will discuss is an example of one such problem which he raised on Physics Forums. https:\/\/www.physicsforums.com\/threads\/find-angle-adb-in-this-isoceles-triangle-given-some-extra-information.1063874\/ The Problem We take the liberty of including the original&#8230;<\/p>\n<\/div><footer class=\"entry-footer\"><\/footer><div class='post_delimiter'><\/div><\/div><div class=\"post_author_timeline\"><\/div><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2026\/02\/ai-problem-solving.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2026-02-28 16:16:26<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-28 16:16:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>AI Enriched Problem Solving<\/span><\/span><\/span><\/article><\/div><\/p><\/div><\/p>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-1aemvbu-96c51015b9b5146610da837d471b9fcb\">\n.flex_column.av-1aemvbu-96c51015b9b5146610da837d471b9fcb{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-1aemvbu-96c51015b9b5146610da837d471b9fcb av_one_half flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-k3xly0fg-28caedcdbec7cc4607b15fc251ccf83b '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><h2>Trending Articles<\/h2>\n\n<!-- WP Popular Posts v7.3.8 - cached -->\n<ul class=\"wpp-list\">\n<li class=\"\"><a href=\"https:\/\/www.physicsforums.com\/insights\/calculating-the-balmer-alpha-line-atomic-hydrogen\/\" target=\"_self\"><img src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35.png\" srcset=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35.png, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35@1.5x.png 1.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35@2x.png 2x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35@2.5x.png 2.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/24814-featured-50x35@3x.png 3x\" width=\"50\" height=\"35\" alt=\"Balmer Alpha Line\" class=\"wpp-thumbnail wpp_featured wpp_cached_thumb\" decoding=\"async\"><\/a> <a href=\"https:\/\/www.physicsforums.com\/insights\/calculating-the-balmer-alpha-line-atomic-hydrogen\/\" class=\"wpp-post-title\" target=\"_self\">Calculating the Balmer Alpha Line: Atomic Hydrogen<\/a> <span class=\"wpp-meta post-stats\"><span class=\"wpp-views\">353 views<\/span> | <span class=\"wpp-author\">by <a href=\"https:\/\/www.physicsforums.com\/insights\/author\/neilparker62\/\">Neil Parker<\/a><\/span> | <span class=\"wpp-date\">posted on July 8, 2019<\/span><\/span><\/li>\n<li class=\"\"><a href=\"https:\/\/www.physicsforums.com\/insights\/hand-wavy-discussion-planck-length\/\" target=\"_self\"><img src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35.png\" srcset=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35.png, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35@1.5x.png 1.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35@2x.png 2x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35@2.5x.png 2.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/4930-featured-50x35@3x.png 3x\" width=\"50\" height=\"35\" alt=\"planck\" class=\"wpp-thumbnail wpp_featured wpp_cached_thumb\" decoding=\"async\"><\/a> <a href=\"https:\/\/www.physicsforums.com\/insights\/hand-wavy-discussion-planck-length\/\" class=\"wpp-post-title\" target=\"_self\">What Planck Length Is and It\u2019s Common Misconceptions<\/a> <span class=\"wpp-meta post-stats\"><span class=\"wpp-views\">173 views<\/span> | <span class=\"wpp-author\">by <a href=\"https:\/\/www.physicsforums.com\/insights\/author\/klotza\/\">Alex Klotz<\/a><\/span> | <span class=\"wpp-date\">posted on September 9, 2015<\/span><\/span><\/li>\n<li class=\"\"><a href=\"https:\/\/www.physicsforums.com\/insights\/can-see-atom\/\" target=\"_self\"><img src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35.png\" srcset=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35.png, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35@1.5x.png 1.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35@2x.png 2x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35@2.5x.png 2.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/5387-featured-50x35@3x.png 3x\" width=\"50\" height=\"35\" alt=\"atoms\" class=\"wpp-thumbnail wpp_featured wpp_cached_thumb\" decoding=\"async\"><\/a> <a href=\"https:\/\/www.physicsforums.com\/insights\/can-see-atom\/\" class=\"wpp-post-title\" target=\"_self\">Can We See an Atom?<\/a> <span class=\"wpp-meta post-stats\"><span class=\"wpp-views\">132 views<\/span> | <span class=\"wpp-author\">by <a href=\"https:\/\/www.physicsforums.com\/insights\/author\/klotza\/\">Alex Klotz<\/a><\/span> | <span class=\"wpp-date\">posted on September 28, 2015<\/span><\/span><\/li>\n<li class=\"\"><a href=\"https:\/\/www.physicsforums.com\/insights\/what-is-a-tensor\/\" target=\"_self\"><img src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35.png\" srcset=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35.png, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35@1.5x.png 1.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35@2x.png 2x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35@2.5x.png 2.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/14577-featured-50x35@3x.png 3x\" width=\"50\" height=\"35\" alt=\"whatisatensor\" class=\"wpp-thumbnail wpp_featured wpp_cached_thumb\" decoding=\"async\"><\/a> <a href=\"https:\/\/www.physicsforums.com\/insights\/what-is-a-tensor\/\" class=\"wpp-post-title\" target=\"_self\">Tensors Explained: Scalars, Vectors, Matrices &amp; Math<\/a> <span class=\"wpp-meta post-stats\"><span class=\"wpp-views\">94 views<\/span> | <span class=\"wpp-author\">by <a href=\"https:\/\/www.physicsforums.com\/insights\/author\/fresh_42\/\">fresh_42<\/a><\/span> | <span class=\"wpp-date\">posted on June 18, 2017<\/span><\/span><\/li>\n<li class=\"\"><a href=\"https:\/\/www.physicsforums.com\/insights\/writing-master-degree-thesis\/\" target=\"_self\"><img src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35.png\" srcset=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35.png, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35@1.5x.png 1.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35@2x.png 2x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35@2.5x.png 2.5x, https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/wordpress-popular-posts\/3687-featured-50x35@3x.png 3x\" width=\"50\" height=\"35\" alt=\"masterdegree\" class=\"wpp-thumbnail wpp_featured wpp_cached_thumb\" decoding=\"async\"><\/a> <a href=\"https:\/\/www.physicsforums.com\/insights\/writing-master-degree-thesis\/\" class=\"wpp-post-title\" target=\"_self\">How to Write a Master Degree Thesis As a Physics Major<\/a> <span class=\"wpp-meta post-stats\"><span class=\"wpp-views\">85 views<\/span> | <span class=\"wpp-author\">by <a href=\"https:\/\/www.physicsforums.com\/insights\/author\/svein\/\">Svein<\/a><\/span> | <span class=\"wpp-date\">posted on June 23, 2015<\/span><\/span><\/li>\n\n<\/ul>\n<\/div><\/section><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-jqnjiy-4776d88a505f64f3733fd37335eb912d\">\n.flex_column.av-jqnjiy-4776d88a505f64f3733fd37335eb912d{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-jqnjiy-4776d88a505f64f3733fd37335eb912d av_one_full first flex_column_div av-zero-column-padding  '     ><section  class='av_textblock_section av-k3xmgddq-873c715fa01a03c22f6687c10e53cae4 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><h2>Recent Entries<\/h2>\n<\/div><\/section><br \/>\n<div  data-slideshow-options=\"{&quot;animation&quot;:&quot;fade&quot;,&quot;autoplay&quot;:false,&quot;loop_autoplay&quot;:&quot;once&quot;,&quot;interval&quot;:5,&quot;loop_manual&quot;:&quot;manual-endless&quot;,&quot;autoplay_stopper&quot;:false,&quot;noNavigation&quot;:false,&quot;show_slide_delay&quot;:90}\" class='avia-content-slider avia-content-grid-active avia-content-slider1 avia-content-slider-odd  av-slideshow-ui av-control-default   av-no-slider-navigation av-slideshow-manual av-loop-once av-loop-manual-endless '  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Blog\" ><div class=\"avia-content-slider-inner\"><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-49988 slide-entry-overview slide-loop-1 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/remote-operated-gate-control-system\/' data-rel='slide-1' class='slide-image' title='Remote Operated Gate Control System'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2026\/02\/gate-system.png\" class=\"wp-image-51647 avia-img-lazy-loading-51647 attachment-portfolio size-portfolio wp-post-image\" alt=\"gate system\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Remote Operated Gate Control System\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/remote-operated-gate-control-system\/' title='Remote Operated Gate Control System'>Remote Operated Gate Control System<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:11:58-06:00\" >February 28, 2026<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/remote-operated-gate-control-system\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nThis project began life in 2017 when the author had just begun experimentation with GPIO pins on a Raspberry Pi 3. At that point in time\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2026\/02\/gate-system.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2026-02-28 16:11:58<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-28 16:12:55<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Remote Operated Gate Control System<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-49914 slide-entry-overview slide-loop-2 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/independent-research-thinking-outside-the-box-versus-knowing-whats-in-the-box\/' data-rel='slide-1' class='slide-image' title='Inside the Scientific Box: History and Challenges Today'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/10\/maxwell-research.png\" class=\"wp-image-49954 avia-img-lazy-loading-49954 attachment-portfolio size-portfolio wp-post-image\" alt=\"\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Inside the Scientific Box: History and Challenges Today\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/independent-research-thinking-outside-the-box-versus-knowing-whats-in-the-box\/' title='Inside the Scientific Box: History and Challenges Today'>Inside the Scientific Box: History and Challenges Today<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-10-13T08:54:14-05:00\" >October 13, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/independent-research-thinking-outside-the-box-versus-knowing-whats-in-the-box\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In Memoriam\r\nIn Memory of Dr. Thomas J. LeCompte (1964-2025), Detector Designer and Champion of Education and Science.\r\nPrologue\r\nDefining \"the box\"\r\nSomeone\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/10\/maxwell-research.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-10-13 08:54:14<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:37:08<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Inside the Scientific Box: History and Challenges Today<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-49851 slide-entry-overview slide-loop-3 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-entangled-photon-polarization-qubits-violate-bells-inequality-per-quantum-information-theory\/' data-rel='slide-1' class='slide-image' title='Why Entangled Photon-Polarization Qubits Violate Bell&#8217;s Inequality per Quantum Information Theory'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/09\/Entangled-Photon-Polarization-Qubits.png\" class=\"wp-image-49908 avia-img-lazy-loading-49908 attachment-portfolio size-portfolio wp-post-image\" alt=\"Entangled Photon Polarization Qubits\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Why Entangled Photon-Polarization Qubits Violate Bell&#039;s Inequality per Quantum Information Theory\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-entangled-photon-polarization-qubits-violate-bells-inequality-per-quantum-information-theory\/' title='Why Entangled Photon-Polarization Qubits Violate Bell&#8217;s Inequality per Quantum Information Theory'>Why Entangled Photon-Polarization Qubits Violate Bell&#8217;s Inequality per Quantum Information Theory<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-09-29T07:54:13-05:00\" >September 29, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/why-entangled-photon-polarization-qubits-violate-bells-inequality-per-quantum-information-theory\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In her YouTube video Bell's Theorem Experiments on Entangled Photons, Dr. Fugate shows how polarization-entangled photons violate Bell's inequality. In\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/09\/Entangled-Photon-Polarization-Qubits.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-09-29 07:54:13<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-09-29 10:06:20<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Why Entangled Photon-Polarization Qubits Violate Bell&#8217;s Inequality per Quantum Information Theory<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-49737 slide-entry-overview slide-loop-4 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/relativator-circular-slide-rule-simulated-with-desmos\/' data-rel='slide-1' class='slide-image' title='Relativator (Circular Slide-Rule) &#8211; Simulated with Desmos'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/09\/relativator.png\" class=\"wp-image-49840 avia-img-lazy-loading-49840 attachment-portfolio size-portfolio wp-post-image\" alt=\"relativator\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Relativator (Circular Slide-Rule) - Simulated with Desmos\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/relativator-circular-slide-rule-simulated-with-desmos\/' title='Relativator (Circular Slide-Rule) &#8211; Simulated with Desmos'>Relativator (Circular Slide-Rule) &#8211; Simulated with Desmos<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-09-02T07:55:33-05:00\" >September 2, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/relativator-circular-slide-rule-simulated-with-desmos\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >The Relativator (revisited)\r\nThis is an update of my 2006 post (reconstructed in 2014) Relativator: The circular slide-rule for physicists.\r\nThis is a\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/09\/relativator.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>robphy<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>robphy<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-09-02 07:55:33<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-09-02 07:55:33<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Relativator (Circular Slide-Rule) &#8211; Simulated with Desmos<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-26196 slide-entry-overview slide-loop-5 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-exactly-is-diracs-delta-function\/' data-rel='slide-1' class='slide-image' title='What Exactly is Dirac&#8217;s Delta Function?'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/08\/dirac-function.png\" class=\"wp-image-49824 avia-img-lazy-loading-49824 attachment-portfolio size-portfolio wp-post-image\" alt=\"dirac function\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: What Exactly is Dirac&#039;s Delta Function?\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-exactly-is-diracs-delta-function\/' title='What Exactly is Dirac&#8217;s Delta Function?'>What Exactly is Dirac&#8217;s Delta Function?<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-08-29T06:51:27-05:00\" >August 29, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/what-exactly-is-diracs-delta-function\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction: \"Convenient Notation\"\r\n\r\n\r\nIn Dirac's Principles of Quantum Mechanics published in 1930 he introduced a \"convenient notation\" he referred\u00a0\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/08\/dirac-function.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>jambaugh<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>jambaugh<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-08-29 06:51:27<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-09-11 10:41:11<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>What Exactly is Dirac&#8217;s Delta Function?<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-49645 slide-entry-overview slide-loop-6 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect\/' data-rel='slide-1' class='slide-image' title='Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/08\/quantum-entanglement.png\" class=\"wp-image-49819 avia-img-lazy-loading-49819 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum entanglement\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect\/' title='Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'>Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-08-27T07:25:02-05:00\" >August 27, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/08\/quantum-entanglement.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-08-27 07:25:02<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-08-27 07:25:02<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-49363 slide-entry-overview slide-loop-7 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/fixing-things-which-can-go-wrong-with-complex-numbers\/' data-rel='slide-1' class='slide-image' title='Fixing Things Which Can Go Wrong With Complex Numbers'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/07\/complex_numbers_article.png\" class=\"wp-image-49577 avia-img-lazy-loading-49577 attachment-portfolio size-portfolio wp-post-image\" alt=\"complex numbers\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Fixing Things Which Can Go Wrong With Complex Numbers\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/fixing-things-which-can-go-wrong-with-complex-numbers\/' title='Fixing Things Which Can Go Wrong With Complex Numbers'>Fixing Things Which Can Go Wrong With Complex Numbers<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-07-20T06:55:08-05:00\" >July 20, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/fixing-things-which-can-go-wrong-with-complex-numbers\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nThis article will build on the hints about treating the complex numbers as a branched surface, briefly described and pictured in section 4.2\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/07\/complex_numbers_article.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PAllen<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PAllen<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-07-20 06:55:08<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-07-22 07:29:49<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Fixing Things Which Can Go Wrong With Complex Numbers<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-49230 slide-entry-overview slide-loop-8 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/fermats-last-theorem\/' data-rel='slide-1' class='slide-image' title='Fermat&#8217;s Last Theorem'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/05\/fermat.png\" class=\"wp-image-49266 avia-img-lazy-loading-49266 attachment-portfolio size-portfolio wp-post-image\" alt=\"Fermat&#039;s Last Theorem\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Fermat&#039;s Last Theorem\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/fermats-last-theorem\/' title='Fermat&#8217;s Last Theorem'>Fermat&#8217;s Last Theorem<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-05-18T17:50:22-05:00\" >May 18, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/fermats-last-theorem\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nFermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/05\/fermat.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-05-18 17:50:22<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-07-22 07:32:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Fermat&#8217;s Last Theorem<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-49127 slide-entry-overview slide-loop-9 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-vector-spaces-explain-the-world-a-historical-perspective\/' data-rel='slide-1' class='slide-image' title='Vector Spaces: Concepts, History, and Applications Guide'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/03\/vector-spaces.png\" class=\"wp-image-49170 avia-img-lazy-loading-49170 attachment-portfolio size-portfolio wp-post-image\" alt=\"vector spaces\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Vector Spaces: Concepts, History, and Applications Guide\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-vector-spaces-explain-the-world-a-historical-perspective\/' title='Vector Spaces: Concepts, History, and Applications Guide'>Vector Spaces: Concepts, History, and Applications Guide<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-03-13T07:45:20-05:00\" >March 13, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/why-vector-spaces-explain-the-world-a-historical-perspective\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >The Concept\r\nA vector space is an additively written abelian group together with a field that operates on it.\r\n\r\nIntuitive picture vs abstract definition\r\nVector\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/03\/vector-spaces.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-03-13 07:45:20<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:37:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Vector Spaces: Concepts, History, and Applications Guide<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-48834 slide-entry-overview slide-loop-10 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/groups-the-path-from-a-simple-concept-to-mysterious-results\/' data-rel='slide-1' class='slide-image' title='Groups, The Path from a Simple Concept to Mysterious Results'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/02\/math-Groups.png\" class=\"wp-image-48978 avia-img-lazy-loading-48978 attachment-portfolio size-portfolio wp-post-image\" alt=\"\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Groups, The Path from a Simple Concept to Mysterious Results\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/groups-the-path-from-a-simple-concept-to-mysterious-results\/' title='Groups, The Path from a Simple Concept to Mysterious Results'>Groups, The Path from a Simple Concept to Mysterious Results<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-02-02T19:47:02-06:00\" >February 2, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/groups-the-path-from-a-simple-concept-to-mysterious-results\/#comments'>9 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nThe concept of a group is as simple as it gets: a set with a binary operation like addition and a couple of natural laws like the requirement\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2025\/02\/math-Groups.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-02-02 19:47:02<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-02-12 08:56:11<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Groups, The Path from a Simple Concept to Mysterious Results<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-47676 slide-entry-overview slide-loop-11 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/modern-video-codecs\/' data-rel='slide-1' class='slide-image' title='Hybrid AI Video Codecs and Modern Streaming Techniques'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-1.png\" class=\"wp-image-44679 avia-img-lazy-loading-44679 attachment-portfolio size-portfolio wp-post-image\" alt=\"digital audio guide\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Hybrid AI Video Codecs and Modern Streaming Techniques\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/modern-video-codecs\/' title='Hybrid AI Video Codecs and Modern Streaming Techniques'>Hybrid AI Video Codecs and Modern Streaming Techniques<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2025-01-24T18:33:22-06:00\" >January 24, 2025<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/modern-video-codecs\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\n  AI and Hybrid Codecs\n  Modern Video codecs are all based on similar principles. Recently, these have been complemented by AI techniques,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-1.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2025-01-24 18:33:22<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:14:18<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Hybrid AI Video Codecs and Modern Streaming Techniques<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-48591 slide-entry-overview slide-loop-12 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/there-is-no-tidal-bulge-2\/' data-rel='slide-1' class='slide-image' title='Why the Tidal Bulge Doesn&#8217;t Exist &#8211; Tidal Theory Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/12\/no-tidal-bulge.png\" class=\"wp-image-48736 avia-img-lazy-loading-48736 attachment-portfolio size-portfolio wp-post-image\" alt=\"no tidal bulge\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Why the Tidal Bulge Doesn&#039;t Exist - Tidal Theory Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/there-is-no-tidal-bulge-2\/' title='Why the Tidal Bulge Doesn&#8217;t Exist &#8211; Tidal Theory Explained'>Why the Tidal Bulge Doesn&#8217;t Exist &#8211; Tidal Theory Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-12-31T08:23:01-06:00\" >December 31, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/there-is-no-tidal-bulge-2\/#comments'>9 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >[CONTENT]\nIntroduction\nOverview\nThat there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/12\/no-tidal-bulge.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>D H<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>D H<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-12-31 08:23:01<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:13:14<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Why the Tidal Bulge Doesn&#8217;t Exist &#8211; Tidal Theory Explained<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-48237 slide-entry-overview slide-loop-13 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-many-faces-of-topology\/' data-rel='slide-1' class='slide-image' title='The Many Faces of Topology'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/12\/topology.png\" class=\"wp-image-48432 avia-img-lazy-loading-48432 attachment-portfolio size-portfolio wp-post-image\" alt=\"topology\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Many Faces of Topology\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-many-faces-of-topology\/' title='The Many Faces of Topology'>The Many Faces of Topology<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-12-06T21:26:45-06:00\" >December 6, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-many-faces-of-topology\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nTopology as a branch of mathematics is a bracket that encompasses many different parts of mathematics. It is sometimes even difficult to see\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/12\/topology.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-12-06 21:26:45<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-17 02:54:22<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Many Faces of Topology<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-47569 slide-entry-overview slide-loop-14 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/brownian-motions-and-quantifying-randomness-in-physical-systems\/' data-rel='slide-1' class='slide-image' title='Brownian Motions and Quantifying Randomness in Physical Systems'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/08\/brownian-motion.png\" class=\"wp-image-47594 avia-img-lazy-loading-47594 attachment-portfolio size-portfolio wp-post-image\" alt=\"brownian motion\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Brownian Motions and Quantifying Randomness in Physical Systems\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/brownian-motions-and-quantifying-randomness-in-physical-systems\/' title='Brownian Motions and Quantifying Randomness in Physical Systems'>Brownian Motions and Quantifying Randomness in Physical Systems<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-08-26T07:14:45-05:00\" >August 26, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/brownian-motions-and-quantifying-randomness-in-physical-systems\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It's now a key player in data science,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/08\/brownian-motion.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>ergospherical<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>ergospherical<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-08-26 07:14:45<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-11-16 10:39:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Brownian Motions and Quantifying Randomness in Physical Systems<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-46583 slide-entry-overview slide-loop-15 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/pbs-video-comment-what-if-physics-is-not-describing-reality\/' data-rel='slide-1' class='slide-image' title='Quantum Reconstruction &#038; Bell Correlations Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/07\/physics-of-reality.png\" class=\"wp-image-46641 avia-img-lazy-loading-46641 attachment-portfolio size-portfolio wp-post-image\" alt=\"physics of reality\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quantum Reconstruction &amp; Bell Correlations Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/pbs-video-comment-what-if-physics-is-not-describing-reality\/' title='Quantum Reconstruction &#038; Bell Correlations Explained'>Quantum Reconstruction &#038; Bell Correlations Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-07-22T11:24:16-05:00\" >July 22, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/pbs-video-comment-what-if-physics-is-not-describing-reality\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Comment on PBS Space Time video\nPBS Space Time produces some very good videos on the foundations of quantum mechanics (QM), so let me comment on their\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/07\/physics-of-reality.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-07-22 11:24:16<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:10:56<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quantum Reconstruction &#038; Bell Correlations Explained<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-46242 slide-entry-overview slide-loop-16 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/aspects-behind-the-concept-of-dimension-in-various-fields\/' data-rel='slide-1' class='slide-image' title='Aspects Behind the Concept of Dimension in Various Fields'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/pvsnp.png\" class=\"wp-image-41832 avia-img-lazy-loading-41832 attachment-portfolio size-portfolio wp-post-image\" alt=\"pvsnp\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Aspects Behind the Concept of Dimension in Various Fields\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/aspects-behind-the-concept-of-dimension-in-various-fields\/' title='Aspects Behind the Concept of Dimension in Various Fields'>Aspects Behind the Concept of Dimension in Various Fields<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-06-21T12:42:18-05:00\" >June 21, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/aspects-behind-the-concept-of-dimension-in-various-fields\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nIt took until the last century for physicists and mathematicians in the Netherlands to question the Euclidean concept of dimension as length,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/pvsnp.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-06-21 12:42:18<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-06 21:31:12<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Aspects Behind the Concept of Dimension in Various Fields<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-46007 slide-entry-overview slide-loop-17 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/views-on-complex-numbers\/' data-rel='slide-1' class='slide-image' title='Views On Complex Numbers'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/06\/complex-numbers-views.png\" class=\"wp-image-46207 avia-img-lazy-loading-46207 attachment-portfolio size-portfolio wp-post-image\" alt=\"complex numbers views\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Views On Complex Numbers\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/views-on-complex-numbers\/' title='Views On Complex Numbers'>Views On Complex Numbers<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-06-07T06:10:00-05:00\" >June 7, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/views-on-complex-numbers\/#comments'>70 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nWhy do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/06\/complex-numbers-views.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-06-07 06:10:00<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-09-30 09:01:04<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Views On Complex Numbers<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-45831 slide-entry-overview slide-loop-18 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/addition-of-velocities-velocity-composition-in-special-relativity\/' data-rel='slide-1' class='slide-image' title='Addition of Velocities (Velocity Composition) in Special Relativity'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/05\/addition_of_velocities.png\" class=\"wp-image-45978 avia-img-lazy-loading-45978 attachment-portfolio size-portfolio wp-post-image\" alt=\"\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Addition of Velocities (Velocity Composition) in Special Relativity\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/addition-of-velocities-velocity-composition-in-special-relativity\/' title='Addition of Velocities (Velocity Composition) in Special Relativity'>Addition of Velocities (Velocity Composition) in Special Relativity<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-05-20T06:37:49-05:00\" >May 20, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/addition-of-velocities-velocity-composition-in-special-relativity\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >The \"Addition of Velocities\" formula (more correctly, the \"Composition of Velocities\" formula) in Special Relativity\r\n\r\n[tex]\\frac{v_{AC}}{c}=\\frac{ \\frac{v_{AB}}{c}+\\frac{v_{BC}}{c}\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/05\/addition_of_velocities.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>robphy<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>robphy<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-05-20 06:37:49<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-09-30 09:15:04<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Addition of Velocities (Velocity Composition) in Special Relativity<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-45596 slide-entry-overview slide-loop-19 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/schrodingers-cat-and-the-qbit\/' data-rel='slide-1' class='slide-image' title='Schr\u00f6dinger&#8217;s Cat and the Qbit'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/03\/shrodingers-cat.png\" class=\"wp-image-45663 avia-img-lazy-loading-45663 attachment-portfolio size-portfolio wp-post-image\" alt=\"Schrodinger&#039;s cat\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Schr\u00f6dinger&#039;s Cat and the Qbit\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/schrodingers-cat-and-the-qbit\/' title='Schr\u00f6dinger&#8217;s Cat and the Qbit'>Schr\u00f6dinger&#8217;s Cat and the Qbit<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-04-02T08:51:19-05:00\" >April 2, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/schrodingers-cat-and-the-qbit\/#comments'>27 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr##\\ddot{\\text{o}}##dinger noted in 1935 writing [1],\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/03\/shrodingers-cat.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-04-02 08:51:19<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-01-06 15:26:42<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Schr\u00f6dinger&#8217;s Cat and the Qbit<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-45556 slide-entry-overview slide-loop-20 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-slinky-drop-experiment-analysed\/' data-rel='slide-1' class='slide-image' title='The Slinky Drop Experiment Analysed'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/03\/slinky-drop-experiment.png\" class=\"wp-image-45639 avia-img-lazy-loading-45639 attachment-portfolio size-portfolio wp-post-image\" alt=\"slinky drop experiment\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Slinky Drop Experiment Analysed\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-slinky-drop-experiment-analysed\/' title='The Slinky Drop Experiment Analysed'>The Slinky Drop Experiment Analysed<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-03-28T16:19:54-05:00\" >March 28, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-slinky-drop-experiment-analysed\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >\r\n\r\nThe slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye.\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/03\/slinky-drop-experiment.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Orodruin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Orodruin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-03-28 16:19:54<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-09-30 09:01:52<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Slinky Drop Experiment Analysed<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-48162 slide-entry-overview slide-loop-21 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/infinite-universe\/' data-rel='slide-1' class='slide-image' title='Open, Flat &#038; Closed Universes: Curvature Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/11\/infinite-universe.png\" class=\"wp-image-48165 avia-img-lazy-loading-48165 attachment-portfolio size-portfolio wp-post-image\" alt=\"infinite universe\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Open, Flat &amp; Closed Universes: Curvature Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/infinite-universe\/' title='Open, Flat &#038; Closed Universes: Curvature Explained'>Open, Flat &#038; Closed Universes: Curvature Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-03-16T10:35:04-05:00\" >March 16, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/infinite-universe\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Standard cosmological models are classified by spatial curvature into three broad types: open, flat, and closed universes. These correspond to negative,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/11\/infinite-universe.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Greg Bernhardt<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Greg Bernhardt<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-03-16 10:35:04<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-04-05 14:05:22<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Open, Flat &#038; Closed Universes: Curvature Explained<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-48225 slide-entry-overview slide-loop-22 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/all-about-the-einstein-field-equations\/' data-rel='slide-1' class='slide-image' title='Einstein Field Equations &#8211; Definition and Fast Facts'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/11\/einstein-field-equations.png\" class=\"wp-image-48226 avia-img-lazy-loading-48226 attachment-portfolio size-portfolio wp-post-image\" alt=\"einstein field equations\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Einstein Field Equations - Definition and Fast Facts\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/all-about-the-einstein-field-equations\/' title='Einstein Field Equations &#8211; Definition and Fast Facts'>Einstein Field Equations &#8211; Definition and Fast Facts<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-02-26T08:29:20-06:00\" >February 26, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/all-about-the-einstein-field-equations\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Definition\/Summary\r\nThe Einstein Field Equations (EFE) are a set of ten interrelated differential equations that form the core of Einstein's general theory\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/11\/einstein-field-equations.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Greg Bernhardt<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Greg Bernhardt<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-02-26 08:29:20<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-04-05 14:07:24<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Einstein Field Equations &#8211; Definition and Fast Facts<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-44868 slide-entry-overview slide-loop-23 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-a-multi-atwood-machine-assembly\/' data-rel='slide-1' class='slide-image' title='How to Solve a Multi-Atwood Machine Assembly'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/02\/Multi-Atwood-Machine-Assembly.png\" class=\"wp-image-45414 avia-img-lazy-loading-45414 attachment-portfolio size-portfolio wp-post-image\" alt=\"Multi-Atwood Machine Assembly\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Solve a Multi-Atwood Machine Assembly\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-a-multi-atwood-machine-assembly\/' title='How to Solve a Multi-Atwood Machine Assembly'>How to Solve a Multi-Atwood Machine Assembly<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-02-16T10:18:12-06:00\" >February 16, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-a-multi-atwood-machine-assembly\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\n\r\n\r\nThe figure on the right shows a \"double-double\" Atwood machine with three ideal pulleys and four masses. \u00a0All pulleys are released from\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/02\/Multi-Atwood-Machine-Assembly.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-02-16 10:18:12<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 10:52:43<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Solve a Multi-Atwood Machine Assembly<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-44731 slide-entry-overview slide-loop-24 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-lambert-w-function-in-finance\/' data-rel='slide-1' class='slide-image' title='The Lambert W Function in Finance'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/02\/Lambert-W-Function-in-Finance.png\" class=\"wp-image-45299 avia-img-lazy-loading-45299 attachment-portfolio size-portfolio wp-post-image\" alt=\"Lambert W Function in Finance\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Lambert W Function in Finance\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-lambert-w-function-in-finance\/' title='The Lambert W Function in Finance'>The Lambert W Function in Finance<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-02-09T08:25:09-06:00\" >February 9, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-lambert-w-function-in-finance\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Preamble\r\nThe classical mathematician practically by instinct views the continuous process as the \"real\" process, and the discrete process as an approximation\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2024\/02\/Lambert-W-Function-in-Finance.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-02-09 08:25:09<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-02-09 08:25:09<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Lambert W Function in Finance<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-44769 slide-entry-overview slide-loop-25 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-division-by-zero-is-a-bad-idea\/' data-rel='slide-1' class='slide-image' title='Why Division by Zero Is Impossible: 10 Mathematical Reasons'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2015\/09\/infinity.png\" class=\"wp-image-4849 avia-img-lazy-loading-4849 attachment-portfolio size-portfolio wp-post-image\" alt=\"infinity\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Why Division by Zero Is Impossible: 10 Mathematical Reasons\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-division-by-zero-is-a-bad-idea\/' title='Why Division by Zero Is Impossible: 10 Mathematical Reasons'>Why Division by Zero Is Impossible: 10 Mathematical Reasons<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2024-01-11T10:41:33-06:00\" >January 11, 2024<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/why-division-by-zero-is-a-bad-idea\/#comments'>33 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs:\r\n\r\nWhat if it was\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2015\/09\/infinity.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2024-01-11 10:41:33<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-04-05 14:09:53<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Why Division by Zero Is Impossible: 10 Mathematical Reasons<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-44649 slide-entry-overview slide-loop-26 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/digital-filtering-and-exact-reconstruction-of-digital-audio\/' data-rel='slide-1' class='slide-image' title='Sinc Function &#038; Upsampling in Digital Audio Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-1.png\" class=\"wp-image-44679 avia-img-lazy-loading-44679 attachment-portfolio size-portfolio wp-post-image\" alt=\"digital audio guide\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Sinc Function &amp; Upsampling in Digital Audio Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/digital-filtering-and-exact-reconstruction-of-digital-audio\/' title='Sinc Function &#038; Upsampling in Digital Audio Explained'>Sinc Function &#038; Upsampling in Digital Audio Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-12-14T14:50:05-06:00\" >December 14, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/digital-filtering-and-exact-reconstruction-of-digital-audio\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\nThis elaborates some of the claims in my insights article on digital audio.\nThe Sinc Function\nUpsampling and Zero Insertion\nThe first link\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-1.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-12-14 14:50:05<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:09:43<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Sinc Function &#038; Upsampling in Digital Audio Explained<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-44584 slide-entry-overview slide-loop-27 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/digital-audio\/' data-rel='slide-1' class='slide-image' title='Modern DACs, Dither, DXD &#038; High-Res Audio Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-introduction.png\" class=\"wp-image-44674 avia-img-lazy-loading-44674 attachment-portfolio size-portfolio wp-post-image\" alt=\"digital audio intro\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Modern DACs, Dither, DXD &amp; High-Res Audio Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/digital-audio\/' title='Modern DACs, Dither, DXD &#038; High-Res Audio Explained'>Modern DACs, Dither, DXD &#038; High-Res Audio Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-12-11T19:08:57-06:00\" >December 11, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/digital-audio\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\nFirst, we need some background in Digital Signals. This can be mathematically quite advanced, but since I would like this article to be accessible\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/12\/digital-audio-introduction.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-12-11 19:08:57<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:09:01<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Modern DACs, Dither, DXD &#038; High-Res Audio Explained<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-44496 slide-entry-overview slide-loop-28 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/series-in-mathematics-from-zeno-to-quantum-theory\/' data-rel='slide-1' class='slide-image' title='Series in Mathematics: From Zeno to Quantum Theory'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/11\/geometric-series.png\" class=\"wp-image-44636 avia-img-lazy-loading-44636 attachment-portfolio size-portfolio wp-post-image\" alt=\"geometric series\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Series in Mathematics: From Zeno to Quantum Theory\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/series-in-mathematics-from-zeno-to-quantum-theory\/' title='Series in Mathematics: From Zeno to Quantum Theory'>Series in Mathematics: From Zeno to Quantum Theory<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-11-07T20:13:49-06:00\" >November 7, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/series-in-mathematics-from-zeno-to-quantum-theory\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nSeries play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/11\/geometric-series.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-11-07 20:13:49<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-06 21:31:10<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Series in Mathematics: From Zeno to Quantum Theory<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-44438 slide-entry-overview slide-loop-29 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/epsilontic-limits-and-continuity\/' data-rel='slide-1' class='slide-image' title='Epsilontic &#8211; Limits and Continuity'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/10\/epsilontic.png\" class=\"wp-image-44474 avia-img-lazy-loading-44474 attachment-portfolio size-portfolio wp-post-image\" alt=\"Epsilontic limits and continuity\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Epsilontic - Limits and Continuity\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/epsilontic-limits-and-continuity\/' title='Epsilontic &#8211; Limits and Continuity'>Epsilontic &#8211; Limits and Continuity<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-10-06T08:41:07-05:00\" >October 6, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/epsilontic-limits-and-continuity\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nI remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/10\/epsilontic.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-10-06 08:41:07<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-06 21:31:13<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Epsilontic &#8211; Limits and Continuity<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43029 slide-entry-overview slide-loop-30 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-poor-mans-milli-ohm-meter\/' data-rel='slide-1' class='slide-image' title='The Poor Man&#8217;s Milli-Ohm Meter'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Milli-Ohm.png\" class=\"wp-image-44426 avia-img-lazy-loading-44426 attachment-portfolio size-portfolio wp-post-image\" alt=\"Milli-Ohm\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Poor Man&#039;s Milli-Ohm Meter\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-poor-mans-milli-ohm-meter\/' title='The Poor Man&#8217;s Milli-Ohm Meter'>The Poor Man&#8217;s Milli-Ohm Meter<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-09-01T16:17:55-05:00\" >September 1, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-poor-mans-milli-ohm-meter\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIn a previous article on measuring battery internal resistance, a simple technique for low-resistance measurement was outlined. In this article,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Milli-Ohm.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-09-01 16:17:55<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 10:49:47<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Poor Man&#8217;s Milli-Ohm Meter<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-44253 slide-entry-overview slide-loop-31 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/differential-equation-systems-and-nature\/' data-rel='slide-1' class='slide-image' title='Differential Equation Systems and Nature'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Differential-Equation-Systems-and-Nature.png\" class=\"wp-image-44413 avia-img-lazy-loading-44413 attachment-portfolio size-portfolio wp-post-image\" alt=\"Differential Equation Systems and Nature\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Differential Equation Systems and Nature\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/differential-equation-systems-and-nature\/' title='Differential Equation Systems and Nature'>Differential Equation Systems and Nature<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-08-27T07:20:35-05:00\" >August 27, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/differential-equation-systems-and-nature\/#comments'>12 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\n\"Mathematics is the native language of nature.\" is a phrase that is often used when it comes to explaining why mathematics is all around in natural\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Differential-Equation-Systems-and-Nature.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-08-27 07:20:35<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-01-09 07:51:58<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Differential Equation Systems and Nature<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43710 slide-entry-overview slide-loop-32 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/precalculus-calculus-and-infinitesimals\/' data-rel='slide-1' class='slide-image' title='Beginners Guide to Precalculus, Calculus and Infinitesimals'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/calc-precalc.png\" class=\"wp-image-44245 avia-img-lazy-loading-44245 attachment-portfolio size-portfolio wp-post-image\" alt=\"calc precalc\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Beginners Guide to Precalculus, Calculus and Infinitesimals\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/precalculus-calculus-and-infinitesimals\/' title='Beginners Guide to Precalculus, Calculus and Infinitesimals'>Beginners Guide to Precalculus, Calculus and Infinitesimals<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-08-18T01:04:41-05:00\" >August 18, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/precalculus-calculus-and-infinitesimals\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nI am convinced students learn Calculus far too late.\u00a0 \u00a0In my view, there has never been a good reason for this.\r\n\r\nIn the US, they go through\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/calc-precalc.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-08-18 01:04:41<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-03-20 21:54:36<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Beginners Guide to Precalculus, Calculus and Infinitesimals<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43790 slide-entry-overview slide-loop-33 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-apply-newtons-second-law-to-variable-mass-systems\/' data-rel='slide-1' class='slide-image' title='How to Apply Newton&#8217;s Second Law to Variable Mass Systems'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Variable-Mass-Systems.png\" class=\"wp-image-44219 avia-img-lazy-loading-44219 attachment-portfolio size-portfolio wp-post-image\" alt=\"Variable Mass Systems\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Apply Newton&#039;s Second Law to Variable Mass Systems\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-apply-newtons-second-law-to-variable-mass-systems\/' title='How to Apply Newton&#8217;s Second Law to Variable Mass Systems'>How to Apply Newton&#8217;s Second Law to Variable Mass Systems<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-08-15T08:45:48-05:00\" >August 15, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-apply-newtons-second-law-to-variable-mass-systems\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nThe applicability of Newton's second law in the oft-quoted \"general form\" \u00a0$$\\begin{align}\\frac{d\\mathbf{P}}{dt}=\\mathbf{F}_{\\text{ext}}\\end{align}$$\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/Variable-Mass-Systems.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-08-15 08:45:48<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-07-14 14:24:06<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Apply Newton&#8217;s Second Law to Variable Mass Systems<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-43536 slide-entry-overview slide-loop-34 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-numbers\/' data-rel='slide-1' class='slide-image' title='What Are Numbers?'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/what-are-numbers.png\" class=\"wp-image-44224 avia-img-lazy-loading-44224 attachment-portfolio size-portfolio wp-post-image\" alt=\"what are numbers\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: What Are Numbers?\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-numbers\/' title='What Are Numbers?'>What Are Numbers?<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-08-14T22:43:45-05:00\" >August 14, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/what-are-numbers\/#comments'>7 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nWhen doing mathematics,\u00a0 we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive.\u00a0 \u00a0Going\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/08\/what-are-numbers.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-08-14 22:43:45<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-11-01 18:53:56<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>What Are Numbers?<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43587 slide-entry-overview slide-loop-35 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/introduction-to-the-world-of-algebras\/' data-rel='slide-1' class='slide-image' title='Introduction to the World of Algebras'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/07\/world-of-algebras.png\" class=\"wp-image-43690 avia-img-lazy-loading-43690 attachment-portfolio size-portfolio wp-post-image\" alt=\"world of algebras\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Introduction to the World of Algebras\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/introduction-to-the-world-of-algebras\/' title='Introduction to the World of Algebras'>Introduction to the World of Algebras<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-07-08T07:35:07-05:00\" >July 8, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/introduction-to-the-world-of-algebras\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nRichard Pierce describes the intention of his book [2] about associative algebras as his attempt to prove that there is algebra after Galois\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/07\/world-of-algebras.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-07-08 07:35:07<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-07-22 07:32:18<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Introduction to the World of Algebras<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43317 slide-entry-overview slide-loop-36 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-chatgpt-is-not-reliable\/' data-rel='slide-1' class='slide-image' title='Why ChatGPT Is Unreliable: Design Limits and Misconceptions'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/07\/chatgpt-reliable.png\" class=\"wp-image-43679 avia-img-lazy-loading-43679 attachment-portfolio size-portfolio wp-post-image\" alt=\"chatgpt-reliable\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Why ChatGPT Is Unreliable: Design Limits and Misconceptions\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-chatgpt-is-not-reliable\/' title='Why ChatGPT Is Unreliable: Design Limits and Misconceptions'>Why ChatGPT Is Unreliable: Design Limits and Misconceptions<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-07-05T06:08:15-05:00\" >July 5, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/why-chatgpt-is-not-reliable\/#comments'>138 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >ChatGPT's reliability\nI'll start with the simple fact: ChatGPT is not a reliable answerer to questions.\nWolfram's explanation\nTo try to explain why from\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/07\/chatgpt-reliable.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-07-05 06:08:15<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 08:06:52<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Why ChatGPT Is Unreliable: Design Limits and Misconceptions<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-43447 slide-entry-overview slide-loop-37 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals-simple-version\/' data-rel='slide-1' class='slide-image' title='What Are Infinitesimals &#8211; Simple Version'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/05\/Infinitesimals.png\" class=\"wp-image-43343 avia-img-lazy-loading-43343 attachment-portfolio size-portfolio wp-post-image\" alt=\"Infinitesimals\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: What Are Infinitesimals - Simple Version\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals-simple-version\/' title='What Are Infinitesimals &#8211; Simple Version'>What Are Infinitesimals &#8211; Simple Version<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-06-04T12:49:41-05:00\" >June 4, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals-simple-version\/#comments'>5 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nWhen I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/05\/Infinitesimals.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-06-04 12:49:41<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:52:41<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>What Are Infinitesimals &#8211; Simple Version<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43331 slide-entry-overview slide-loop-38 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theory-solves-the-only-mystery-of-quantum-mechanics\/' data-rel='slide-1' class='slide-image' title='How Quantum Information Theory Solves &#8220;the only mystery&#8221; of Quantum Mechanics'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/06\/quantum-information2.png\" class=\"wp-image-43433 avia-img-lazy-loading-43433 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum information\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How Quantum Information Theory Solves &quot;the only mystery&quot; of Quantum Mechanics\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theory-solves-the-only-mystery-of-quantum-mechanics\/' title='How Quantum Information Theory Solves &#8220;the only mystery&#8221; of Quantum Mechanics'>How Quantum Information Theory Solves &#8220;the only mystery&#8221; of Quantum Mechanics<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-06-03T08:49:50-05:00\" >June 3, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theory-solves-the-only-mystery-of-quantum-mechanics\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In Chapter 37 of \"The Feynman Lectures on Physics Volume 1,\" Richard Feynman famously wrote that the mystery of wave-particle duality in the double-slit\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/06\/quantum-information2.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-06-03 08:49:50<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:59:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How Quantum Information Theory Solves &#8220;the only mystery&#8221; of Quantum Mechanics<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-43241 slide-entry-overview slide-loop-39 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals\/' data-rel='slide-1' class='slide-image' title='What Are Infinitesimals &#8211; Advanced Version'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/05\/Infinitesimals.png\" class=\"wp-image-43343 avia-img-lazy-loading-43343 attachment-portfolio size-portfolio wp-post-image\" alt=\"Infinitesimals\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: What Are Infinitesimals - Advanced Version\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals\/' title='What Are Infinitesimals &#8211; Advanced Version'>What Are Infinitesimals &#8211; Advanced Version<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-05-24T03:01:58-05:00\" >May 24, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/what-are-infinitesimals\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nWhen I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/05\/Infinitesimals.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-05-24 03:01:58<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:51:21<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>What Are Infinitesimals &#8211; Advanced Version<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-43063 slide-entry-overview slide-loop-40 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/opinion-when-pro-scientists-explain-using-pop-science\/' data-rel='slide-1' class='slide-image' title='Popular Science Communication: Bridging Science &#038; Public'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/04\/pro-scientist-pop-science.png\" class=\"wp-image-43125 avia-img-lazy-loading-43125 attachment-portfolio size-portfolio wp-post-image\" alt=\"Carl Sagan\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Popular Science Communication: Bridging Science &amp; Public\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/opinion-when-pro-scientists-explain-using-pop-science\/' title='Popular Science Communication: Bridging Science &#038; Public'>Popular Science Communication: Bridging Science &#038; Public<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-04-30T12:05:43-05:00\" >April 30, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/opinion-when-pro-scientists-explain-using-pop-science\/#comments'>19 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\nFamous Science Communicators\nThere is so much to say about the many endeavors by professional scientists to explain to us the world. The list\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/04\/pro-scientist-pop-science.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-04-30 12:05:43<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:58:21<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Popular Science Communication: Bridging Science &#038; Public<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42985 slide-entry-overview slide-loop-41 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-art-of-integration\/' data-rel='slide-1' class='slide-image' title='The Art of Integration'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/04\/art-of-integration.png\" class=\"wp-image-43017 avia-img-lazy-loading-43017 attachment-portfolio size-portfolio wp-post-image\" alt=\"art of integration\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Art of Integration\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-art-of-integration\/' title='The Art of Integration'>The Art of Integration<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-04-10T07:36:52-05:00\" >April 10, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-art-of-integration\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nMy school teacher used to say\r\n\"Everybody can differentiate, but it takes an artist to integrate.\"\r\nThe mathematical reason behind this phrase\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/04\/art-of-integration.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-04-10 07:36:52<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-01-07 06:01:07<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Art of Integration<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42356 slide-entry-overview slide-loop-42 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-lesson-in-teaching-physics-you-cant-give-it-away\/' data-rel='slide-1' class='slide-image' title='A Lesson In Teaching Physics: You Can&#8217;t Give It Away'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/03\/teaching-physics.png\" class=\"wp-image-42957 avia-img-lazy-loading-42957 attachment-portfolio size-portfolio wp-post-image\" alt=\"teaching physics\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: A Lesson In Teaching Physics: You Can&#039;t Give It Away\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-lesson-in-teaching-physics-you-cant-give-it-away\/' title='A Lesson In Teaching Physics: You Can&#8217;t Give It Away'>A Lesson In Teaching Physics: You Can&#8217;t Give It Away<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-03-16T08:06:33-05:00\" >March 16, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/a-lesson-in-teaching-physics-you-cant-give-it-away\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >A central principle of Physics Forums regarding homework help is not to provide solutions on demand but to guide students along a path to the answer. The\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/03\/teaching-physics.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-03-16 08:06:33<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-03-13 08:05:02<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>A Lesson In Teaching Physics: You Can&#8217;t Give It Away<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-42892 slide-entry-overview slide-loop-43 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/an-overview-of-complex-differentiation-and-integration\/' data-rel='slide-1' class='slide-image' title='An Overview of Complex Differentiation and Integration'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/03\/integration_differentiation.png\" class=\"wp-image-42943 avia-img-lazy-loading-42943 attachment-portfolio size-portfolio wp-post-image\" alt=\"integration and complex differentiation\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: An Overview of Complex Differentiation and Integration\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/an-overview-of-complex-differentiation-and-integration\/' title='An Overview of Complex Differentiation and Integration'>An Overview of Complex Differentiation and Integration<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-03-14T08:24:25-05:00\" >March 14, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/an-overview-of-complex-differentiation-and-integration\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nI want to shed some light on complex analysis without getting all the technical details in the way which are necessary for the precise treatments\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/03\/integration_differentiation.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-03-14 08:24:25<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-06-02 15:46:27<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>An Overview of Complex Differentiation and Integration<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41870 slide-entry-overview slide-loop-44 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-measure-internal-resistance-of-a-battery\/' data-rel='slide-1' class='slide-image' title='How to Measure Internal Resistance of a Battery'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/02\/Measure-Internal-Resistance-of-Battery.png\" class=\"wp-image-42846 avia-img-lazy-loading-42846 attachment-portfolio size-portfolio wp-post-image\" alt=\"Measure Internal Resistance of Battery\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Measure Internal Resistance of a Battery\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-measure-internal-resistance-of-a-battery\/' title='How to Measure Internal Resistance of a Battery'>How to Measure Internal Resistance of a Battery<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-02-14T08:49:27-06:00\" >February 14, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-measure-internal-resistance-of-a-battery\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\nA commonly encountered school-level Physics practical is the determination of the internal resistance of a battery - typically an AA or D\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/02\/Measure-Internal-Resistance-of-Battery.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-02-14 08:49:27<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:55:36<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Measure Internal Resistance of a Battery<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42711 slide-entry-overview slide-loop-45 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-lie-groups-became-physics\/' data-rel='slide-1' class='slide-image' title='When Lie Groups Became Physics'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/02\/lie-group-physics.png\" class=\"wp-image-42798 avia-img-lazy-loading-42798 attachment-portfolio size-portfolio wp-post-image\" alt=\"lie group physics\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: When Lie Groups Became Physics\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-lie-groups-became-physics\/' title='When Lie Groups Became Physics'>When Lie Groups Became Physics<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-02-08T07:44:28-06:00\" >February 8, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/when-lie-groups-became-physics\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Abstract\r\nWe explain by simple examples (one-parameter Lie groups), partly in the original language, and along the historical papers of Sophus Lie, Abraham\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/02\/lie-group-physics.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-02-08 07:44:28<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-04-05 20:15:42<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>When Lie Groups Became Physics<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-29861 slide-entry-overview slide-loop-46 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-there-are-maximum-mass-limits-for-compact-objects\/' data-rel='slide-1' class='slide-image' title='Why There Are Maximum Mass Limits for Compact Objects'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/white-dwarfs.png\" class=\"wp-image-42721 avia-img-lazy-loading-42721 attachment-portfolio size-portfolio wp-post-image\" alt=\"white dwarfs\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Why There Are Maximum Mass Limits for Compact Objects\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/why-there-are-maximum-mass-limits-for-compact-objects\/' title='Why There Are Maximum Mass Limits for Compact Objects'>Why There Are Maximum Mass Limits for Compact Objects<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-01-27T08:01:59-06:00\" >January 27, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/why-there-are-maximum-mass-limits-for-compact-objects\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/white-dwarfs.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-01-27 08:01:59<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:52:50<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Why There Are Maximum Mass Limits for Compact Objects<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42435 slide-entry-overview slide-loop-47 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-implications\/' data-rel='slide-1' class='slide-image' title='Oppenheimer-Snyder Model of Gravitational Collapse: Implications'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/gravity-collapse3.png\" class=\"wp-image-42698 avia-img-lazy-loading-42698 attachment-portfolio size-portfolio wp-post-image\" alt=\"gravity collapse\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Oppenheimer-Snyder Model of Gravitational Collapse: Implications\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-implications\/' title='Oppenheimer-Snyder Model of Gravitational Collapse: Implications'>Oppenheimer-Snyder Model of Gravitational Collapse: Implications<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-01-15T21:27:43-06:00\" >January 15, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-implications\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Part 1: Overview\r\n\r\nPart 2: Mathematical Details\r\n\r\nPart 3: Implications\r\n\r\nIn the last article in this series, we finished up with a metric for the Oppenheimer-Snyder\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/gravity-collapse3.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-01-15 21:27:43<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-11-24 11:58:00<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Oppenheimer-Snyder Model of Gravitational Collapse: Implications<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-14113 slide-entry-overview slide-loop-48 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-tensors-and-why-are-they-used-in-relativity\/' data-rel='slide-1' class='slide-image' title='What Are Tensors and Why Are They Used in Relativity?'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2020\/08\/tensors-relativity.png\" class=\"wp-image-44146 avia-img-lazy-loading-44146 attachment-portfolio size-portfolio wp-post-image\" alt=\"tensors relativity\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: What Are Tensors and Why Are They Used in Relativity?\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/what-are-tensors-and-why-are-they-used-in-relativity\/' title='What Are Tensors and Why Are They Used in Relativity?'>What Are Tensors and Why Are They Used in Relativity?<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-01-11T07:57:09-06:00\" >January 11, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/what-are-tensors-and-why-are-they-used-in-relativity\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >If you try learning general relativity, and sometimes special relativity, on your own, you will undoubtedly run into tensors. This article will outline\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2020\/08\/tensors-relativity.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Isaac0427<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Isaac0427<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-01-11 07:57:09<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:45:39<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>What Are Tensors and Why Are They Used in Relativity?<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-42415 slide-entry-overview slide-loop-49 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-mathematical-details\/' data-rel='slide-1' class='slide-image' title='Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/gravity-collapse2.png\" class=\"wp-image-42659 avia-img-lazy-loading-42659 attachment-portfolio size-portfolio wp-post-image\" alt=\"gravity collapse\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-mathematical-details\/' title='Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details'>Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-01-09T08:01:01-06:00\" >January 9, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/oppenheimer-snyder-model-of-gravitational-collapse-mathematical-details\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Part 1: Overview\r\n\r\nPart 2: Mathematical Details\r\n\r\nPart 3: Implications\r\n\r\nIn a previous article, I described in general terms the model of gravitational\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/gravity-collapse2.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-01-09 08:01:01<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-04-02 10:15:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42488 slide-entry-overview slide-loop-50 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-discussing-the-twin-paradox-read-this-first\/' data-rel='slide-1' class='slide-image' title='Twin Paradox Guide: Spacetime Geometry Explained Clearly'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/twin-paradox.png\" class=\"wp-image-42603 avia-img-lazy-loading-42603 attachment-portfolio size-portfolio wp-post-image\" alt=\"twin paradox\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Twin Paradox Guide: Spacetime Geometry Explained Clearly\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-discussing-the-twin-paradox-read-this-first\/' title='Twin Paradox Guide: Spacetime Geometry Explained Clearly'>Twin Paradox Guide: Spacetime Geometry Explained Clearly<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2023-01-02T08:55:15-06:00\" >January 2, 2023<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/when-discussing-the-twin-paradox-read-this-first\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\nThis article is intended for anyone who wants to start a thread here at Physics Forums on the twin paradox. There are already many, many threads\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2023\/01\/twin-paradox.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2023-01-02 08:55:15<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:51:15<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Twin Paradox Guide: Spacetime Geometry Explained Clearly<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-23731 slide-entry-overview slide-loop-51 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-oppenheimer-snyder-model-of-gravitational-collapse-an-overview\/' data-rel='slide-1' class='slide-image' title='The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/gravity-collapse.png\" class=\"wp-image-42464 avia-img-lazy-loading-42464 attachment-portfolio size-portfolio wp-post-image\" alt=\"gravity collapse\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-oppenheimer-snyder-model-of-gravitational-collapse-an-overview\/' title='The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview'>The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-12-28T11:07:47-06:00\" >December 28, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-oppenheimer-snyder-model-of-gravitational-collapse-an-overview\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Part 1: Overview\r\n\r\nPart 2: Mathematical Details\r\n\r\nPart 3: Implications\r\n\r\nMost people who have spent any time at all studying GR are familiar with the\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/gravity-collapse.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeterDonis<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeterDonis<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-12-28 11:07:47<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-09-30 08:59:43<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-42298 slide-entry-overview slide-loop-52 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/subtleties-overlooked-in-friction-questions-object-slides-down-ramp\/' data-rel='slide-1' class='slide-image' title='Subtleties Overlooked in Friction Questions: Object Slides Down Ramp'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/object-slide-down-ramp-physics-1.png\" class=\"wp-image-42325 avia-img-lazy-loading-42325 attachment-portfolio size-portfolio wp-post-image\" alt=\"object slide down ramp physics\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Subtleties Overlooked in Friction Questions: Object Slides Down Ramp\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/subtleties-overlooked-in-friction-questions-object-slides-down-ramp\/' title='Subtleties Overlooked in Friction Questions: Object Slides Down Ramp'>Subtleties Overlooked in Friction Questions: Object Slides Down Ramp<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-12-06T09:22:09-06:00\" >December 6, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/subtleties-overlooked-in-friction-questions-object-slides-down-ramp\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Problem statement (simplified)\r\nAn object slides down a ramp at angle \u03b8 to encounter level ground. Both surfaces have kinetic friction: \u03bc' on the ramp,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/12\/object-slide-down-ramp-physics-1.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Derek Bolton<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Derek Bolton<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-12-06 09:22:09<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-12-21 00:14:58<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Subtleties Overlooked in Friction Questions: Object Slides Down Ramp<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42189 slide-entry-overview slide-loop-53 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/classification-of-mathematics-by-42-branches\/' data-rel='slide-1' class='slide-image' title='Mathematics Fields &#038; Applications: A Structured Guide'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/10\/math-classifications.png\" class=\"wp-image-42262 avia-img-lazy-loading-42262 attachment-portfolio size-portfolio wp-post-image\" alt=\"math classifications\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Mathematics Fields &amp; Applications: A Structured Guide\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/classification-of-mathematics-by-42-branches\/' title='Mathematics Fields &#038; Applications: A Structured Guide'>Mathematics Fields &#038; Applications: A Structured Guide<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-10-25T09:06:07-05:00\" >October 25, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/classification-of-mathematics-by-42-branches\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\nI often read questions about our classification scheme that we use on physicsforums.com to sort posts by science fields and subjects, what\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/10\/math-classifications.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-10-25 09:06:07<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:50:31<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Mathematics Fields &#038; Applications: A Structured Guide<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42135 slide-entry-overview slide-loop-54 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/reduction-of-order-for-recursions\/' data-rel='slide-1' class='slide-image' title='Reduction of Order For Recursions'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/10\/recursion-math.png\" class=\"wp-image-42187 avia-img-lazy-loading-42187 attachment-portfolio size-portfolio wp-post-image\" alt=\"recursion\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Reduction of Order For Recursions\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/reduction-of-order-for-recursions\/' title='Reduction of Order For Recursions'>Reduction of Order For Recursions<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-10-04T09:30:24-05:00\" >October 4, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/reduction-of-order-for-recursions\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >This is not meant as a full introduction to recursion relations but it should suffice for just about any level of the student.\r\n\r\nMost of us remember recursion\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/10\/recursion-math.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>topsquark<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>topsquark<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-10-04 09:30:24<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-04-02 10:17:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Reduction of Order For Recursions<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-42071 slide-entry-overview slide-loop-55 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/counting-to-p-adic-calculus-all-number-systems-that-we-have\/' data-rel='slide-1' class='slide-image' title='Counting to p-adic Calculus: All Number Systems That We Have'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/09\/history-of-numbers.png\" class=\"wp-image-42106 avia-img-lazy-loading-42106 attachment-portfolio size-portfolio wp-post-image\" alt=\"history of numbers\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Counting to p-adic Calculus: All Number Systems That We Have\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/counting-to-p-adic-calculus-all-number-systems-that-we-have\/' title='Counting to p-adic Calculus: All Number Systems That We Have'>Counting to p-adic Calculus: All Number Systems That We Have<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-09-18T15:11:13-05:00\" >September 18, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/counting-to-p-adic-calculus-all-number-systems-that-we-have\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >An entire book could easily be written about the history of numbers from ancient Babylon and India, over Abu Dscha'far Muhammad ibn Musa al-Chwarizmi (##\\sim\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/09\/history-of-numbers.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-09-18 15:11:13<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-06 21:31:11<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Counting to p-adic Calculus: All Number Systems That We Have<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-42024 slide-entry-overview slide-loop-56 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/intro-to-evariste-galois-and-galois-theory\/' data-rel='slide-1' class='slide-image' title='\u00c9variste Galois and His Theory'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/09\/evariste-galois.png\" class=\"wp-image-42059 avia-img-lazy-loading-42059 attachment-portfolio size-portfolio wp-post-image\" alt=\"evariste galois\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: \u00c9variste Galois and His Theory\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/intro-to-evariste-galois-and-galois-theory\/' title='\u00c9variste Galois and His Theory'>\u00c9variste Galois and His Theory<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-09-05T19:40:52-05:00\" >September 5, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/intro-to-evariste-galois-and-galois-theory\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >&nbsp;\r\n\r\n\r\n* Oct. 25th, 1811\u00a0 \u2020 May 31st, 1832\r\n... or why squaring the circle is doomed.\r\nGalois died in a duel at the age of twenty. Yet, he gave\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/09\/evariste-galois.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-09-05 19:40:52<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-08-15 09:04:12<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>\u00c9variste Galois and His Theory<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41907 slide-entry-overview slide-loop-57 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/yardsticks-to-metric-tensor-fields\/' data-rel='slide-1' class='slide-image' title='Yardsticks to Metric Tensor Fields'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/definition-differences.png\" class=\"wp-image-41991 avia-img-lazy-loading-41991 attachment-portfolio size-portfolio wp-post-image\" alt=\"definition differences\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Yardsticks to Metric Tensor Fields\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/yardsticks-to-metric-tensor-fields\/' title='Yardsticks to Metric Tensor Fields'>Yardsticks to Metric Tensor Fields<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-08-27T10:57:47-05:00\" >August 27, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/yardsticks-to-metric-tensor-fields\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >I asked myself why different scientists understand the same thing seemingly differently, especially the concept of a metric tensor. If we ask a topologist,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/definition-differences.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-08-27 10:57:47<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-06 21:31:11<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Yardsticks to Metric Tensor Fields<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-41842 slide-entry-overview slide-loop-58 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/programming-an-atmega8a-using-arduino\/' data-rel='slide-1' class='slide-image' title='Program ATmega8A with Arduino: Step-by-Step Guide'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/ATmega8A.png\" class=\"wp-image-41898 avia-img-lazy-loading-41898 attachment-portfolio size-portfolio wp-post-image\" alt=\"ATmega8A\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Program ATmega8A with Arduino: Step-by-Step Guide\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/programming-an-atmega8a-using-arduino\/' title='Program ATmega8A with Arduino: Step-by-Step Guide'>Program ATmega8A with Arduino: Step-by-Step Guide<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-08-13T07:50:26-05:00\" >August 13, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/programming-an-atmega8a-using-arduino\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\n  If you are interested in programming and electronics, you probably do not need an introduction to Arduino. If you want to make your Arduino\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/ATmega8A.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Wrichik Basu<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Wrichik Basu<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-08-13 07:50:26<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:48:28<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Program ATmega8A with Arduino: Step-by-Step Guide<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41797 slide-entry-overview slide-loop-59 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/p-vs-np-conjecture-calculations-and-meaning\/' data-rel='slide-1' class='slide-image' title='P vs. NP and what is a Turing Machine (TM)?'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/pvsnp.png\" class=\"wp-image-41832 avia-img-lazy-loading-41832 attachment-portfolio size-portfolio wp-post-image\" alt=\"pvsnp\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: P vs. NP and what is a Turing Machine (TM)?\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/p-vs-np-conjecture-calculations-and-meaning\/' title='P vs. NP and what is a Turing Machine (TM)?'>P vs. NP and what is a Turing Machine (TM)?<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-07-25T08:13:16-05:00\" >July 25, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/p-vs-np-conjecture-calculations-and-meaning\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >P or NP\r\nThis article deals with the complexity of calculations and in particular the meaning of\r\n##P\\stackrel{?}{\\neq}NP##\r\nBefore we explain what P and\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/pvsnp.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-07-25 08:13:16<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-07-25 09:22:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>P vs. NP and what is a Turing Machine (TM)?<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41743 slide-entry-overview slide-loop-60 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-computing-for-beginners\/' data-rel='slide-1' class='slide-image' title='Quantum Computing Explained: Qubits, Algorithms &#038; Applications'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/quantum-computers-101.png\" class=\"wp-image-41754 avia-img-lazy-loading-41754 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum computers 101\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quantum Computing Explained: Qubits, Algorithms &amp; Applications\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-computing-for-beginners\/' title='Quantum Computing Explained: Qubits, Algorithms &#038; Applications'>Quantum Computing Explained: Qubits, Algorithms &#038; Applications<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-07-14T21:35:57-05:00\" >July 14, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/quantum-computing-for-beginners\/#comments'>6 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Overview\n  This article provides an accessible introduction to quantum computing, a cutting-edge technology that processes certain types of information\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/07\/quantum-computers-101.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bob Walance<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bob Walance<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-07-14 21:35:57<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:47:28<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quantum Computing Explained: Qubits, Algorithms &#038; Applications<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-41423 slide-entry-overview slide-loop-61 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-physics-misconception-with-gauss-law\/' data-rel='slide-1' class='slide-image' title='A Physics Misconception with Gauss&#8217; Law'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/06\/gauss-law-misconceptions.png\" class=\"wp-image-41690 avia-img-lazy-loading-41690 attachment-portfolio size-portfolio wp-post-image\" alt=\"gauss law misconceptions\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: A Physics Misconception with Gauss&#039; Law\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-physics-misconception-with-gauss-law\/' title='A Physics Misconception with Gauss&#8217; Law'>A Physics Misconception with Gauss&#8217; Law<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-06-12T09:34:50-05:00\" >June 12, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/a-physics-misconception-with-gauss-law\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIt is relatively common to see the following type of argument:\r\nThe surface area is ##A## and the enclosed charge is ##Q##. The electric\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/06\/gauss-law-misconceptions.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Orodruin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Orodruin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-06-12 09:34:50<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-06-12 09:34:50<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>A Physics Misconception with Gauss&#8217; Law<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41241 slide-entry-overview slide-loop-62 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-conducting-pipe\/' data-rel='slide-1' class='slide-image' title='How to Model a Magnet Falling Through a Conducting Pipe'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/06\/model-magent2.png\" class=\"wp-image-41681 avia-img-lazy-loading-41681 attachment-portfolio size-portfolio wp-post-image\" alt=\"model magnet\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Model a Magnet Falling Through a Conducting Pipe\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-conducting-pipe\/' title='How to Model a Magnet Falling Through a Conducting Pipe'>How to Model a Magnet Falling Through a Conducting Pipe<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-06-11T06:58:05-05:00\" >June 11, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-conducting-pipe\/#comments'>7 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIn an earlier article, we examined a magnet falling through a solenoid. We argued that the point dipole model can account for the basic features\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/06\/model-magent2.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-06-11 06:58:05<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-06-11 06:58:05<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Model a Magnet Falling Through a Conducting Pipe<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40829 slide-entry-overview slide-loop-63 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-solenoid\/' data-rel='slide-1' class='slide-image' title='How to Model a Magnet Falling Through a Solenoid'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/model-magent.png\" class=\"wp-image-41595 avia-img-lazy-loading-41595 attachment-portfolio size-portfolio wp-post-image\" alt=\"model magnet\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Model a Magnet Falling Through a Solenoid\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-solenoid\/' title='How to Model a Magnet Falling Through a Solenoid'>How to Model a Magnet Falling Through a Solenoid<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-06-05T12:48:47-05:00\" >June 5, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-model-a-magnet-falling-through-a-solenoid\/#comments'>11 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nModeling a magnet realistically is a task best done numerically. \u00a0Even the simplified model of two separated disks with uniform surface\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/model-magent.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-06-05 12:48:47<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-06-11 07:07:53<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Model a Magnet Falling Through a Solenoid<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-41012 slide-entry-overview slide-loop-64 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-can-we-jump-when-the-ground-does-no-work\/' data-rel='slide-1' class='slide-image' title='How Can We Jump When the Ground Does No Work?'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/why-can-we-jump.png\" class=\"wp-image-41451 avia-img-lazy-loading-41451 attachment-portfolio size-portfolio wp-post-image\" alt=\"why can we jump\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How Can We Jump When the Ground Does No Work?\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-can-we-jump-when-the-ground-does-no-work\/' title='How Can We Jump When the Ground Does No Work?'>How Can We Jump When the Ground Does No Work?<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-05-30T16:09:36-05:00\" >May 30, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-can-we-jump-when-the-ground-does-no-work\/#comments'>20 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Common mistaken argument\nIt is relatively common on Physics Forums to see arguments that are effectively similar to the following:\nWhen we jump off the\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/why-can-we-jump.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Orodruin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Orodruin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-05-30 16:09:36<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:46:25<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How Can We Jump When the Ground Does No Work?<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40500 slide-entry-overview slide-loop-65 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-history-and-importance-of-the-riemann-hypothesis\/' data-rel='slide-1' class='slide-image' title='The History and Importance of the Riemann Hypothesis'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/Riemann-Hypothesis-History.png\" class=\"wp-image-41099 avia-img-lazy-loading-41099 attachment-portfolio size-portfolio wp-post-image\" alt=\"Riemann Hypothesis History\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The History and Importance of the Riemann Hypothesis\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-history-and-importance-of-the-riemann-hypothesis\/' title='The History and Importance of the Riemann Hypothesis'>The History and Importance of the Riemann Hypothesis<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-05-21T11:29:54-05:00\" >May 21, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-history-and-importance-of-the-riemann-hypothesis\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Riemann Hypothesis History\r\nThe Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the field\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/Riemann-Hypothesis-History.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-05-21 11:29:54<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-12-01 12:24:01<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The History and Importance of the Riemann Hypothesis<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40779 slide-entry-overview slide-loop-66 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/symmetry-arguments-and-the-infinite-wire-with-a-current\/' data-rel='slide-1' class='slide-image' title='Symmetry Arguments and the Infinite Wire with a Current'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/magnetism-current.png\" class=\"wp-image-40916 avia-img-lazy-loading-40916 attachment-portfolio size-portfolio wp-post-image\" alt=\"magnetism current\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Symmetry Arguments and the Infinite Wire with a Current\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/symmetry-arguments-and-the-infinite-wire-with-a-current\/' title='Symmetry Arguments and the Infinite Wire with a Current'>Symmetry Arguments and the Infinite Wire with a Current<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-05-17T07:56:44-05:00\" >May 17, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/symmetry-arguments-and-the-infinite-wire-with-a-current\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/05\/magnetism-current.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Orodruin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Orodruin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-05-17 07:56:44<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-05-17 08:06:59<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Symmetry Arguments and the Infinite Wire with a Current<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-40650 slide-entry-overview slide-loop-67 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-a-cpu-with-avx-512\/' data-rel='slide-1' class='slide-image' title='Parallel Programming on a CPU with AVX-512'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/cpu-programming.png\" class=\"wp-image-40749 avia-img-lazy-loading-40749 attachment-portfolio size-portfolio wp-post-image\" alt=\"cpu programming\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Parallel Programming on a CPU with AVX-512\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-a-cpu-with-avx-512\/' title='Parallel Programming on a CPU with AVX-512'>Parallel Programming on a CPU with AVX-512<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-04-23T08:56:07-05:00\" >April 23, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-a-cpu-with-avx-512\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >This article is the second of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/cpu-programming.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark44<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark44<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-04-23 08:56:07<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:45:29<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Parallel Programming on a CPU with AVX-512<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40425 slide-entry-overview slide-loop-68 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-an-nvidia-gpu\/' data-rel='slide-1' class='slide-image' title='CUDA Regression Line: GPU Parallel Programming Guide'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/programming-gpu.png\" class=\"wp-image-40737 avia-img-lazy-loading-40737 attachment-portfolio size-portfolio wp-post-image\" alt=\"programming gpu\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: CUDA Regression Line: GPU Parallel Programming Guide\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-an-nvidia-gpu\/' title='CUDA Regression Line: GPU Parallel Programming Guide'>CUDA Regression Line: GPU Parallel Programming Guide<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-04-16T15:08:29-05:00\" >April 16, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/parallel-programming-on-an-nvidia-gpu\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Overview\nThis article is the first of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/programming-gpu.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark44<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark44<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-04-16 15:08:29<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:43:34<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>CUDA Regression Line: GPU Parallel Programming Guide<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40680 slide-entry-overview slide-loop-69 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-novel-technique-of-calculating-unit-hypercube-integrals\/' data-rel='slide-1' class='slide-image' title='A Novel Technique of Calculating Unit Hypercube Integrals'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/hypercube-integral.png\" class=\"wp-image-40700 avia-img-lazy-loading-40700 attachment-portfolio size-portfolio wp-post-image\" alt=\"hypercube integral\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: A Novel Technique of Calculating Unit Hypercube Integrals\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-novel-technique-of-calculating-unit-hypercube-integrals\/' title='A Novel Technique of Calculating Unit Hypercube Integrals'>A Novel Technique of Calculating Unit Hypercube Integrals<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-04-14T08:02:00-05:00\" >April 14, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/a-novel-technique-of-calculating-unit-hypercube-integrals\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIn this insight article, we will build all the machinery necessary to evaluate unit hypercube integrals by a novel technique. We will first\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/hypercube-integral.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>benorin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>benorin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-04-14 08:02:00<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-05-31 00:36:20<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>A Novel Technique of Calculating Unit Hypercube Integrals<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-40573 slide-entry-overview slide-loop-70 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-extended-riemann-hypothesis-and-ramanujans-sum\/' data-rel='slide-1' class='slide-image' title='The Extended Riemann Hypothesis and Ramanujan&#8217;s Sum'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/Riemann-Hypothesis.png\" class=\"wp-image-40628 avia-img-lazy-loading-40628 attachment-portfolio size-portfolio wp-post-image\" alt=\"Riemann Hypothesis\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Extended Riemann Hypothesis and Ramanujan&#039;s Sum\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-extended-riemann-hypothesis-and-ramanujans-sum\/' title='The Extended Riemann Hypothesis and Ramanujan&#8217;s Sum'>The Extended Riemann Hypothesis and Ramanujan&#8217;s Sum<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-04-04T14:37:59-05:00\" >April 4, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-extended-riemann-hypothesis-and-ramanujans-sum\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Riemann Hypothesis and Ramanujan's Sum Explanation\r\n\r\n \tRH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line.\r\n \tERH: All\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/04\/Riemann-Hypothesis.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-04-04 14:37:59<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-05-28 09:35:34<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Extended Riemann Hypothesis and Ramanujan&#8217;s Sum<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40428 slide-entry-overview slide-loop-71 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-amazing-relationship-between-integration-and-eulers-number\/' data-rel='slide-1' class='slide-image' title='The Amazing Relationship Between Integration And Euler&#8217;s Number'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/03\/Hyperbola-1.png\" class=\"wp-image-40492 avia-img-lazy-loading-40492 attachment-portfolio size-portfolio wp-post-image\" alt=\"Hyperbola\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Amazing Relationship Between Integration And Euler&#039;s Number\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-amazing-relationship-between-integration-and-eulers-number\/' title='The Amazing Relationship Between Integration And Euler&#8217;s Number'>The Amazing Relationship Between Integration And Euler&#8217;s Number<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-03-28T17:09:06-05:00\" >March 28, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-amazing-relationship-between-integration-and-eulers-number\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >We use integration to measure lengths, areas, or volumes. This is a geometrical interpretation, but we want to examine an analytical interpretation that\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/03\/Hyperbola-1.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-03-28 17:09:06<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-07-22 07:32:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Amazing Relationship Between Integration And Euler&#8217;s Number<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40248 slide-entry-overview slide-loop-72 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/superdeterminism-and-the-mermin-device\/' data-rel='slide-1' class='slide-image' title='Superdeterminism and the Mermin Device'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/03\/mermin-device-quantum-entanglement.png\" class=\"wp-image-40394 avia-img-lazy-loading-40394 attachment-portfolio size-portfolio wp-post-image\" alt=\"mermin device quantum entanglement\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Superdeterminism and the Mermin Device\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/superdeterminism-and-the-mermin-device\/' title='Superdeterminism and the Mermin Device'>Superdeterminism and the Mermin Device<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-03-20T08:01:19-05:00\" >March 20, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/superdeterminism-and-the-mermin-device\/#comments'>141 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Superdeterminism as a way to resolve the mystery of quantum entanglement is generally not taken seriously in the foundations community, as explained in\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/03\/mermin-device-quantum-entanglement.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-03-20 08:01:19<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-04-17 10:24:07<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Superdeterminism and the Mermin Device<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-40061 slide-entry-overview slide-loop-73 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/relativity-on-rotated-graph-paper-a-graphical-motivation\/' data-rel='slide-1' class='slide-image' title='Relativity on Rotated Graph Paper (a graphical motivation)'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/02\/relativity-rotated-graph.png\" class=\"wp-image-40180 avia-img-lazy-loading-40180 attachment-portfolio size-portfolio wp-post-image\" alt=\"relativity rotated graph\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Relativity on Rotated Graph Paper (a graphical motivation)\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/relativity-on-rotated-graph-paper-a-graphical-motivation\/' title='Relativity on Rotated Graph Paper (a graphical motivation)'>Relativity on Rotated Graph Paper (a graphical motivation)<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-02-16T09:02:06-06:00\" >February 16, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/relativity-on-rotated-graph-paper-a-graphical-motivation\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >(based on https:\/\/www.physicsforums.com\/threads\/teaching-sr-without-simultaneity.1011051\/post-6588952 and https:\/\/physics.stackexchange.com\/a\/689291\/148184\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/02\/relativity-rotated-graph.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>robphy<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>robphy<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-02-16 09:02:06<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-02-16 21:24:54<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Relativity on Rotated Graph Paper (a graphical motivation)<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40064 slide-entry-overview slide-loop-74 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/probabilistic-factors-involved-in-disease-and-virus-testing\/' data-rel='slide-1' class='slide-image' title='Probabilistic Factors Involved in Disease and Virus Testing'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/02\/probabilities-virus-testing.png\" class=\"wp-image-40097 avia-img-lazy-loading-40097 attachment-portfolio size-portfolio wp-post-image\" alt=\"probabilities virus testing\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Probabilistic Factors Involved in Disease and Virus Testing\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/probabilistic-factors-involved-in-disease-and-virus-testing\/' title='Probabilistic Factors Involved in Disease and Virus Testing'>Probabilistic Factors Involved in Disease and Virus Testing<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-02-06T17:13:53-06:00\" >February 6, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/probabilistic-factors-involved-in-disease-and-virus-testing\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nThis Insight looks at the various probabilistic factors and related terminology involved in disease and virus testing.\r\n\r\nAs we all know,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/02\/probabilities-virus-testing.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>PeroK<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>PeroK<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-02-06 17:13:53<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:37:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Probabilistic Factors Involved in Disease and Virus Testing<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-40022 slide-entry-overview slide-loop-75 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-physics-via-quantum-tomography-a-new-approach-to-quantum-mechanics\/' data-rel='slide-1' class='slide-image' title='Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/01\/quantum-mechanics-new-approach.png\" class=\"wp-image-40043 avia-img-lazy-loading-40043 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum mechanics new approach\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-physics-via-quantum-tomography-a-new-approach-to-quantum-mechanics\/' title='Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics'>Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-01-08T10:33:06-06:00\" >January 8, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/quantum-physics-via-quantum-tomography-a-new-approach-to-quantum-mechanics\/#comments'>176 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >This Insight article presents the main features of a conceptual foundation of quantum physics with the same characteristic features as classical physics\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/01\/quantum-mechanics-new-approach.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Arnold Neumaier<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Arnold Neumaier<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-01-08 10:33:06<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-10-28 12:47:59<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-39963 slide-entry-overview slide-loop-76 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-trick-to-memorizing-trig-special-angle-values-table\/' data-rel='slide-1' class='slide-image' title='A Trick to Memorizing Trig Special Angle Values Table'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/01\/trig-special-functions.png\" class=\"wp-image-40016 avia-img-lazy-loading-40016 attachment-portfolio size-portfolio wp-post-image\" alt=\"trig special functions\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: A Trick to Memorizing Trig Special Angle Values Table\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/a-trick-to-memorizing-trig-special-angle-values-table\/' title='A Trick to Memorizing Trig Special Angle Values Table'>A Trick to Memorizing Trig Special Angle Values Table<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2022-01-01T09:25:53-06:00\" >January 1, 2022<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/a-trick-to-memorizing-trig-special-angle-values-table\/#comments'>3 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In calculus classes when you are asked to evaluate a trig function at a specific angle, it's 99.9% of the time at one of the so-called special angles we\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/01\/trig-special-functions.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>benorin<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>benorin<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2022-01-01 09:25:53<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-03-20 08:08:07<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>A Trick to Memorizing Trig Special Angle Values Table<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39904 slide-entry-overview slide-loop-77 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-setup-a-raspberry-pi-cluster\/' data-rel='slide-1' class='slide-image' title='Raspberry Pi Cluster Guide: Parts, MPI &#038; Slurm Tips'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/12\/setup-raspberry-pi-cluster.png\" class=\"wp-image-39933 avia-img-lazy-loading-39933 attachment-portfolio size-portfolio wp-post-image\" alt=\"setup raspberry pi cluster\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Raspberry Pi Cluster Guide: Parts, MPI &amp; Slurm Tips\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-setup-a-raspberry-pi-cluster\/' title='Raspberry Pi Cluster Guide: Parts, MPI &#038; Slurm Tips'>Raspberry Pi Cluster Guide: Parts, MPI &#038; Slurm Tips<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-12-22T09:58:56-06:00\" >December 22, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-setup-a-raspberry-pi-cluster\/#comments'>10 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >INTRODUCTION\nAs a long-time computer programmer and almost as long a High-Performance Computer (HPC) user, I didn't know anything about how these machines\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/12\/setup-raspberry-pi-cluster.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Dr Transport<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Dr Transport<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-12-22 09:58:56<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:42:23<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Raspberry Pi Cluster Guide: Parts, MPI &#038; Slurm Tips<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39570 slide-entry-overview slide-loop-78 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/an-introduction-to-theorema-primum\/' data-rel='slide-1' class='slide-image' title='An Introduction to Theorema Primum'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/11\/Theorema-Primum-tutorial.png\" class=\"wp-image-39877 avia-img-lazy-loading-39877 attachment-portfolio size-portfolio wp-post-image\" alt=\"Theorema Primum tutorial\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: An Introduction to Theorema Primum\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/an-introduction-to-theorema-primum\/' title='An Introduction to Theorema Primum'>An Introduction to Theorema Primum<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-11-27T12:18:05-06:00\" >November 27, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/an-introduction-to-theorema-primum\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nWhilst no doubt most frequenters of \"Physics Forums\" will be familiar with Nicolaus Copernicus as the scientist who advanced the (at the\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/11\/Theorema-Primum-tutorial.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-11-27 12:18:05<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-03-20 08:09:38<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>An Introduction to Theorema Primum<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-39733 slide-entry-overview slide-loop-79 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/pythons-sympy-module-and-the-cayley-hamilton-theorem\/' data-rel='slide-1' class='slide-image' title='Python&#8217;s Sympy Module and the Cayley-Hamilton Theorem'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/11\/python-sympy-module.png\" class=\"wp-image-39788 avia-img-lazy-loading-39788 attachment-portfolio size-portfolio wp-post-image\" alt=\"python sympy module\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Python&#039;s Sympy Module and the Cayley-Hamilton Theorem\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/pythons-sympy-module-and-the-cayley-hamilton-theorem\/' title='Python&#8217;s Sympy Module and the Cayley-Hamilton Theorem'>Python&#8217;s Sympy Module and the Cayley-Hamilton Theorem<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-11-09T18:48:33-06:00\" >November 9, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/pythons-sympy-module-and-the-cayley-hamilton-theorem\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Two of my favorite areas of study are linear algebra and computer programming. In this article I combine these areas by using Python to confirm that a\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/11\/python-sympy-module.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark44<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark44<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-11-09 18:48:33<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2021-11-10 10:42:51<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Python&#8217;s Sympy Module and the Cayley-Hamilton Theorem<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39593 slide-entry-overview slide-loop-80 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/geodesic-congruences-in-frw-schwarzschild-and-kerr-spacetimes\/' data-rel='slide-1' class='slide-image' title='Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/10\/spacetime-kerr.png\" class=\"wp-image-39620 avia-img-lazy-loading-39620 attachment-portfolio size-portfolio wp-post-image\" alt=\"Kerr Spacetime\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/geodesic-congruences-in-frw-schwarzschild-and-kerr-spacetimes\/' title='Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes'>Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-10-06T12:53:57-05:00\" >October 6, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/geodesic-congruences-in-frw-schwarzschild-and-kerr-spacetimes\/#comments'>5 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nThe theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/10\/spacetime-kerr.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>ergospherical<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>ergospherical<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-10-06 12:53:57<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2021-10-06 12:53:57<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39307 slide-entry-overview slide-loop-81 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/applications-of-the-tan-rule-in-trigonometry\/' data-rel='slide-1' class='slide-image' title='Physical Applications of the &#8220;Tan Rule&#8221;'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/09\/tan-rule-trigonometry.png\" class=\"wp-image-39563 avia-img-lazy-loading-39563 attachment-portfolio size-portfolio wp-post-image\" alt=\"tan rule\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Physical Applications of the &quot;Tan Rule&quot;\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/applications-of-the-tan-rule-in-trigonometry\/' title='Physical Applications of the &#8220;Tan Rule&#8221;'>Physical Applications of the &#8220;Tan Rule&#8221;<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-09-20T07:49:49-05:00\" >September 20, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/applications-of-the-tan-rule-in-trigonometry\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nEvery secondary school student who has encountered trigonometry in his\/her Math syllabus will most likely have come across the sine, cosine,\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/09\/tan-rule-trigonometry.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-09-20 07:49:49<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:33:43<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Physical Applications of the &#8220;Tan Rule&#8221;<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-39537 slide-entry-overview slide-loop-82 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/corrections-to-mit-open-courseware-systems-of-varying-mass\/' data-rel='slide-1' class='slide-image' title='Corrections to MIT Open Courseware: Systems of Varying Mass'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/09\/MIT-course-corrections.png\" class=\"wp-image-39544 avia-img-lazy-loading-39544 attachment-portfolio size-portfolio wp-post-image\" alt=\"MIT course corrections\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Corrections to MIT Open Courseware: Systems of Varying Mass\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/corrections-to-mit-open-courseware-systems-of-varying-mass\/' title='Corrections to MIT Open Courseware: Systems of Varying Mass'>Corrections to MIT Open Courseware: Systems of Varying Mass<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-09-14T13:24:01-05:00\" >September 14, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/corrections-to-mit-open-courseware-systems-of-varying-mass\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Corrections to\r\nMIT Open Courseware 8-01sc classical mechanics,\r\nfall 2016\r\nApplying Newton's Laws to systems of Varying Mass\r\nPDF Course Link\r\nMy concerns\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/09\/MIT-course-corrections.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Derek Bolton<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Derek Bolton<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-09-14 13:24:01<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:32:14<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Corrections to MIT Open Courseware: Systems of Varying Mass<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39200 slide-entry-overview slide-loop-83 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theorists-revealed-the-relativity-principle-at-the-foundation-of-quantum-mechanics\/' data-rel='slide-1' class='slide-image' title='How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/quantum-information.png\" class=\"wp-image-39304 avia-img-lazy-loading-39304 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum information\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theorists-revealed-the-relativity-principle-at-the-foundation-of-quantum-mechanics\/' title='How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics'>How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-07-25T07:48:35-05:00\" >July 25, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-quantum-information-theorists-revealed-the-relativity-principle-at-the-foundation-of-quantum-mechanics\/#comments'>12 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >This Insight is a condensed version of No Preferred Reference Frame at the Foundation of Quantum Mechanics. Reference numbers here correspond to that paper.\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/quantum-information.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Mark Stuckey<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Mark Stuckey<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-07-25 07:48:35<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-01-06 12:03:41<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39109 slide-entry-overview slide-loop-84 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/investigating-some-euler-sums\/' data-rel='slide-1' class='slide-image' title='Investigating Some Euler Sums'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/euler-sums.png\" class=\"wp-image-39265 avia-img-lazy-loading-39265 attachment-portfolio size-portfolio wp-post-image\" alt=\"euler sums\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Investigating Some Euler Sums\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/investigating-some-euler-sums\/' title='Investigating Some Euler Sums'>Investigating Some Euler Sums<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-07-21T09:56:00-05:00\" >July 21, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/investigating-some-euler-sums\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >So, why only odd powers? Mostly because the even powers were solved by Leonard Euler in the 18th century. Since the \u201cmathematical toolbox\u201d at that\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/euler-sums.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Svein<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Svein<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-07-21 09:56:00<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-03-20 08:10:05<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Investigating Some Euler Sums<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-37527 slide-entry-overview slide-loop-85 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/quaternions-in-projectile-motion\/' data-rel='slide-1' class='slide-image' title='Quaternions in Projectile Motion'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/Quaternions-in-Projectile-Motion.png\" class=\"wp-image-39106 avia-img-lazy-loading-39106 attachment-portfolio size-portfolio wp-post-image\" alt=\"Quaternions in Projectile Motion\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quaternions in Projectile Motion\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/quaternions-in-projectile-motion\/' title='Quaternions in Projectile Motion'>Quaternions in Projectile Motion<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-07-15T06:49:12-05:00\" >July 15, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/quaternions-in-projectile-motion\/#comments'>2 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIn a previous Physics Forums article entitled \u201cHow to Master Projectile Motion Without Quadratics\u201d, PF user\u00a0@kuruman\u00a0brought to our\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/07\/Quaternions-in-Projectile-Motion.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-07-15 06:49:12<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-05 06:46:17<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quaternions in Projectile Motion<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-36312 slide-entry-overview slide-loop-86 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-mechanics-and-the-famous-double-slit-experiment\/' data-rel='slide-1' class='slide-image' title='Quantum Mechanics and the Famous Double-slit Experiment'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/01\/quantum-double-slit.png\" class=\"wp-image-41697 avia-img-lazy-loading-41697 attachment-portfolio size-portfolio wp-post-image\" alt=\"quantum double slit experiment\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Quantum Mechanics and the Famous Double-slit Experiment\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/quantum-mechanics-and-the-famous-double-slit-experiment\/' title='Quantum Mechanics and the Famous Double-slit Experiment'>Quantum Mechanics and the Famous Double-slit Experiment<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-07-01T11:55:18-05:00\" >July 1, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/quantum-mechanics-and-the-famous-double-slit-experiment\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Double-slit Key Points\r\n\r\n \tQuantum mechanics is known for its strangeness, including phenomena like wave\u2013particle duality, which allows particles to\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/01\/quantum-double-slit.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>James Stone<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>James Stone<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-07-01 11:55:18<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-01-22 06:48:47<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Quantum Mechanics and the Famous Double-slit Experiment<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-39017 slide-entry-overview slide-loop-87 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-science-is-not-enough-legal-and-health-implications-of-questions\/' data-rel='slide-1' class='slide-image' title='Safety Factors: Why Forums Avoid Design Advice Online'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/safety.png\" class=\"wp-image-39027 avia-img-lazy-loading-39027 attachment-portfolio size-portfolio wp-post-image\" alt=\"safety\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Safety Factors: Why Forums Avoid Design Advice Online\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/when-science-is-not-enough-legal-and-health-implications-of-questions\/' title='Safety Factors: Why Forums Avoid Design Advice Online'>Safety Factors: Why Forums Avoid Design Advice Online<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-06-26T16:08:31-05:00\" >June 26, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/when-science-is-not-enough-legal-and-health-implications-of-questions\/#comments'>7 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Forum Guidelines\nThere are often questions on Physics Forums related to building machines or structures that are left unanswered because of this guideline\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/safety.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>jack action<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>jack action<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-06-26 16:08:31<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:40:55<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Safety Factors: Why Forums Avoid Design Advice Online<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-38983 slide-entry-overview slide-loop-88 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/lcevc-8k-tv\/' data-rel='slide-1' class='slide-image' title='LCEVC and EVC: Efficient Video Encoding Guide for 8K'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/LCEVC-8k-tv.png\" class=\"wp-image-39030 avia-img-lazy-loading-39030 attachment-portfolio size-portfolio wp-post-image\" alt=\"LCEVC 8k tv\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: LCEVC and EVC: Efficient Video Encoding Guide for 8K\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/lcevc-8k-tv\/' title='LCEVC and EVC: Efficient Video Encoding Guide for 8K'>LCEVC and EVC: Efficient Video Encoding Guide for 8K<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-06-19T18:00:08-05:00\" >June 19, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/lcevc-8k-tv\/#comments'>5 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\n  Background: H.264 and H.265\n  First, for background, here is an overview of the most common video compression standard in use today, H264:\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/LCEVC-8k-tv.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Bill Hobba<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Bill Hobba<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-06-19 18:00:08<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:40:25<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>LCEVC and EVC: Efficient Video Encoding Guide for 8K<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-22627 slide-entry-overview slide-loop-89 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-projectile-motion-problems-in-one-or-two-lines\/' data-rel='slide-1' class='slide-image' title='How to Solve Projectile Motion Problems in One or Two Lines'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/solving-projectile-motion.png\" class=\"wp-image-38935 avia-img-lazy-loading-38935 attachment-portfolio size-portfolio wp-post-image\" alt=\"solving projectile motion\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Solve Projectile Motion Problems in One or Two Lines\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-projectile-motion-problems-in-one-or-two-lines\/' title='How to Solve Projectile Motion Problems in One or Two Lines'>How to Solve Projectile Motion Problems in One or Two Lines<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-06-08T16:19:49-05:00\" >June 8, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-solve-projectile-motion-problems-in-one-or-two-lines\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nWe show how one can solve most if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/06\/solving-projectile-motion.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>kuruman<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>kuruman<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-06-08 16:19:49<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:27:50<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Solve Projectile Motion Problems in One or Two Lines<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-38245 slide-entry-overview slide-loop-90 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/10-math-things-we-all-learnt-wrong-at-school\/' data-rel='slide-1' class='slide-image' title='10 Math Things We All Learnt Wrong At School'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/blackboard.png\" class=\"wp-image-38292 avia-img-lazy-loading-38292 attachment-portfolio size-portfolio wp-post-image\" alt=\"blackboard\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: 10 Math Things We All Learnt Wrong At School\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/10-math-things-we-all-learnt-wrong-at-school\/' title='10 Math Things We All Learnt Wrong At School'>10 Math Things We All Learnt Wrong At School<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-04-21T16:20:23-05:00\" >April 21, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/10-math-things-we-all-learnt-wrong-at-school\/#comments'>10 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Some of these could even lead to heavy debates within the scientific community, so maybe I should say: from my point of view. So before you get excited\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/blackboard.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>fresh_42<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>fresh_42<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-04-21 16:20:23<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:26:59<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>10 Math Things We All Learnt Wrong At School<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-36839 slide-entry-overview slide-loop-91 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/fourier-series-and-the-riemann-zeta-function\/' data-rel='slide-1' class='slide-image' title='Computing the Riemann Zeta Function Using Fourier Series'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/Fourier-Series-Rieman-Zeta-Function.png\" class=\"wp-image-37515 avia-img-lazy-loading-37515 attachment-portfolio size-portfolio wp-post-image\" alt=\"Fourier Series Riemann Zeta Function\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Computing the Riemann Zeta Function Using Fourier Series\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/fourier-series-and-the-riemann-zeta-function\/' title='Computing the Riemann Zeta Function Using Fourier Series'>Computing the Riemann Zeta Function Using Fourier Series<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-04-09T06:35:32-05:00\" >April 9, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/fourier-series-and-the-riemann-zeta-function\/#comments'>5 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >\r\nEuler's amazing identity\r\nThe mathematician Leonard Euler developed some surprising mathematical formulas involving the number ##\\pi##. The most famous\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/Fourier-Series-Rieman-Zeta-Function.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>stevendaryl<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>stevendaryl<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-04-09 06:35:32<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2025-08-29 06:59:41<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Computing the Riemann Zeta Function Using Fourier Series<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-36954 slide-entry-overview slide-loop-92 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-link'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='' data-rel='slide-1' class='slide-image' title='Tolman Law in a Nutshell'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/tolman-law-beginner.png\" class=\"wp-image-37149 avia-img-lazy-loading-37149 attachment-portfolio size-portfolio wp-post-image\" alt=\"tolman law beginner\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Tolman Law in a Nutshell\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='' title='Tolman Law in a Nutshell'>Tolman Law in a Nutshell<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-04-02T07:48:09-05:00\" >April 2, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='#comments'>46 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >\r\nThe Tolman law describes how the temperature in a fixed gravitational field depends on the position (see https:\/\/arxiv.org\/abs\/1803.04106 for a pedagogic\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/04\/tolman-law-beginner.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Demystifier<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Demystifier<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-04-02 07:48:09<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2022-05-15 12:08:13<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Tolman Law in a Nutshell<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-36697 slide-entry-overview slide-loop-93 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/maximizing-horizontal-range-of-a-projectile\/' data-rel='slide-1' class='slide-image' title='Maximizing Horizontal Range of a Projectile'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/physics-cannonball-projectile.png\" class=\"wp-image-36949 avia-img-lazy-loading-36949 attachment-portfolio size-portfolio wp-post-image\" alt=\"physics cannonball projectile\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Maximizing Horizontal Range of a Projectile\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/maximizing-horizontal-range-of-a-projectile\/' title='Maximizing Horizontal Range of a Projectile'>Maximizing Horizontal Range of a Projectile<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-03-29T05:56:02-05:00\" >March 29, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/maximizing-horizontal-range-of-a-projectile\/#comments'>7 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nA recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/physics-cannonball-projectile.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-03-29 05:56:02<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:25:00<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Maximizing Horizontal Range of a Projectile<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-36635 slide-entry-overview slide-loop-94 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/numerical-em-solver-duality\/' data-rel='slide-1' class='slide-image' title='A Numerical Electromagnetic Solver Using Duality'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/electromagnetic-computations-2.png\" class=\"wp-image-36795 avia-img-lazy-loading-36795 attachment-portfolio size-portfolio wp-post-image\" alt=\"electromagnetic computations duality\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: A Numerical Electromagnetic Solver Using Duality\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/numerical-em-solver-duality\/' title='A Numerical Electromagnetic Solver Using Duality'>A Numerical Electromagnetic Solver Using Duality<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-03-18T08:17:58-05:00\" >March 18, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/numerical-em-solver-duality\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >In the previous insights article (How to Use Duality in Computational Electromagnetic Problems), I covered some uniqueness theorems for the Riemann-Silberstein\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/electromagnetic-computations-2.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Paul Colby<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Paul Colby<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-03-18 08:17:58<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-09-02 09:21:04<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>A Numerical Electromagnetic Solver Using Duality<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-36735 slide-entry-overview slide-loop-95 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-electric-field-seen-by-an-observer-a-relativistic-calculation-with-tensors\/' data-rel='slide-1' class='slide-image' title='The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/Electric-Field-Seen-by-an-Observer.png\" class=\"wp-image-36782 avia-img-lazy-loading-36782 attachment-portfolio size-portfolio wp-post-image\" alt=\"Electric Field Seen by an Observer\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/the-electric-field-seen-by-an-observer-a-relativistic-calculation-with-tensors\/' title='The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors'>The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-03-13T09:41:23-06:00\" >March 13, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/the-electric-field-seen-by-an-observer-a-relativistic-calculation-with-tensors\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >This Insight was inspired by the discussion in \"electric field seen by an observer in motion\", which tries to understand the relation between two expressions:\r\n\r\n\r\n\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/03\/Electric-Field-Seen-by-an-Observer.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>robphy<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>robphy<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-03-13 09:41:23<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2023-08-11 08:07:27<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-36640 slide-entry-overview slide-loop-96 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/valentines-reflections-mathematical-matters-of-the-heart\/' data-rel='slide-1' class='slide-image' title='Valentine&#8217;s Reflections: Mathematical Matters of the Heart'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/valentines-reflections-graphs.png\" class=\"wp-image-36690 avia-img-lazy-loading-36690 attachment-portfolio size-portfolio wp-post-image\" alt=\"valentines reflections graphs\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Valentine&#039;s Reflections: Mathematical Matters of the Heart\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/valentines-reflections-mathematical-matters-of-the-heart\/' title='Valentine&#8217;s Reflections: Mathematical Matters of the Heart'>Valentine&#8217;s Reflections: Mathematical Matters of the Heart<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-03-01T08:23:21-06:00\" >March 1, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/valentines-reflections-mathematical-matters-of-the-heart\/#comments'>4 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nBeing a somewhat geeky Maths 'nerd', I spent days leading up to Valentine's Day trying to find a Maths function appropriate to the day. In\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/valentines-reflections-graphs.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-03-01 08:23:21<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:22:41<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Valentine&#8217;s Reflections: Mathematical Matters of the Heart<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-36605 slide-entry-overview slide-loop-97 slide-parity-odd  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/posterior-predictive-distributions-in-bayesian-statistics\/' data-rel='slide-1' class='slide-image' title='Posterior Predictive Distributions in Bayesian Statistics'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/bayesian-statistics-part-4.png\" class=\"wp-image-36632 avia-img-lazy-loading-36632 attachment-portfolio size-portfolio wp-post-image\" alt=\"Bayesian statistics part 4\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Posterior Predictive Distributions in Bayesian Statistics\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/posterior-predictive-distributions-in-bayesian-statistics\/' title='Posterior Predictive Distributions in Bayesian Statistics'>Posterior Predictive Distributions in Bayesian Statistics<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-02-17T09:24:09-06:00\" >February 17, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/posterior-predictive-distributions-in-bayesian-statistics\/#comments'>7 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Confessions of a moderate Bayesian, part 4\r\nBayesian statistics by and for non-statisticians\r\n\r\nRead part 1: How to Get Started with Bayesian Statistics\r\n\r\nRead\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/bayesian-statistics-part-4.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Dale<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Dale<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-02-17 09:24:09<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:21:43<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Posterior Predictive Distributions in Bayesian Statistics<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-31941 slide-entry-overview slide-loop-98 slide-parity-even  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-use-duality-in-computational-electromagnetic-problems\/' data-rel='slide-1' class='slide-image' title='How to Use Duality in Computational Electromagnetic Problems'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/electromagnetic-computations.png\" class=\"wp-image-36599 avia-img-lazy-loading-36599 attachment-portfolio size-portfolio wp-post-image\" alt=\"electromagnetic computations\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: How to Use Duality in Computational Electromagnetic Problems\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/how-to-use-duality-in-computational-electromagnetic-problems\/' title='How to Use Duality in Computational Electromagnetic Problems'>How to Use Duality in Computational Electromagnetic Problems<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-02-14T19:46:56-06:00\" >February 14, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/how-to-use-duality-in-computational-electromagnetic-problems\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Some weeks ago I happened across a post that caught my eye. Dale asked a question about the number of photons in an electromagnetic field. His question\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/02\/electromagnetic-computations.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Paul Colby<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Paul Colby<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-02-14 19:46:56<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-11-24 11:57:31<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>How to Use Duality in Computational Electromagnetic Problems<\/span><\/span><\/span><\/article><article class='slide-entry flex_column  post-entry post-entry-41878 slide-entry-overview slide-loop-99 slide-parity-odd  av_one_third  real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/geometry-of-side-side-angle-ssa-and-impossible-triangles\/' data-rel='slide-1' class='slide-image' title='Ambiguous SSA Case in Triangles \u2014 Law of Sines Explained'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/impossible-triangles.png\" class=\"wp-image-42006 avia-img-lazy-loading-42006 attachment-portfolio size-portfolio wp-post-image\" alt=\"impossible triangles\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Ambiguous SSA Case in Triangles \u2014 Law of Sines Explained\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/geometry-of-side-side-angle-ssa-and-impossible-triangles\/' title='Ambiguous SSA Case in Triangles \u2014 Law of Sines Explained'>Ambiguous SSA Case in Triangles \u2014 Law of Sines Explained<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-01-28T10:50:35-06:00\" >January 28, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/geometry-of-side-side-angle-ssa-and-impossible-triangles\/#respond'>0 Comments<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >What is the ambiguous case?\nIn U.S. high schools, students are often introduced to geometric proofs for the first time. A common task is to use a small\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2022\/08\/impossible-triangles.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Jameson<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Jameson<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-01-28 10:50:35<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2026-02-17 07:39:42<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Ambiguous SSA Case in Triangles \u2014 Law of Sines Explained<\/span><\/span><\/span><\/article><\/div><div class=\"slide-entry-wrap\"><article class='slide-entry flex_column  post-entry post-entry-31483 slide-entry-overview slide-loop-100 slide-parity-odd  post-entry-last  av_one_third first real-thumbnail posttype-post post-format-standard'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><a href='https:\/\/www.physicsforums.com\/insights\/equations-of-motion-revisited\/' data-rel='slide-1' class='slide-image' title='Equations of Motion Revisited'><img decoding=\"async\" loading=\"lazy\" width=\"240\" height=\"135\" src=\"https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/01\/equations-of-motion.png\" class=\"wp-image-36302 avia-img-lazy-loading-36302 attachment-portfolio size-portfolio wp-post-image\" alt=\"equations of motion\" \/><\/a><div class=\"slide-content\"><header class=\"entry-content-header\" aria-label=\"Slide: Equations of Motion Revisited\"><h3 class='slide-entry-title entry-title '  itemprop=\"headline\" ><a href='https:\/\/www.physicsforums.com\/insights\/equations-of-motion-revisited\/' title='Equations of Motion Revisited'>Equations of Motion Revisited<\/a><\/h3><span class=\"av-vertical-delimiter\"><\/span><\/header><div class=\"slide-meta\"><time class='slide-meta-time updated'  itemprop=\"datePublished\" datetime=\"2021-01-11T15:47:32-06:00\" >January 11, 2021<\/time><div class=\"slide-meta-del\">\/<\/div><div class=\"slide-meta-comments\"><a href='https:\/\/www.physicsforums.com\/insights\/equations-of-motion-revisited\/#comments'>1 Comment<\/a><\/div><\/div><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" >Introduction\r\nIn any school Physics course, the Newtonian equations of motion are very much a 'stock' item. Students learn the equations and are given\u2026<\/div><\/div><footer class=\"entry-footer\"><\/footer><span class='hidden'>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" >\n\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2021\/01\/equations-of-motion.png<\/span>\n\t\t\t\t\t\t<span itemprop='height'>135<\/span>\n\t\t\t\t\t\t<span itemprop='width'>240<\/span>\n\t\t\t\t<\/span>\n\t\t\t\t<span class='av-structured-data'  itemprop=\"publisher\" itemtype=\"https:\/\/schema.org\/Organization\" itemscope=\"itemscope\" >\n\t\t\t\t\t\t<span itemprop='name'>Neil Parker<\/span>\n\t\t\t\t\t\t<span itemprop='logo' itemscope itemtype='https:\/\/schema.org\/ImageObject'>\n\t\t\t\t\t\t\t<span itemprop='url'>https:\/\/www.physicsforums.com\/insights\/wp-content\/uploads\/2019\/02\/Physics_Forums_Insights_logo.png<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/span><span class='av-structured-data'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><span itemprop='name'>Neil Parker<\/span><\/span><span class='av-structured-data'  itemprop=\"datePublished\" datetime=\"2026-02-28T16:16:26-06:00\" >2021-01-11 15:47:32<\/span><span class='av-structured-data'  itemprop=\"dateModified\" itemtype=\"https:\/\/schema.org\/dateModified\" >2024-08-18 09:19:26<\/span><span class='av-structured-data'  itemprop=\"mainEntityOfPage\" itemtype=\"https:\/\/schema.org\/mainEntityOfPage\" ><span itemprop='name'>Equations of Motion Revisited<\/span><\/span><\/span><\/article><\/div><\/div><div class='pagination-wrap pagination-slider'><nav class='pagination'><span class='pagination-meta'>Page 1 of 7<\/span><span class='current'>1<\/span><a href='https:\/\/www.physicsforums.com\/insights\/wp-json\/wp\/v2\/pages\/25754\/?avia-element-paging=2' class='inactive next_page' >2<\/a><a 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