# Expert Math and Science Articles

## The Rise of AI in Classrooms, Labs and Industry – Part 3

We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many great responses we need to split them into parts, here are the first several. This is part 3. Read part 1 here and part 2 here. Enjoy!…

## Recent Entries

### The Rise of AI in STEM - Part 2

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We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many…

### The Rise of Artificial intelligence in STEM Labs, Classrooms, and Industry

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We asked our PF Advisors "How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?". We got so many great…

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### Are Electromagnetic Waves Always Transverse?

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In this insight we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko's…

### How to Solve Second-Order Partial Derivatives

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Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…

### Is Pressure A Source Of Gravity?

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In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…

### Massive Meets Massless: Compton Scattering Revisited

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Introduction In a previous article entitled "Alternate Approach to 2D Collisions" we analysed collisions between a moving and stationary object by defining…

### Is Science An Authority?

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In a previous article, I discussed why scientists (among others) are almost never interested in considering a new theory proposed by a non-scientist: because…

### The Analytic Continuation of the Lerch and the Zeta Functions

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The Analytic Continuation of the Lerch Transcendent and the Riemann Zeta FunctionIntroduction In this brief Insight article the analytic continuations…

### Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data

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In Part 1 of this 3-part series, I explained kinematics in Einstien-deSitter (EdS) cosmology and in Part 2, I explained kinematics in ##\Lambda##CDM cosmology…

### Dark Energy Part 2: LCDM Cosmology

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This is Part 2 of a 3-part series explaining evidence for so-called “dark energy” leading to a current positive cosmological acceleration. The evidence…

### A Beginner's Guide to Baryons

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Introduction At the beginning of the 20th century it was thought that all matter consisted of only three particles: the electron, the neutron and the…

### Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

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In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…

### The Reappearance of Supernova (SN) Refsdal

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Space is always changing. Over thousands of years, astronomers have attempted to understand the workings. Trying to explain astronomical events offers…

### Dark Energy Part 1: Einstein-deSitter Cosmology

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In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein's equations of general relativity…

### Universe FAQ ‘Is there Evidence for the Big Bang?’

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Evidence for the big bang can be provided from observational astronomy using Hubble’s law (redshift of galaxies) also known as the ‘Doppler effect’…

### The Evolution of the Universe, Cosmic Web and Connections

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The universe was not perfectly uniform when it started, some areas had higher density than others. During the evolution of the universe, these areas of…

### Gaia and the Race to Detect More Gravitational Waves

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Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most…

### 3 Possible Models For Why Uranus Spins on Its Side

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Uranus spins on its side. Uranus has an obliquity (tilt) of 98º, making its axis of rotation closer to the ecliptic plane than any other planet. It is…

### Black Holes Are Not Empty Voids. A Black Hole at the Heart!

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Black Holes (BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects…

### A Path to Fractional Integral Representations of Some Special Functions

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0. Introduction As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here…

### Can We Do Better Than Mechanical Energy Conservation?

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Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the…

### An Alternate Approach to Solving 2 Dimensional Elastic Collisions

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Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article we determined the equal…

### Is Mechanical Energy Conservation Free of Ambiguity?

Introduction "Close to any question that is in the textbook, there is another question that has never been answered that is interesting." [Stephen Wolfram,…

### How to Recognize Split Electric Fields

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Introduction In a previous Insight, A New Interpretation of Dr. Walter Lewin’s Paradox, I introduced the fact that there are two kinds of E fields. …

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### What is Evolution: A Beginner's Guide

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Introduction to Evolution The study of evolution has dominated the field of biology for over a century. Explaining why the life we see is as it is fascinates…

### An Alternative Approach to Solving Collision Problems

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Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…

### Mathematician Mary Somerville Features in Google Doodle

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The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science writer, and with Caroline Herschel, the joint first…

### Why We Don't Discuss Perpetual Motion Machines (PMM)

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Authorship Contributions From: AnorlundaYou may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention.…

### Guide to C++ Programming For Beginners

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Contents 1. Getting a C++ Compiler and Compiling Your First Program 2. Simple Datatypes and Declarations 3. Operators and Expressions 4. Input and…

### Accurate Fluid Dynamics By Video Analysis

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IntroductionProviding accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility,…

### Want to Tell One Wood from Another? Learn Basic Wood Anatomy

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As a long-time woodworker I have an interest in being able to tell one wood from another and in the process of learning how to do that, I've developed…

### Explore the Fascinating Sums of Odd Powers of 1/n

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The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…

### Fundamentals of the Diffraction Grating Spectrometer

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Introduction In this article we will discuss the fundamentals of the diffraction grating spectrometer.  The operation of the instrument is based upon…

### Ionization Energy of Atomic Hydrogen

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Introduction In previous articles relating to various transition energies in Hydrogen, Helium and Deuterium we have employed the following formula for…

### Grab Bag Science Quiz

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Time to test your science knowledge with a fun 10 question quiz with random questions across all sciences. Difficulty is easy to medium. As always, post…

### SOHCAHTOA: Seemingly Simple, Conceivably Complex

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Preface My first experience with derivatives was seeing how they are obtained from the usual definition f'(x)=\underset{\text{$\Delta$x}\to 0}{\text{Lim}}\frac{f…

### An Intro to the Systemless Interface of Rooting Android Phones

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What you can learn from this article:What is meant by rooting an Android phone Steps to take before proceeding to root your phone Google’s…

### Answering Mermin's Challenge with Wilczek's Challenge

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Nearly four decades ago, Mermin revealed the conundrum of quantum entanglement for a general audience [1] using his "simple device," which I will refer…

### Bell States and Conservation of Spin Angular Momentum

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In a recent thread, I outlined how to compute the correlation function for the Bell basis states\begin{split}|\psi_-\rangle &=…

### Modern Physics Understood as an Unrecognized Kuhnian Revolution

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People often claim on Physics Forums and in the foundations community proper that quantum mechanics is "incomplete." Indeed, Lee Smolin recently wrote…

### Relativistic Treatment of the DC Conducting Straight Wire

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Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely…

### Revisiting The Deuterium Lyman Alpha Line Experiment

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Introduction In this article we will be revisiting a somewhat understudied (and seemingly unrepeated) experiment to measure the Deuterium Lyman Alpha…

### Signature of the Sun: Analyzing the Solar Balmer Series Lines

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Introduction We are in many ways a fortunate generation having so many wonderful tools at our disposal on account of the "silicon revolution" . The advent…

### Clearing Misconceptions and Some Tips on Debloating Android Phones

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What is bloatware? When you unbox your new phone, it comes with Android that is pre-installed by the manufacturer. This is termed as “stock firmware”.…

### Recursion in Programming and When to Use or Not to Use It

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Recursion is actually quite simple. It's a subroutine calling itself. Its surprising but some problems that look quite hard can be trivial using recursion…

### Understanding Bohr's Helium Lines

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Introduction In a previous article "Calculating the Balmer Alpha Line" we mentioned how accurate predictions of the spectral lines of singly ionized Helium…

### Maxwell's Equations in Magnetostatics and Solving with the Curl Operator

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Introduction: Maxwell's equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}}  ##  with ## \dot{\vec{E}}=0…

### What Are the Thermodynamics of Black Holes? A 5 Minute Introduction

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Definition/Summary The four laws of black hole thermodynamics are as follows...The Zeroth Law Surface gravity $(\kappa)$ is constant…

### What is Impedance? A 5 Minute Introduction

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Definition/Summary The impedance of a load (a combination of components) in an AC current is a complex number $Z\ =\ R+jX$ where $R$…