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PAllen's latest activity
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PAllen
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Simple mass/scale puzzle
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All the scenarios are the same, including the original. A string or spring under tension T means each element has a pair of Newtonian...
Jul 25, 2025
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PAllen
replied to the thread
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Simple mass/scale puzzle
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Just replace string with spring in the argument. If the spring moves freely, it measures 0. If held stationary, it measures the force -...
Jul 24, 2025
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PAllen
replied to the thread
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Simple mass/scale puzzle
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The tension in the string is the result of one end fixed and the other end under force. The nature of the fixing of one end is...
Jul 23, 2025
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PAllen
replied to the thread
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Simple mass/scale puzzle
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Going with this idea, consider two rockets with equal thrust pulling on both end of a string. This presents the same ‘seeming’...
Jul 23, 2025
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PAllen
replied to the thread
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Time dilation for two clocks at different altitudes on Earth
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If you imagine two places on earth such that the total work to raise a small body from the surface to very far from earth was greater at...
Jul 22, 2025
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PAllen
replied to the thread
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More similar triangle problems
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Here it is worked out: Sum of small triangles plus rectangle = large triangle $$\frac {1}{2}4a + \frac{1}{2}2b + ab =...
Jul 22, 2025
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PAllen
replied to the thread
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More similar triangle problems
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Exercise for the reader: calling the 4 and 2 segments c and d, show that for a given rectangle area A, any choice of a and b, with ab=A...
Jul 22, 2025
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PAllen
replied to the thread
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More similar triangle problems
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Your first instinct is correct.
Jul 22, 2025
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PAllen
replied to the thread
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More similar triangle problems
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Write out your method and you will see you get an identity. Same for computing each triangle hypotenuse and relating them. The issue is...
Jul 22, 2025
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PAllen
replied to the thread
Insights
Fixing Things Which Can Go Wrong With Complex Numbers
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I'll wait to see if any other requests for improvement come in, so I can do all at once.
Jul 21, 2025
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PAllen
replied to the thread
Insights
Fixing Things Which Can Go Wrong With Complex Numbers
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If Greg restores ability to edit, I am willing to do this within all latex brackets. Where I just refer to log as text, I would rather...
Jul 21, 2025
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PAllen
posted the thread
Insights
Fixing Things Which Can Go Wrong With Complex Numbers
in
General Math
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Greg tells me the feature to generate a new insight announcement is broken, so I am doing this...
Jul 20, 2025
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PAllen
replied to the thread
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Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Read what I wrote more carefully. “You won’t necessarily get convergence”. The question is when it can be guaranteed. If any iteration...
Jul 20, 2025
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PAllen
replied to the thread
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Weyl tensor and coordinate acceleration
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It seems to me some very different things are being confused. In flat spacetime, there are obviously no coordinates that produce nonzero...
Jul 20, 2025
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PAllen
replied to the thread
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Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Rechecking my work, I find that this is a very interesting case. The root is about .755, and g’(root) just under 1 in absolute value...
Jul 20, 2025
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