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PAllen's latest activity
P
PAllen
replied to the thread
B
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
P
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
P
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
P
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
P
PAllen
replied to the thread
I
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
P
PAllen
replied to the thread
A
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
P
PAllen
replied to the thread
I
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
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Looking over the convergence proof in the book I referenced, it seems tweaking the argument can remove the need to prohibit g’ being...
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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The question was about convergence. For that, the requirement is the the derivative condition holding in a neighborhood of the root.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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A sufficient contrition is different from a necessary condition.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
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Also, note that g’(x) greater than one near the root.
Jul 20, 2025
P
PAllen
replied to the thread
I
Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
.
The derivative can’t be zero at any guess. This is assumed in derivations of convergence of the method. It is also required that an...
Jul 20, 2025
P
PAllen
replied to the thread
I can no longer render LaTeX
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Can you clarify? I see you would never want to use a posted insight; that's why I suggested a dummy (draft) insight. Once the latex...
Jul 14, 2025
P
PAllen
replied to the thread
I can no longer render LaTeX
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One other possible workaround is to keep a dummy insight around. Latex preview in Wordpress works just fine. When done, cut and paste to...
Jul 14, 2025
P
PAllen
replied to the thread
Latex help page not rendering
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θ What other alternative is there? The $$ and ## is the only thing I have ever used! Are there any instructions for the alternative...
Jul 10, 2025
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