chwala's latest activity
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chwala reacted to neilparker62's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with
Like.
Neat geometric derivation of ##\tan(A+B)=\frac{\tan A + \tan B}{1-\tan A \tan B}## if we divide all terms in ##\frac{ay+bx}{by-ax}## by... -
chwala replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.a different line for ##\tan 4S## ##\tan (4S)= \tan (2S +2S) = \dfrac{\tan 2S + \tan 2S}{1 - \tan^2 (2S)}## ##\tan (2S) =...
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chwala reacted to Steve4Physics's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
For an essentially geometric proof (no standard trig' identities used) see this 3 minute (appox.) video.
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chwala reacted to neilparker62's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
$$\tan x=\frac{1}{5} \implies \tan2x=\frac{5}{12} \implies \tan4x=\frac{120}{119}$$ $$\tan \left( \tan^{-1} \left( \frac{1}{239}...
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chwala reacted to Gavran's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with
Informative.
There are four formulas of this kind. Euler's formula $$ \arctan\frac12+\arctan\frac13=\frac\pi4 $$ Hermann's formula $$... -
My condolences! It was very sad to hear this. He will surely be missed. And remembered.
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chwala replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.I note that in my proof, i did not have the ##4S## and instead worked with ##S## ... that was wrong. Your working clearly shows that...
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I got out ahead of my skis on that, trying to make it look pretty, but I've fixed what I originally wrote. It's now ##\int u~dv = uv -...
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chwala commented on neilparker62's profile post.Thanks @neilparker62
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Ok - so what I was thinking of doing is writing a short article on one of your many interesting posts and subsequent threads...
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It will highlight your solution as well as illustrate a treasure trove of underlying geometry 'dug up' by AI. I will include an...
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chwala commented on neilparker62's profile post.@neilparker62 , mate, let me just go with what is there, i fully understand it if there is no official letterhead. Any letter will do...
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Hi. Did you get your reference from someone on PF ? I can write something like I see you regularly posting interesting Maths/geometry...
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chwala commented on neilparker62's profile post.@neilparker62 I will appreciate it, ...not yet gotten any reference... the reference am assuming will have letterhead physicsforums (an...
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chwala replied to the thread Paul Hinds has passed.Noted, @berkeman. Is there a way to establish an award in the area of expertise of those profound members who have passed away? or a...