Recent content by neilparker62

"All in one" derivation of compound angle formulae - based on the video construction.

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 ##by##.

$$\tan x=\frac{1}{5} \implies \tan2x=\frac{5}{12} \implies \tan4x=\frac{120}{119}$$ $$\tan \left( \tan^{-1} \left( \frac{1}{239} \right)+\frac{\pi}{4}\right)=\frac{1+\frac{1}{239}}{1-\frac{1}{239}}=\frac{120}{119}$$

Hi. Did you get your reference from someone on PF ? I can write something like I see you regularly posting interesting Maths/geometry problems and contributing to discussions around those.

Thanks for the link.

I'm sure they don't and wouldn't worry much if they did! I wish I was more clued up on those particular topic areas but in all honesty I'm not.

Welcome to the PF community - I'm sure you'll find some expert advice on those topic areas (not that I personally know much about them!)

Deepest condolences - Robert to you and all the family. It's been an honour to share this forum with stalwarts such as your Dad. We'll hugely miss his always sage and thoughtful posts.

Seconded. And if I may put it this way - it's reward enough to be part of the PF community and (occasionally) to post something that others find useful/interesting . Or to start a thread which usually yields any number of useful responses.

@PeroK . Stop complaining about AI - you're better by far!

Yes - as mentioned above the technique is strikingly similar to that employed in Diophantus II VIII which is "to divide a square into two other squares" - I take the liberty of copy/pasting the image from Wikipedia which illustrates the technique when the given square is 16. y=mx-4 is...

Perhaps worth noting (in retrospect) that you will get this equation directly by implementation of @GiorgioPastore 's suggestion in post #73. Very interesting discussion on parameterization of this problem. Am still trying to get my head round some of those posts! See also...