Recent content by neilparker62

May I respectfully submit that the article did not have any intention to compare human solutions with AI solutions nor indeed to compare solutions generally. AI came up with a couple of interesting additions to an already interesting thread and those were presented in the article alongside the...

The roots of the equation in part (i) are the same as the roots in part (ii). Since in both cases we have equations of the form ax^2 + bx + c = 0 with a=1 , 'c' = -c we must also have -p=(1+c)/c.

Thanks for the comment(s). Re functions: Yes - the AI engine wanted to go that way but I got a little confused by all the "defs" it came up with and couldn't keep track. As I mention in the article it's so easy for AI to make subtle programming errors which you won't notice unless you know...

"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.