0

Firstly, I must state that I know this fact to be true, because I have seen a proof on this site to show that $\mathrm{arctg}(m/n) \neq q \pi$, for any choice of non-zero natural $m$, $n$ and for non-zero rational $q$. The proof was in the comment section.

However, the proof itself included mathematics that was not accesible to a high-schooler. Moreover, the post is very old and I can't find it anymore.

I am confortable with real analasys, trigonometry and algebra to a certain degree. Does any of you know whether there is a proof involving these 3 braches, so that a high-school student could understand it? If not, any proof you know would be welcomed.

Ernie060
  • 6,073
Andrei Secuiu
  • 11
  • 1
  • The answers here may be of interest: https://math.stackexchange.com/questions/79861/arctan2-a-rational-multiple-of-pi. – Minus One-Twelfth May 18 '19 at 20:07
  • $\arctan(1)=\pi/4$. But if $1\ne s\in \Bbb Q^+$ then $(\arctan s)/\pi \not \in \Bbb Q. $... Eisenstein's Criterion and deMoivre's Theorem have brief elementary proofs and we can use them for a brief elementary answer . But it would be a rare high-school student who has heard of Eisenstein's Criterion. – DanielWainfleet May 19 '19 at 08:02

0 Answers0