A proof of the irrationality of $\pi$ motivated by nested radicals with roots of $2$

Abstract

In this work, we prove the irrationality of $\pi$ motivated by nested radicals with roots of $2$ of the kind $c_k=\sqrt{2+c_{k-1}}$ and $c_0=0$. Sample computations showing how the rational approximation tends to $\pi$ as the integer $k$ increases are presented.

32 pages