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arXiv · 2511.21776

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

Sanjar M. Abrarov·Rehan Siddiqui·Rajinder Kumar Jagpal·Brendan M. Quine
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Abstract

In this work, we prove the irrationality of $π$ 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 $π$ as the integer $k$ increases are presented.

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Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine. 2026-09-23. A proof of the irrationality of $π$ motivated by nested radicals with roots of $2$. https://arxiv.org/abs/2511.21776

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