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arXiv · 2509.21409

Currie's Mysterious Pattern and Iterated Functions

Dan Kalman
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Abstract

In his book "Mathematics Rhyme and Reason," Currie discusses what he calls a $mysterious$ $pattern$ involving the sequence $ a_{n} = 2^n \sqrt{2 - \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2}}}},$ where $n$ is the number of radicals. Part of the mystery is that $a_n$ converges to $\pi.$ In this paper we discuss a general framework for results like the mysterious pattern in the context of iterated functions.

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Dan Kalman. 2025-09-24. Currie's Mysterious Pattern and Iterated Functions. https://arxiv.org/abs/2509.21409

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