Statistical estimation of $\pi$: varying choices over dimensions

Syon Bhattacharjee; Subhra Sankar Dhar

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arXiv · 2510.23830

Statistical estimation of $\pi$: varying choices over dimensions

Syon Bhattacharjee·Subhra Sankar Dhar

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Abstract

This article studies statistical estimation of $\pi$ based on the fact that the ratio of the volumes of a $d$-dimensional hypersphere and a $d$-dimensional hypercube is a certain function of $\pi$, and the function depends on the dimension $d$. The estimation of $\pi$ is carried out for various choices of $d$ (strictly speaking, $d\in\{1, 2, \ldots, 20\}$) using the idea of Monte Carlo simulations. Various intriguing facts are observed, and the estimation of $\pi$ using infinite dimensional observations is outlined. Moreover, the R codes associated with relevant numerical studies are provided.

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Syon Bhattacharjee, Subhra Sankar Dhar. 2025-10-27. Statistical estimation of $\pi$: varying choices over dimensions. https://arxiv.org/abs/2510.23830

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