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arXiv · 2411.16935

Buffon Needle Problem Over Convex Sets

M. Dannenberg·W. Hagerstrom·G. Hart·A. Iosevich·T. Le·I. Li·N. Skerrett
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Abstract

We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length $l$ originating in a bounded convex set $X\subset\mathbb{R}^2$ lies entirely within $X$. Using techniques from convex geometry, we prove an isoperimetric type inequality, showing that among sets $X$ with equal perimeter, the disk maximizes this probability.

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M. Dannenberg, W. Hagerstrom, G. Hart, A. Iosevich, T. Le, I. Li, N. Skerrett. 2024-11-25. Buffon Needle Problem Over Convex Sets. https://arxiv.org/abs/2411.16935

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