Buffon's Problem determines Gaussian Curvature in three Geometries

2020/09/14 by Abelgas, Aizelle, Carrillo, Bryan, Palacios, John +2
#60D99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.06755

Abstract

A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand-Diguet-Puiseux Theorem establishes between Gaussian curvature and both circumference and area deficits.

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• Curvatures of Smooth and Discrete Surfaces
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