Buffon's Problem determines Gaussian Curvature in three Geometries

Aizelle Abelgas; Bryan Carrillo; John Palacios; David Weisbart; Adam Yassine

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arXiv · 2009.06755

Buffon's Problem determines Gaussian Curvature in three Geometries

Aizelle Abelgas·Bryan Carrillo·John Palacios·David Weisbart·Adam Yassine

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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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Aizelle Abelgas, Bryan Carrillo, John Palacios, David Weisbart, Adam Yassine. 2020-09-14. Buffon's Problem determines Gaussian Curvature in three Geometries. https://arxiv.org/abs/2009.06755

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