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Buffon's Problem determines Gaussian Curvature in three Geometries
Aizelle Abelgas, Bryan Carrillo, John Palacios, David Weisbart, · 2020-09-15 · via math.PR updates on arXiv.org

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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