Buffon's Problem determines Gaussian Curvature in three Geometries
Probability
2024-05-21 v2
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.
Cite
@article{arxiv.2009.06755,
title = {Buffon's Problem determines Gaussian Curvature in three Geometries},
author = {Aizelle Abelgas and Bryan Carrillo and John Palacios and David Weisbart and Adam Yassine},
journal= {arXiv preprint arXiv:2009.06755},
year = {2024}
}
Comments
12 pages, 1 figure