Buffon's problem determines Gaussian curvature in three geometries

被引：0

作者：

Abelgas, Aizelle ^{[1
]}

Carrillo, Bryan ^{[2
]}

Palacios, John ^{[3
]}

Weisbart, David ^{[1
,4
]}

Yassine, Adam M.

机构：

[1] Univ Calif Riverside, Dept Math, 900 Univ Ave,Skye Hall, Riverside, CA 92521 USA

[2] Saddleback Coll, Dept Math, 28000 Marguerite Pkwy, Mission Viejo, CA 92692 USA

[3] Univ Calif Irvine, Ctr Complex Biol Syst, 2620 Biol Sci 3, Irvine, CA 92697 USA

[4] Pomona Coll, Dept Math & Stat, 610 N Coll Ave, Claremont, CA 91711 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2024年

关键词：

Buffon's problem; Gaussian curvature; area deficit; circumference deficit; Bertrand-Diguet-Puiseux theorem; geometric probability;

D O I：

10.1017/jpr.2023.114

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：12

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