论文标题
布冯的问题决定了三个几何形状的高斯曲率
Buffon's Problem determines Gaussian Curvature in three Geometries
论文作者
论文摘要
平面中的经典布冯问题的一个版本自然延伸至具有恒定高斯曲率的任何riemannian表面的设置。 Buffon概率决定了Buffon缺陷。高斯曲率与布冯不足之间的关系类似于Bertrand-Diguet-Puiseux定理在高斯曲率与周长和面积不足之间建立的关系。
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.
