高维空间中Buffon投针的交点数分布及期望

The Distributions and Average of the Intersection Numbers of Buffon's Needle in High Dimensional Spaces

研究了高维欧氏空间中的Buffon投针交点数分布及其期望问题,利用积分几何的方法,对Buf-fon投线段针情形做了统一的讨论,在此基础上讨论了格型投针的交点数期望问题,并获得了相关结果.

The distribution and expectation of the intersection number in Buffon＇s needle problem in Euclidean spaces of higher dimensions are studied.By integral geometric method,such problems are discussed uniformly.Furthermore,the expectations of intersection number in some lattice-type Buffon needle problems are obtained.