多凸域型网格的Buffon问题

ON THE BUFFON PROBLEM OF A COMPLICATED GRID

本文研究了以多个凸域的并为基本区域的网格的Buffon问题.利用包含测度的有关结论,获得了Buffon问题的普遍公式,并作为举例具体计算了一种三个凸域的情况的表达式和特殊化的数值.

In the paper, we consider the Buffon＇s problem for the lattice which has the fundamental region composed by the union of many convex domains. We obtain a universal formula by using the related conclusion of containment measure, and as an example, calculate the situation of three convex domains, obtain the concrete result, also specialize the problem, obtain the concrete value.