Extensions of Laplace Type Problemsin the Euclidean Space

摘要

The classical Buffon needle problem is to find the probability thata needle of length n when dropped on a floor made of boards of widthb will cross a crack between the boards. This problem can be solvedby evaluating a simple single integral. In his extension of the problem,Laplace considered a floor tiled by congruent rectangles and consideredthe probability of the needle crossing one or two of the cracks bettweenthe rectangles. In 1974 M. Stoka studies an extension of the BuffonLaplaceneedle problem in the space Rn. In this paper we consider twoextension of the Laplace problem in E3