Abstract:

Two new concepts, the generalized support function and restricted chord func-tion, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l < a.

Key words: Geometric probability, integral geometry, Buffon problem, lattice of regions, kinematic measure