On Buffon Needle Problem for an Irregular Lattice

Abstract: In the previous papers [1] and [6] the authors introduced in the Buffon-Laplace type problems so-called obstacles. They considered two lattices and considering a classic Buffon type problem introducing in the first moment the maximum value of probability, i.e. reducing the probability interval and in the second considering an irregular lattice. In [5] Caristi and Ferrara considered also a Buffon type problem considering the possibles deformations of the lattice and in [2] Caristi, Puglisi and Stoka considered another particular regular lattices with eight sides. Fengfan and Deyi [4] study similar problem using two concepts, the generalized support function and restricted chord function, both referring to the convex set, which were introduced by Delin in [3]. In this paper, we consider another particular irregular lattice (see fig. 1) and considering the formula of the kinematic measure of Poincar´e [7] and the result of Stoka [9] we study a Buffon problem for this irregular lattice. We determine the probability of intersection of a body test needle of length l, l < a/3.