A Laplace type problems for a lattice with cell composed by two triangles and a trapezium

Dedicated to Professor Marius Stoka on the occasion of his 80th birthday Copyright c © 2014 D. Barilla, G. Caristi and E. Saitta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In some previous papers [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors studies same Laplace problems with different fundamental cells. In this paper we consider a lattice with cell represented as in figure 1 and we compute the probability that a segment of random position and constant length intersects a side of lattice. Then we prove that there are values for parameters that determine the lattice and the length of segment for which the probability determined is maximum