**TITLE**

On Buffon Needle Problem for an Irregular Lattice

**PDF**

**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.

**KEYWORDS**

Geometric probability, integral geometry, Buffon problem, lattice of regions, kinematic measure_x000D_

2000 MRS Classification: 53C65; 52A22

**REFERENCES**

[1] D. Barilla, G. Caristi, A. Puglisi and M. Stoka, A Buffon-Laplace type problems for an irregular lattice with maximum probability, Applied Mathematical Sciences, vol. 8 (2014),no. 165, pp. 8287-8293.

[2] G. Caristi, A. Puglisi and M. Stoka, A Laplace type problem for regular lattices with octagonal cell, Far East Journal of Mathematical Sciences, vol. 48, issue 1, January 2011, pp. 103-118.

[3] R. Delin, Topics in Integral Geometry, Singapore, New Jersey, London, and Hongkong: World Scientic, 1994.

[4] X. Fengfan and L. Deyi, On generalized Buffon Needle problem for lattices, Acta Mathematica Scientia 2011, 31B(1), pp. 303-308.

[5] G. Caristi and M. Ferrara, On Buffon’s problem for a lattice and its deformations. Beitrage zur Algebra und Geometrie, 2004, 45(1), pp. 13-20.

[6] G. Caristi and M. Stoka, A Buffon-Laplace type problem for an irregular lattice with ”body test” rectangle, Applied Mathematical Sciences, vol. 8 (2014), pp. 8395–8401.

[7] H. Poincar'e, Calcul des probabilit'es, 2nd ed., Gauthier-Villard, Paris, 1912.

[8] L. A. Santal'o, Integral Geometry and Geometric Probability, London: Addison-Wesley Publishing Company, 1976.

**Cite this paper**

D. Barilla, G. Caristi, A. Puglisi. (2018) On Buffon Needle Problem for an Irregular Lattice. *International Journal of Economics and Management Systems, ***3**, 36-38

Copyright © 2018 Author(s) retain the copyright of this article.

This article is published under the terms of the Creative Commons Attribution License 4.0