We consider the Buffon’s problem for the lattice Rα,a which has the fundamental cell composed by the union of octagon, with all sides of lengths a and the angles (π − α) and (π 2 + α) with α ∈ ] 0, π 2 [, and of the square with side of length a (see Fig. 1). We determine the probability of intersection of a body test needle of length l, l < a. For α = π 4 we also give the estimate of this probability for the cases, when the segment is non-small with respect to Rπ 4 ,a (see [1], [2]). MSC 2000: 60D05, 52A22 Keywords: geometric probability, stochastic geometry, random sets, random convex sets and integral geometry

On Buffon's problem for a lattice and its deformations

CARISTI, Giuseppe
2004

Abstract

We consider the Buffon’s problem for the lattice Rα,a which has the fundamental cell composed by the union of octagon, with all sides of lengths a and the angles (π − α) and (π 2 + α) with α ∈ ] 0, π 2 [, and of the square with side of length a (see Fig. 1). We determine the probability of intersection of a body test needle of length l, l < a. For α = π 4 we also give the estimate of this probability for the cases, when the segment is non-small with respect to Rπ 4 ,a (see [1], [2]). MSC 2000: 60D05, 52A22 Keywords: geometric probability, stochastic geometry, random sets, random convex sets and integral geometry
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/1588519
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