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
2004-01-01
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 geometryFile in questo prodotto:
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