Original scientific paper

Buffon's problem with a cluster of line segments and a lattice of parallelograms

Uwe Bäsel ; HTWK Leipzig, Faculty of Mechanical and Energy Engineering, Leipzig, Germany

Abstract

A cluster $\Zn$ of $n$ line segments ($1\leq n<\infty$) is dropped at random onto two given lattices $\Ra$ and $\Rb$ of equidistant lines in the plane with angle $\beta$ ($0<\beta\leq\pi/2$) between the lines of $\Ra$ and the lines of $\Rb$. Formulas for the probabibilities $\p$ of exactly $i$ ($0\leq i\leq 2n$) intersections between $\Zn$ and $\R=\Ra\cup\Rb$ are derived. The limit distribution of the random variable {\em relative number of intersections between $\Zn$ and $\R$} as $n\rightarrow\infty$ is calculated.

Keywords

geometric probability; stochastic geometry; random sets; random convex sets; integral geometry; method of moments

Hrčak ID:

68638

URI

https://hrcak.srce.hr/68638

Publication date:

10.6.2011.

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