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Convex bodies instead of needles in Buffon's experiment

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Author

Summary, in English

An arbitrary fixed convex set in ${\bf R}^2$ is considered as are two families of equally spaced parallel lines making angle $\alpha$ with each other. It is assumed that the inter-line distance in each family of parallel lines is greater than the maximum width of the convex set. A congruent copy of the convex set is placed randomly (centroid uniform in one particular parallelogram cell and orientation uniform on $[0,2\pi))$. A simple formula for the probability that the randomly placed set intersects at least one of the lines is obtained. A consequence of the formula is that there exists at least one angle $\alpha$ (depending on the convex set) such that the event of intersecting some line in one of the two families of parallel lines is independent of the event of intersecting some line in the other family.

Publishing year

1997

Language

English

Pages

301-308

Publication/Series

Geometriae Dedicata

Volume

67

Issue

3

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • random convex sets - hitting probability - independent hitting events

Status

Published

ISBN/ISSN/Other

  • ISSN: 0046-5755