Convex bodies instead of needles in Buffon's experiment

Research output: Contribution to journalArticle


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.


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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • random convex sets - hitting probability - independent hitting events
Original languageEnglish
Pages (from-to)301-308
JournalGeometriae Dedicata
Issue number3
Publication statusPublished - 1997
Publication categoryResearch
Externally publishedYes