Convex bodies instead of needles in Buffon's experiment
Research output: Contribution to journal › Article
Abstract
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 interline 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.
Details
Authors  

External organisations 

Research areas and keywords  Subject classification (UKÄ) – MANDATORY
Keywords

Original language  English 

Pages (fromto)  301308 
Journal  Geometriae Dedicata 
Volume  67 
Issue number  3 
Publication status  Published  1997 
Publication category  Research 
Peerreviewed  Yes 
Externally published  Yes 