Back to the Advanced Problem Archives
An infinite number of (pairwise) parallel planes in space are arranged so that the (perpendicular) distance between adjacent planes is L. A line segment of length 1 is randomly placed in space (its midpoint and orientation being uniformly distributed). What is the probability that the segment meets one of the planes?
Note that this is a generalization of the Buffon needle problem to three dimensions.
The solution will be posted shortly.
Back to the Advanced Problem Archives