### Abstract

In the 18th century, Georges-Louis Leclerc, Comte de Buffon posed and
later solved the following problem, which is often called the first
problem ever solved in geometric probability: Given a floor divided
into vertical strips of the same width, what is the probability that a
needle thrown onto the floor randomly will cross two strips? This
entry formally defines the problem in the case where the needle's
position is chosen uniformly at random in a single strip around the
origin (which is equivalent to larger arrangements due to symmetry).
It then provides proofs of the simple solution in the case where the
needle's length is no greater than the width of the strips and
the more complicated solution in the opposite case.

BSD License