Email Gateway (Aug 22 2022 at 15:36): Email Gateway (Aug 22 2022 at 15:36):From: Tobias Nipkow <nipkow@in.tum.de>
Buffon's Needle Problem
Manuel Eberl
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.
https://www.isa-afp.org/entries/Buffons_Needle.shtml
This is another one off the list of 100 Theorems.
smime.p7s
Last updated: Nov 21 2024 at 12:39 UTC