🔗 Buffon's Needle Problem

🔗 Statistics

In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is

${\displaystyle p={\frac {2}{\pi }}{\frac {l}{t}}.}$

This can be used to design a Monte Carlo method for approximating the number π, although that was not the original motivation for de Buffon's question.