Buffon's Needle: A Classical Problem in Geometric Probability

Abstract

This essay presents an expository overview of Buffon's needle problem, a foundational question in geometric probability. It covers both classical cases: the short needle (length less than or equal to line spacing) and the long needle (length greater than spacing), detailing the probability computations involved. The discussion then extends to notable generalizations, including needle drops on two- and three-dimensional grids, and curved "noodles". These extensions illustrate the problem’s depth and its surprising link to π, highlighting its continued relevance in mathematics and probability theory.