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+---- Thread: Buffon's needle problem (/showthread.php?tid=1434)
Buffon's needle problem - mklabgr - 07-30-2026
Buffon's needle problem
Summary
Buffon's needle problem is a classic question in probability theory—first posed by Georges-Louis Leclerc, Comte de Buffon, in the 18th century—that asks for the likelihood that a needle of length $l$, when dropped randomly onto a floor with parallel lines spaced $t$ units apart, will land across one of the lines.
As one of the earliest solved problems in geometric probability, its solution reveals that when the needle is shorter than or equal to the line spacing ($l \le t$), the probability of a line-crossing is $P = \frac{2l}{t\pi}$, where the appearance of $\pi$ stems from the uniform rotational symmetry of the needle's landing angle. Consequently, repeatedly dropping needles and recording how many cross a line provides a practical, physical Monte Carlo method for experimentally estimating the value of $\pi$.
ARTICLE