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Math Trek

Buffon's Needling Ants

By
2:39pm, October 24, 2002

The classic probability experiment known as Buffon's needle produces a statistical estimate of the value of pi, the ratio of a circle's circumference to its diameter.

The experiment consists of randomly dropping a needle over and over again onto a wooden floor made up of parallel planks. If the needle's length is no greater than the width of the boards, the probability of the needle meeting or crossing a seam between boards is twice the needle's length, l, divided by the plank width, d, times pi: 2l/dp.

The idea of estimating pi by randomly casting a needle onto an infinite plane ruled with parallel lines was first proposed by the naturalist and mathematician Georges Louis Leclerc Comte de Buffon (1707–1788). He himself apparently tried to measure pi by throwing sticklike loaves of French bread over his shoulder onto a tiled floor and counting the number of times the loaves fell across the lines

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