Buffon's needle
A floor is ruled with parallel lines a distance apart. A needle of length is dropped at random. What is the probability that it lands across one of the lines?
History and references
Solved in 1777 by Georges-Louis Leclerc, Comte de Buffon.
Buffon posed the problem in 1733 and published its solution in 1777, making it one of the first problems in geometric probability. Take the distance from the needle's center to the nearest line and the angle between needle and lines as independent and uniform, and integrate to get the answer . The number appears because the needle's direction is uniform over all angles. The formula suggests estimating by dropping many needles. Mario Lazzarini reported in 1901 that 3408 tosses gave , a result now regarded as arranged to reproduce a known approximation rather than a genuine experiment.
References
Solutions 0
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