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Buffon's problem with a long needle

Published online by Cambridge University Press:  14 July 2016

Persi Diaconis
Persi Diaconis*
Affiliation:
Stanford University
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Abstract

A needle of length l dropped at random on a grid of parallel lines of distance d apart can have multiple intersections if l > d. The distribution of the number of intersections and approximate moments for large l are derived. The distribution is shown to converge weakly to an arc sine law as l/d→∞.

Keywords

BUFFON'S PROBLEMGEOMETRICAL PROBABILITYMETHOD OF MOMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 614 - 618
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York.Google Scholar
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[3] Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
[4] Knopp, K. (1964) Theorie und Anwendung der Unendlichen Reihen, 5th edn. Springer, Berlin.Google Scholar
[5] Uspensky, J. V. (1937) Introduction to Mathematical Probability, 1st edn. McGraw-Hill, New York.Google Scholar