Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-10T06:14:26.902Z Has data issue: false hasContentIssue false
  • English
  • Français

Buffon's problem with a long needle

Published online by Cambridge University Press:  14 July 2016

Persi Diaconis
Persi Diaconis*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 614 - 618
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York.Google Scholar
[2] Gridgeman, N. T. (1960) Geometric probability and the number p. Scripta Mathematica 25, 183–195.Google Scholar
[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