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Bounds for the probability of complete intersection of random chords in a circle

Published online by Cambridge University Press:  14 July 2016

John Gates
John Gates*
Affiliation:
Thames Polytechnic
*
∗ Postal address: School of Mathematics, Statistics and Computing, Thames Polytechnic, Wellington St., London SE18 6PF, U.K.
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Abstract

Upper and lower bounds are obtained for the integral giving the probability that n invariant chords to a circle all intersect each other.

Keywords

INTERSECTION PROBABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 419 - 424
Copyright
Copyright © Applied Probability Trust 1984 

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References

Ahlfors, L. V. (1953) Complex Analysis. McGraw-Hill, New York.Google Scholar
Gates, J. (1982) The number of intersections of random chords to a circle. J. Appl. Prob. 19, 355–372.Google Scholar
Sulanke, R. (1965) Schnittpunkte zufälliger Geraden. Arch. Math. 16, 320–324.Google Scholar