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Recognition of triangles and quadrilaterals by chord length distribution

Published online by Cambridge University Press:  14 July 2016

J. Gates
J. 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

It is shown how a triangle can be recognised from the odd moments of the length of random chords and how a quadrilateral can be recognised from the derivative of its chord length density.

Keywords

GEOMETRIC PROBABILITYRANDOM CHORDCHQRD LENGTH DISTRIBUTIONPOLYGON RECOGNITION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 873 - 879
Copyright
Copyright © Applied Probability Trust 1982 

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References

[1] Coleman, R. (1969) Random paths through convex bodies. J. Appl. Prob. 6, 430–441.CrossRefGoogle Scholar
[2] Kingman, J. F. C. (1969) Random secants of a convex body. J. Appl. Prob. 6, 660–672.CrossRefGoogle Scholar
[3] Mallows, C. L. and Clark, J. M. (1970) Linear intercept distributions do not characterise plane sets. J. Appl. Prob. 7, 240–244.Google Scholar
[4] Ruben, H. (1978) On the distance between points in polygons. In Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, ed. Miles, R. E. and Serra, J. Springer-Verlag, Berlin.Google Scholar
[5] Santaló, L. A. (1976) Integral Geometry and Geometric Probability. Encyclopaedia of Mathematics and its Applications, 1. Addison-Wesley, Reading, Ma. Google Scholar