Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-23T19:25:24.986Z Has data issue: false hasContentIssue false

Recognition of triangles and quadrilaterals by chord length distribution

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1982 

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.)

References

[1] Coleman, R. (1969) Random paths through convex bodies. J. Appl. Prob. 6, 430441.CrossRefGoogle Scholar
[2] Kingman, J. F. C. (1969) Random secants of a convex body. J. Appl. Prob. 6, 660672.CrossRefGoogle Scholar
[3] Mallows, C. L. and Clark, J. M. (1970) Linear intercept distributions do not characterise plane sets. J. Appl. Prob. 7, 240244.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