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Plane polygons and a conjecture of Blaschke’s

Published online by Cambridge University Press:  01 July 2016

Peter Waksman
Peter Waksman*
Affiliation:
University of Southern California
*
∗Department of Mathematics, University of Southern California, Los Angeles, CA 900891113, USA.
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Abstract

The Radon transform of a plane domain is a random variable assigning to each line in the plane the chord length of its intersection with the domain. The probability distribution of this random variable does not characterize the domain, but it is shown to characterize a sufficiently asymmetric convex polygon. Under weaker assumptions, a convex polygon is characterized by this distribution, up to a finite number of rearrangements.

Keywords

CONVEX POLYGONRADON TRANSFORMLINEAR INTERSECT DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 4 , December 1985 , pp. 774 - 793
Copyright
Copyright © Applied Probability Trust 1985 

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References

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