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Random secants of a convex body generated by surface randomness

Published online by Cambridge University Press:  14 July 2016

P. Frank Ehlers  and
Ernest G. Enns
P. Frank Ehlers
Affiliation:
Okanagan College
Ernest G. Enns
Affiliation:
University of Calgary
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Abstract

Length distributions for random secants through a convex region K are derived for three types of randomness. The results are formulated in terms of geometric properties of K, e.g. the overlap surface content of K with its translated self. The distribution of distance between two random points in K, expressed in terms of the overlap volume, is shown to extend to non-convex (including disjoint) regions.

Keywords

GEOMETRICAL PROBABILITYCONVEXITYRANDOM SECANTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 157 - 166
Copyright
Copyright © Applied Probability Trust 

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References

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