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Shape distributions for planar triangles by dual construction

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

John Gates
John Gates*
Affiliation:
University of Greenwich
*
* Postal address: School of Mathematics, Statistics and Computing, The University of Greenwich, Woolwich Campus, Wellington Street, London SE18 6PF, UK.
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Abstract

A random triangle in the plane is constructed using three independent elements from a convex set of lines. Expressions are given to calculate the shape distribution from the internal width function of the line set. Two examples are given together with their maximum angle distributions; a simple inequality implies a zero collinearity constant in general. A relationship between the shape distribution and inter-line angle distribution is given.

Keywords

DUAL CONVEXITYSHAPE DISTRIBUTIONINTER-LINE ANGLE DISTRIBUTION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 324 - 333
Copyright
Copyright © Applied Probability Trust 1994 

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