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February 2006 The shape of a sequence of dual random triangles
John Gates
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Bernoulli 12(1): 55-63 (February 2006).


Using the concept of the convex hull of a set of lines, a dual random triangle is defined by selecting three lines from a parent triangle of lines. The angles of the constructed triangle define the shape; calculation of the shape distribution is described. For a sequence of nested triangles constructed in this way it is shown that there is convergence to collinearity and to the collinear shape distribution derived by Mannion for a sequence of vertex-generated triangles.


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John Gates. "The shape of a sequence of dual random triangles." Bernoulli 12 (1) 55 - 63, February 2006.


Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1101.60006
MathSciNet: MR2202320

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 1 • February 2006
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