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arXiv · 1007.0261

Perimeter Variance of Uniform Random Triangles

Steven Finch
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Abstract

Let T be a random triangle in a disk D of radius R (meaning that vertices are independent and uniform in D). We determine the bivariate density for two arbitrary sides a,b of T. In particular, we compute that E(a*b)=(0.837...)*R^2, which implies that Var(perimeter)=(0.649...)*R^2. No closed-form expression for either coefficient is known. The Catalan numbers also arise here.

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Steven Finch. 2010-07-01. Perimeter Variance of Uniform Random Triangles. https://arxiv.org/abs/1007.0261

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