Perimeter Variance of Uniform Random Triangles
Probability
2010-07-05 v1 Combinatorics
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1007.0261,
title = {Perimeter Variance of Uniform Random Triangles},
author = {Steven Finch},
journal= {arXiv preprint arXiv:1007.0261},
year = {2010}
}
Comments
9 pages