Uniform Triangles with Equality Constraints
Probability
2014-12-01 v2 Metric Geometry
Abstract
The equality constraint a+b+c=1 for random triangle sides corresponds to breaking a stick in two places. An analog a^2+b^2+c^2=1 has a remarkable feature: the bivariate density for angles coincides with that for 3D Gaussian triangles. Interesting complications also arise for a+b=1 and for a^2+b^2=1, with the understanding that the angle gamma opposite side c is Uniform[0,pi]. Closed-form expressions for several side moments remain open.
Keywords
Cite
@article{arxiv.1411.5216,
title = {Uniform Triangles with Equality Constraints},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1411.5216},
year = {2014}
}
Comments
17 pages, 2 figures; addendum & two references