A probabilistic proof of the spherical excess formula
History and Overview
2019-09-11 v1 Metric Geometry
Abstract
This note offers a probabilistic proof of Girard's angle excess formula for the area of a spherical triangle, based on the observation that an unbounded 3-dimensional convex cone, with single vertex at the origin, has only three kinds of 2-dimensional orthogonal projections: a 2-dimensional convex cone with one vertex, a 2-dimensional half-plane (this is an outcome of probability zero), and a 2-dimensional plane.
Cite
@article{arxiv.1909.04505,
title = {A probabilistic proof of the spherical excess formula},
author = {Daniel A. Klain},
journal= {arXiv preprint arXiv:1909.04505},
year = {2019}
}
Comments
3 pages, 3 figures