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arXiv · 1909.04505

A probabilistic proof of the spherical excess formula

Daniel A. Klain
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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.

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Daniel A. Klain. 2019-09-09. A probabilistic proof of the spherical excess formula. https://arxiv.org/abs/1909.04505

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