Area formula for spherical polygons via prequantization
Differential Geometry
2025-12-18 v3 Symplectic Geometry
Abstract
We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measuring angles, the new formula mimics Green's theorem and is applicable to a wider range of degenerate spherical curves and polygons.
Cite
@article{arxiv.2303.14555,
title = {Area formula for spherical polygons via prequantization},
author = {Albert Chern and Sadashige Ishida},
journal= {arXiv preprint arXiv:2303.14555},
year = {2025}
}