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arXiv · 2303.14555

Area formula for spherical polygons via prequantization

Albert Chern·Sadashige Ishida
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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.

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Albert Chern, Sadashige Ishida. 2023-03-25. Area formula for spherical polygons via prequantization. https://arxiv.org/abs/2303.14555

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