Area Formula for Spherical Polygons via Prequantization
Albert Chern, Sadashige Ishida · SIAM Journal on Applied Algebra and Geometry · 2024
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.