球面三角形面积公式的一个积分证明

An Integral Proof of Area Formula of Spherical Triangle

球面三角形面积的计算公式是球面几何中的一个经典公式。运用曲面积分方法和两平面夹角的计算给出了该公式的一个严格证明,并进一步推导了由球面三角形顶点处经纬度直接计算面积的公式,从实用角度看,该公式优于经典公式。

The calculation formula of spherical triangle area is a classical one in spherical geometry. It is proved strictly through surface integral calculation and two plane angle calculation,from which a formula to calculate the area directly through the latitude and longitude of the vertex of spherical triangle is then derived. The derivation formula is better than the classical one from the practical point of view.