常曲率平面上的Crofton公式的一个统一证明

A Unified Demonstration of Crofton Formulae on the Plane of Constant Curvature

首先将常曲率平面上的正弦定理、第一、第二余弦定理改写为统一的形式,然后通过计算测地线段的测度对常曲率平面上的Crofton公式给出了一个统一的证明.

In this paper,firstly,we rewrite the law of sine,the first and second law of cosines of a geodesic triangle in the plane of constant curvature as a unified form,then,by computing the measure of the geodesic lines,a unified proof of Crofton formulae in the plane of constant curvature has been derived.