平面几何研究的图形是直线(线段),角,三角形,…等等.在球面上我们也可以类似地研究球面上的“直线”、“角”、“三角形”….那么我们首先要问:球面上什么样的曲线可以扮演平面上直线的角色?我们知道,在平面上直线最重要的一个性质是:两点之间所有连线中直线段最短.那么在球面 The geometry of plane geometry studies are lines (line segments), angles, triangles, ... etc. On the sphere we can also similarly study the “straight line”, “angle”, and “triangle” on the sphere.... Then we first ask: What kind of curve on the sphere can play the role of a straight line on the plane? We know that the most important property of a straight line in the plane is: the straight line in all the lines between the two points is the shortest. Then in the sphere