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在高中数学课本(人教版第二册下A)球一节中告诉我们:在球面上,两点之间的最短连线的长度,就是经过这两点的大圆在这两点间的一段劣弧的长度.我们把这个弧长叫做两点的球面距离.在教学过程中有学生就问到:为什么两点间的球面距离是最短的?而课本上又没有证明过程,本文提供一种证明方法,供大家参考.
In high school mathematics textbook (PEP 2 under A) the ball tells us: on the sphere, the length of the shortest connection between the two points is the Great Circle through these two points in the period between these two points We call this arc length as the spherical distance of two points. During the teaching process some students asked why the spherical distance between the two points is the shortest, and the textbook does not prove the process. This article provides a Proof method for your reference.