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以下是我听课而经历的高三习题评讲课的一个片段,开课老师评讲的其中一道题为:地球表面上从北纬45度,东经120度的 A 地到北纬45度,东经30度的 B 地的最短距离为( ).A.R B.(2~(1/2)/4)R C.πR/3 D.πR/2教师:球面上 A、B 两点的最短距离是指这两点的球面距离,即经过这两点的大圆在这两点间的一段劣弧的长度.因此,我们只需算出球心角∠AOB 即可……没等老师说完,一个常到数学办公室问问题的学生抢着说:老师,球面上两点间的最短距离为什么就是这两点的球面距离?教师(有一点迷惘):这是一个公理,不要求学生证明.学生:老师,这个公理能证明吗?
The following is an excerpt from the senior high school exercises lectures on which I attended the lectures. One of the lectures by teachers on the lectures was entitled: From the A point on the Earth’s surface at 45 degrees north latitude and 120 degrees east longitude to B at 30 degrees north latitude The shortest distance is () .AR B. (2 ~ (1/2) / 4) R C.πR / 3 D.πR / 2 Teacher: A, B on the sphere The shortest distance between two points refers to these two points Spherical distance, that is, after these two points of the big circle between these two points of a poor arc length. Therefore, we only need to calculate the center of the ball angle ∠ AOB ... ... can not wait for the teacher to finish, one often to the math office to ask questions Students rushing to say: Teacher, the shortest distance between two points on the sphere Why is the spherical distance between these two points? Teacher (a little confused): This is an axiom and does not require student proof Student: Teacher, this axiom can prove ?