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读了贵刊朱刚英老师的《谈可展曲面表面上两点间的最短线路问题》深受启发,本人觉得有所补充,现把它写出来,供同行们参考. 在求锥体表面最短线路时,一般都是先将侧面沿母线展开,然后再求两点间的距离.但是如果在棱台中也如此解题常常会出错. 题目:已知正四棱台ABCD-A1B1C1D1的上、下底面半径分别为1cm,2cm,侧棱长为1cm,则从下底面顶点B沿棱台表面至上底面和B相对的顶点D;的最短路程为__ 学生解答如下:
After reading the book “On the shortest route between two points on the surface of the expansible surface” by the teacher Zhu Gangying, you have been inspired. I feel that I have supplemented it. I will write it out for my colleagues. The shortest line on the cone surface In general, the sides are first stretched along the generatrix, and then the distance between the two points is calculated. However, it is often wrong to solve the problem in the truncated pyramid. Topic: The radius of the upper and lower bases of the known ABCD-A1B1C1D1 They are 1cm, 2cm, and side ribs are 1cm in length. From the bottom base vertex B, from the ridge table surface to the top bottom surface and B, the opposite vertex D; the shortest distance is __ The student answers as follows: