半球面上一个几何优化问题  

A Geometric Optimization Problem on Hemispherical

作　　者：王玉铮 孙翔 陈钰 曾振柄[1] WANG Yu-zheng;SUN Xiang;CHEN Yu;ZENG Zhen-bing(Department of Mathematics,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学数学系,上海200444

出　　处：《数学的实践与认识》2022年第1期196-211,共16页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471209)。

摘　　要：单位球面x^(2)+y^(2)+z^(2)=1的赤道上(z=0)任意给定不同的三点A,B,c,求上半球面上(z≥0)上的一点D,使得距离和|AD|+|BD|+|CD|取得最大值.通过数值搜索知道,使距离和取得最大值的点D很多情况下位于赤道上,少数情况下位于半球面内部.通过角度计算,同时借助计算机辅助推导,发现了点D在大多数情况下位于赤道上的原因,同时得到了点D位置的计算公式.On the equator(z=0)of unit sphere x^(2)+y^(2)+z^(2)=1 given three different points A,B,C,find a point D on the upper hemisphere(z≥0),and maximize the sum of distance|AD|+|BD|+|CD|.Through numerical search,in many cases,the point that maximizes the sum of distances is located on the equator,in a few cases,it is located inside the hemisphere.In this paper,using angle calculation and computer-aided derivation,we found the reason why the point D is located on the equator in most cases.At the same time,the calculation formula of point D position is obtained.

关 键 词：角度计算 半球面 几何优化 

分 类 号：O181[理学—数学] O224[理学—基础数学]