高维欧氏空间中的广义度量方程及其应用

The Generalization of Metric Equations in the High-Dimensional Euclidean Space and Their Applications

本文利用代数的方法,证明了:对于两个等数量有限基本元素构成的集合,杨路和张景中关于高维欧氏空间En中的度量方程仍然成立,得到了一个广义度量方程,其特殊情况就是著名的Cayley定理.作为初步应用,给出了两个单形外接超球球心距和棱切超球球心距的两个公式.

In this article, using the algebraic method, the metric equations in the highdimensional Euclidean space, given by Yang lu and Zhang Jingzhong, are generalized to two sites of limited elementary material, the generalized metric equations are obtained, especially and the Cayley theorem is generalized yet. As their primary applications, two formula of the distance of the center of circumscribed and edgetangent sphere about two simplexes are given.