高维情形的Routh定理

HIGHER DIMENSIONAL ROUTH THEOREM

本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理.

In the article, we study the problem on the volumes of n-dimensional simplexes in the n-dimensional Euclidean space En. By using theory of distance geometry and analytic method n-dimensional Routh theorem is established. As a special case, n-dimensional Ceva theorem is established.