n维单形体积的两个结果及其应用

TWO RESULTS FOR VOLUMES OF N-DIMENSIONAL SIMPLEXES AND SOME APPLICATIONS

本文利用度量几何的理论与方法,研究了n维欧氏空间E^n中n维单形体积问题,获得了其内接单形体积的一个结果,建立了切点单形、旁心单形体积的一个不等式,作为其特例获得了n维情形的Menelaus定理.

Using the theory and method of metric geometry,the problem for volumes of n-dimensional simplexes in the n-dimensional Euclidean space is studied.We obtain a result on the volume of its inscribed simplex,establish an inequality for the volumes of the tangent points simplex and the escenters simplex.As a special case,we get an n-dimensional Menelaus theorem.