N维单形各侧面垂足与重心的几何不等式

Geometric Inequalities of Pedal and Centroid in Each Side of N-Simplex

摘要: 本文证明了n维单形各顶点在其所对侧面的垂足所组成的垂足单形之体积小于等于原n维单形各侧面重心所组成的重心单形之体积，等号当且仅当该n维单形为正则单形时成立。

Abstract: This paper proves that the volume of the pedal simplex composed of the pedals about the vertexes of the n-simplex on the opposite sides is less than or equal to the volume of the centroid simplex composed of the centroids in each side of the primitive n-simplex, the equal sign can be tenable if and only if the n-simplex is regular.