有关垂心存在的n维单形之性质

On The Properties of N-Dimensional Simplex with Orthocenter Existence

摘要: 众所周知，任意三角形必存在垂心，但任意四面体不一定存在垂心，只有垂心四面体才会存在垂心。可以推断，当n≥3时，任意的n维单形也不一定存在垂心。本文尝试对存在垂心的n维单形作出定义，称为n维垂心单形，给出了n维垂心单形的垂心性质。众所周知，任意三角形必存在垂心，但任意四面体不一定存在垂心，只有垂心四面体才会存在垂心。可以推断，当n≥3时，任意的n维单形也不一定存在垂心。本文尝试对存在垂心的n维单形作出定义，称为n维垂心单形，给出了n维垂心单形的垂心性质。

Abstract: As everyone knows, any triangle must have a orthocenter, but any tetrahedron does not necessarily have a orthocenter, only the orthocenter tetrahedron can have the orthocenter. It can be inferred, when n≥3, any n-dimensional simplex does not necessarily have a orthocenter. In this paper, we try to define a n-dimensional simplex with a orthocenter, it’s called n-dimensional orthocenter simplex, the orthocenter property of n-dimensional orthocenter simplex is given.