Orthic Axes of Triangles of a Simplex

Abstract

The orthic axis of a triangle T is the axis of perspectivity of T and its orthic triangle formed of the feet of its altitudes [5]. The purpose of this paper is to study the distribution and location of the orthic axes of the triangles of a simplex in a space of n dimensions, or briefly in an n-space, or of an n-simplex, according as it is Semi-Uni-or Demi-orthocentric ([6], [11], [15], [20]-[23]).