Orthocenters of triangles in the n-dimensional space

• Horst Martini Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany
• Wilson Pacheco Departamento de Matematicas Facultad Experimental de Ciencias Universidad del Zulia Maracaibo
• Aljadis Varela Departamento de Matematicas Facultad Experimental de Ciencias Universidad del Zulia Maracaibo
• John Vargas Departamento de Matematicas Facultad Experimental de Ciencias Universidad del Zulia Maracaibo

Keywords: orthocenter, triangle, tetrahedron, orthocentric system, Feuerbach sphere

Abstract

We present a way to define a set of orthocenters for a triangle in the $n$-dimensional space $\mathbb{R}^{n}$, and we show some analogies between these orthocenters and the classical orthocenter of a triangle in the Euclidean plane. We also define a substitute of the orthocenter for tetrahedra which we call $G$-orthocenter. We show that the $G$-orthocenter of a tetrahedron has some properties similar to those of the classical orthocenter of a triangle.

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