Altitudes of a Tetrahedron and Traceless Quadratic Forms
Metric Geometry
2024-02-13 v1
Abstract
It is well known that the three altitudes of a triangle are concurrent at the so-called orthocenter of the triangle. So one might expect that the altitudes of a tetrahedron also meet at a point. However, it was already pointed out in 1827 by the Swiss geometer Jakob Steiner (1796--1863) that the altitudes of a general tetrahedron are mutually skew, for they are generators of an equilateral hyperboloid.
Keywords
Cite
@article{arxiv.1304.0179,
title = {Altitudes of a Tetrahedron and Traceless Quadratic Forms},
author = {Hans Havlicek and Gunter Weiß},
journal= {arXiv preprint arXiv:1304.0179},
year = {2024}
}