Altitudes of a Tetrahedron and Traceless Quadratic Forms
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.
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