EINE TETRAEDER-DREIECK ZUORDNUNG IN DER ELEMENTARGEOMETRIE

Abstract

Let us consider a tetrahedron ABCD and assign to this the triangle H having sides AB· CD, BC· AD, CA· BD. Investigating this assignment, we show the common root of some results in solid geometry. We give a simple proof for the von Staudt formula concerning the radius of the circumsphere of a tetrahedron. Furthermore, we present the solution of a solid geometric problem which is analogous to the Fagnano extremum problem in plane, namely, in a special case we construct that octahedron enclosed in a given tetrahedron where the sum of the edges is minimal.