Extensión a 3D del teorema de Desargues, sustituyendo triángulos por tetraedros

Abstract

The extension to 3 dimensions of Desargues theorem, substituting triangles by tetrahedrons, is treated. Given two tetrahedrons in perceptive position from a point, the homology centered in this point that applies the vertices of one of the tetrahedrons over thF- vertices of the other one can be considered. Then the corresponding edge-lines in this homology are intersecting lines and their six points of concurrence are coplanary and they are vertices of a complete quadrilateral. As classical 2D Desargues theorem the inverse of this theorem of homological tetrahedrons is itself. After an experimental solution of the problem using a computer algebra system, several elementary proves of the theorem obtained are shown: a synthetic proof, an analytic proof and a purely projective proof.