Extensión a 3D del teorema de Desargues, sustituyendo triángulos por tetraedros
- Eugenio Roanes Macías
- Eugenio Roanes Lozano
- Julio Fernández Biarge
ISSN: 1135-0261
Argitalpen urtea: 2007
Zenbakia: 75
Orrialdeak: 13-28
Mota: Artikulua
Beste argitalpen batzuk: Boletín de la Sociedad Puig Adam de profesores de matemáticas
Laburpena
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.