Extensión natural a 3D del teorema de Pappus y su configuración completa
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Autores: Eugenio Roanes Macías
, Eugenio Roanes Lozano
- Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 80, 2008, págs. 38-56
- Idioma: español
- Texto completo no disponible (Saber más ...)
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Resumen
Pappus's hexagon theorem states that: "the three intersection points of opposite sides of an hexagon, whose vertices lie alternatively on two lines, are collinear". The following natural extension of Pappus theorem to 3D is considered: "given an octagon, whose vertices lie alternatively on two planes, and whose opposite side-lines are secant, the four in-tersection points of opposite side-lines are coplanar". In this extension to 3D of Pappus theorem some vertices of the polygonal line can not be freely chosen, but an interesting property has been found: the four diago-nal lines passing through opposite vertices share a point. This property leads to a simple method to generate the configuration. Moreover, condi-tions of existence of this configuration are determined and the so called complete configuration is also described in detail.
