Table of Contents
Geometry
Volume 2014, Article ID 276108, 7 pages
http://dx.doi.org/10.1155/2014/276108
Research Article

Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space

Department of Applied Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Received 22 August 2014; Accepted 15 November 2014; Published 18 December 2014

Academic Editor: Isaac Pesenson

Copyright © 2014 Dimitrios Kodokostas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

With the use of only the incidence axioms we prove and generalize Desargues’ two-triangle Theorem in three-dimensional projective space considering an arbitrary number of points on each one of the two distinct planes allowing corresponding points on the two planes to coincide and three points on any of the planes to be collinear. We provide three generalizations and we define the notions of a generalized line and a triangle-connected plane set of points.