Proving and Generalizing Desargues' Two-Triangle Theorem in 3-Dimensional Projective Space. (17th December 2014)

• Record Type: Journal Article
• Authors: Kodokostas, Dimitrios
• Other Names: Pesenson Isaac Academic Editor.
• Is Part Of: Geometry. Volume 2014(2014)
• Publication Date: 2014-12-17
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2014/276108
• Languages: English
• ISSNs: 2314-422X

Abstract

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.