Journal for Geometry and Graphics 17 (2013), No. 1, 069--080
Copyright Heldermann Verlag 2013
About Some Mappings Defined by a Classical Desargues Configuration
Gunter Weiss
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria
Friedrich Manhart
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria
manhart@dmg.tuwien.ac.at
A Desargues configuration is a planar figure consisting of ten undistinguished points and ten lines with the well-known meaning of a geometric-algebraic axiom for interpretation as an image of a three-dimensional figure. We consider the ten homologies defined by such a configuration. We give an analytic proof for the fact that such a configuration defines a unique polarity too. The (labelled) Desargues figure, i.e., two perspective triangles together with the perspectivity center and axis, can be extended to perspective n-gons, which allow higher dimensional generalizations of the classical interpretation of a Desargues figure in space. Furthermore we consider multi-perspective triangles and an iteration process defined by a pair of not-perspective triangles.
Keywords: Desargues configuration, homology, correlation, polarity, crossratio.
MSC: 51A20; 51A30, 51A05
[ Fulltext-pdf (643 KB)] for subscribers only.