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Foundations: The Synthetic Approach

  • Eric Lord

Abstract

The axioms for Euclidean, Affine and Projective geometries in two and three dimensions are discussed, with particular emphasis on the status of the theorems of Pappus and Desargues. The origin of Projective geometry in the art of ‘perspective drawing’ is explained. The arithmetic satisfied by the points of a line in affine space is demonstrated and shown to lead to the possibility of affine coordinate systems. After a digression on the symmetry groups of configurations, a set of axioms for Projective geometry of N dimensions is presented.

Keywords

Euclidean Geometry Projective Geometry Picture Plane Affine Plane Harmonic Conjugate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Eric Lord
    • 1
  1. 1.BangaloreIndia

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