Synthetic vs Analytic Geometry for Computers

  • Walter Whiteley
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 14)

Abstract

Computer geometry usually means analytic geometry. Analytic geometry usually means Cartesian coordinates and Euclidean geometry. We consider alternatives: synthetic geometries, such as projective geometry, and coordinate-free analytic geometries. Using classical invariants and Cayley algebra (extended exterior algebra), we describe translations from coordinate analytic geometry to coordinate-free ‘invarant’ analytic geometry and the unsolved problem of translating back to synthetic geometry. The goal is to include more appropriate geometry in computer-aided geometry - and produce ‘better’ proofs from Automated Theorem Provers.

Keywords

Stein Dition 

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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Walter Whiteley
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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