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.
This work was supported by grants from FCAR (Québec) and NSERC (Canada).
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© 1996 Birkhäuser Boston
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Whiteley, W. (1996). Synthetic vs Analytic Geometry for Computers. In: Kueker, D.W., Smith, C.H. (eds) Learning and Geometry: Computational Approaches. Progress in Computer Science and Applied Logic, vol 14. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4088-4_6
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DOI: https://doi.org/10.1007/978-1-4612-4088-4_6
Publisher Name: Birkhäuser Boston
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