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.
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