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Affine and projective universal geometry | Norman J. Wildberger
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18 Dec 2006 | Subject: | Metric Geometry; Algebraic Geometry | Abstract: | By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are introduced here, and the main formulas extend those of rational trigonometry in the plane. This gives a unified, computational model of both spherical and hyperbolic geometries, allows the extension of many results of Euclidean geometry to the relativistic setting, and provides a new metrical approach to algebraic geometry. | Source: | arXiv, math/0612499 | Services: | Forum | Review | PDF | Favorites |
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