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29 March 2024
 
  » arxiv » math/0612499

 Article overview


Affine and projective universal geometry
Norman J. Wildberger ;
Date 18 Dec 2006
Subject Metric Geometry; Algebraic Geometry
AbstractBy 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
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