中文

Affine and projective universal geometry

度量几何 2007-05-23 v1 代数几何

摘要

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.

关键词

引用

@article{arxiv.math/0612499,
  title  = {Affine and projective universal geometry},
  author = {Norman J. Wildberger},
  journal= {arXiv preprint arXiv:math/0612499},
  year   = {2007}
}

备注

22 pages