Universal Hyperbolic Geometry I: Trigonometry

Details Universal Hyperbolic Geometry I: Trigonometry Universal Hyperbolic Geometry I: Trigonometry

2009-09-08

arxiv.org/abs/0909.1377v1

Mathematics

Metric Geometry

47 pages

Scientific paper

Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry of Lorentz, Einstein and Minkowski comes from a projective point of view, with trigonometric laws that extend to `points at infinity', here called `null points', and beyond to `ideal points' associated to a hyperboloid of one sheet. The theory works over a general field not of characteristic two, and the main laws can be viewed as deformations of those from planar rational trigonometry. There are many new features.

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