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*Non-Euclidean (Hyperbolic) Geometry

  • John Snygg
Chapter

Abstract

You should be forewarned that a prerequisite for this chapter is a strong familiarity with the basic manipulations of complex numbers – multiplication, the polar representation, and the notion of complex conjugate. The non-Euclidean geometry of Bolyai and Lobachevsky eventually became known as hyperbolic geometry because the ordinary trigonometric functions sine and cosine that appear in formulas for the surface of a sphere are replaced by the hyperbolic functions sinhϕ and coshϕ for surfaces of constant negative Gaussian curvature.

Keywords

Unit Disk Equilateral Triangle Euclidean Geometry Hyperbolic Geometry Cross Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.East OrangeUSA

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