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Other Models of the Hyperbolic Plane

  • James W. Anderson
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

Up to this point, we have focused our attention exclusively on the upper half-plane model ℍ of the hyperbolic plane, but there are many other useful models. We explore in this chapter a second particular model, the Poincaré disc model ≄, of the hyperbolic plane, which we construct starting from the upper half-plane model. We go on to show that the construction used for the Poincaré disc is but one instance of a general construction for producing planar models of the hyperbolic plane.

Keywords

Jordan Curve Hyperbolic Plane Hyperbolic Geometry Hyperbolic Distance Underlying Space 
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.

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Copyright information

© Springer-Verlag London 1999

Authors and Affiliations

  • James W. Anderson
    • 1
  1. 1.Faculty of Mathematical StudiesUniversity of Southampton, HighfieldSouthamptonUK

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