Other Models of the Hyperbolic Plane
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.
KeywordsJordan Curve Hyperbolic Plane Hyperbolic Geometry Hyperbolic Distance Underlying Space
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