The Hyperbolic Plane
Historically speaking, the hyperbolic plane was the result of the search for a non-euclidean plane—a surface with unbounded straight lines and, for each line L and point P ∉ L, more than one line through P which does not meet L. Such a surface departs from the euclidean plane in the opposite way to the sphere, and the hyperbolic plane, in fact, emerged from the study of surfaces which “curve” in the opposite way to the sphere. The train of thought, in brief, was this.
KeywordsEuclidean Plane Hyperbolic Plane Modular Group Hyperbolic Geometry Invariant Line
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