The Hyperbolic Plane

  • John Stillwell
Part of the Universitext book series (UTX)


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 PL, 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.


Euclidean Plane Hyperbolic Plane Modular Group Hyperbolic Geometry Invariant Line 
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 Science+Business Media New York 1992

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Mathematics DepartmentMonash UniversityClaytonAustralia

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