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Non-Euclidean Geometry

  • Robin Hartshorne
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Certainly one of the greatest mathematical discoveries of the nineteenth century was that of non-Euclidean geometry: seen but not revealed by Gauss, and developed in all its glory by Bolyai and Lobachevsky. The purpose of this chapter is to give an account of this theory, but we do not always follow the historical development. Rather, with hindsight we use those methods that seem to shed the most light on the subject. For example, continuity arguments have been replaced by a more axiomatic treatment.

Keywords

Rigid Motion Hyperbolic Plane Perpendicular Bisector Cartesian Plane Angle Bisector 
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

© Robin Hartshorne 2000

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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