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 For example, continuity arguments have been replaced by a more axiomatic treatment.
KeywordsRigid Motion Hyperbolic Plane Perpendicular Bisector Cartesian Plane Angle Bisector
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