The Hyperbolic Plane

Chapter

Abstract

The last chapter showed us what we can say if we assume the first four postulates of Euclid while maintaining a neutral attitude toward the fifth postulate. There are two possibilities: the Euclidean case, where every triangle is Euclidean, and the hyperbolic case, where every triangle has a positive angular defect. In this chapter, we consider properties of the plane in the latter case.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKennesaw State UniversityMariettaUSA

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