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Models for the Hyperbolic Plane

  • Meighan I. Dillon
Chapter

Abstract

The role of models in geometry is tied to the subject’s historical connection to axiomatics. While The Elements of Euclid is the archetype of an axiomatic system, the real plane, \({\mathbb R}^2\), is the archetype of a model for an axiomatic system, in this case, that of the Euclidean plane. The existence of a model for an axiomatic system is proof that the system is consistent.

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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