Euclidean Geometry

  • John G. Ratcliffe
Part of the Graduate Texts in Mathematics book series (GTM, volume 149)

Abstract

In this chapter, we review Euclidean geometry. We begin with an informal historical account of how criticism of Euclid’s parallel postulate led to the discovery of hyperbolic geometry. In Section 1.2, the proof of the independence of the parallel postulate by the construction of a Euclidean model of the hyperbolic plane is discussed and all four basic models of the hyperbolic plane are introduced. In Section 1.3, we begin our formal study with a review of n-dimensional Euclidean geometry. The metrical properties of curves are studied in Sections 1.4 and 1.5. In particular, the concepts of geodesic and arc length are introduced.

Keywords

Euclidean Geometry Hyperbolic Plane Hyperbolic Geometry Geodesic Segment Geodesic 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 1994

Authors and Affiliations

  • John G. Ratcliffe
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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