Advertisement

Some Neutral Theorems of Plane Geometry

  • Arlan Ramsay
  • Robert D. Richtmyer
Part of the Universitext book series (UTX)

Abstract

We discuss some of those theorems of Euclidean plane geometry that are independent of the parallel axiom. They will be needed in the development of hyperbolic geometry. We assume they are more or less known, so that our treatment is not as complete as a full treatment of Euclidean geometry would be. Some of the theorems are weaker than the corresponding Euclidean ones, because the more complete form would require the parallel axiom. Some of them go a little beyond Euclid in that they use the notion of continuity as it appears in calculus. Results in the last two sections go beyond Euclid in that the ideas in them are more recent, as in the Jordan Curve Theorem or the study of isometries.

Keywords

Plane Geometry Hyperbolic Plane Isosceles Triangle Hyperbolic Geometry Polygonal Path 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Arlan Ramsay
    • 1
  • Robert D. Richtmyer
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

Personalised recommendations