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Convexity, Area, and Trigonometry

  • James W. Anderson
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In this chapter, we explore some of the finer points of hyperbolic geometry. We first describe the notion of convexity and explore convex sets, including the class of hyperbolic polygons. Restricting our attention to hyperbolic polygons, we go on to discuss the measurement of hyperbolic area, including the Gauss-Bonnet formula, which gives a formula for the hyperbolic area of a hyperbolic polygon in terms of its angles. We go on to use the Gauss-Bonnet formula to show that non-trivial dilations of the hyperbolic plane do not exist. We close the chapter with a discussion of the laws of trigonometry in the hyperbolic plane.

Keywords

Hyperbolic Plane Hyperbolic Geometry Interior Angle Hyperbolic Line Ideal Vertex 
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-Verlag London 1999

Authors and Affiliations

  • James W. Anderson
    • 1
  1. 1.Faculty of Mathematical StudiesUniversity of Southampton, HighfieldSouthamptonUK

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