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Geometry pp 236-271 | Cite as

Area

  • Richard S. Millman
  • George D. Parker
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In this chapter we shall be interested in the concept of area in a neutral geometry. We shall start off with the definition of an area function and an investigation of the properties of a Euclidean area function. In Sections 10.2 and 10.3 we will prove the existence of area functions for Euclidean and hyperbolic geometries respectively. In the last section we will consider a beautiful theorem due to J. Bolyai which says that if two polygonal regions have the same area then one may be cut into a finite number of pieces and rearranged to form the other.

Keywords

Convex Polygon Euclidean Geometry Area Function Hyperbolic Geometry Pythagorean Theorem 
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 Inc. 1981

Authors and Affiliations

  • Richard S. Millman
    • 1
  • George D. Parker
    • 2
  1. 1.Department of Mathematical and Computer ScienceMichigan Technological UniversityHoughtonUSA
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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