Geometry pp 236-271 | Cite as


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


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.


Convex Polygon Euclidean Geometry Area Function Hyperbolic Geometry Pythagorean Theorem 
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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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