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The Elementary Concept of Area and Volume

  • Heinz Hopf
Part of the Lecture Notes in Mathematics book series (LNM, volume 1000)

Abstract

In elementary geometry area (volume) is defined in the following manner:
  1. (i)

    A rectangle (right rectangular prism) with sidelengths 1,ℓ, (1,1,ℓ) units is called a normal rectangle with an area (volume) of ℓ sqaure (cubic) units.

     
  2. (ii)

    The area (volume) of any polygon (polyhedra) P which can be decomposed into a finite number of parts so that these parts can be rearranged to form a normal rectangle (rectangular prism) R is equal to the area (volume) of R.

     

Keywords

Dihedral Angle Interior Point Rectangular Prism Pythagorean Theorem Equivalence Show 
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 Berlin Heidelberg 1983

Authors and Affiliations

  • Heinz Hopf
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichSwitzerland

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