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The Elementary Concept of Area and Volume

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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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© 1983 Springer-Verlag Berlin Heidelberg

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Hopf, H. (1983). The Elementary Concept of Area and Volume. In: Differential Geometry in the Large. Lecture Notes in Mathematics, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21563-0_4

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  • DOI: https://doi.org/10.1007/978-3-662-21563-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12004-9

  • Online ISBN: 978-3-662-21563-0

  • eBook Packages: Springer Book Archive