The Elementary Concept of Area and Volume

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


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.



Dihedral Angle Interior Point Rectangular Prism Pythagorean Theorem Equivalence Show 
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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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