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