Abstract
In elementary geometry area (volume) is defined in the following manner:
-
(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.
-
(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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
