Reference : Derivative relationships between volume and surface area of compact regions in Rd
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/2088
Derivative relationships between volume and surface area of compact regions in Rd
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Applied Mathematics Unit (SMA)]
Dorff, Michael mailto [Brigham Young University, Utah, USA > Department of Mathematics]
2007
Rocky Mountain Journal of Mathematics
Rocky Mountain Mathematics Consortium
37
2
551-571
Yes
International
0035-7596
1945-3795
[en] We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r=d V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/2088
10.1216/rmjm/1181068766
http://arxiv.org/abs/math/0702635

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