[en] We explore the idea that the derivative of the volume, V , of a region in Rp with respect to r equals its surface area, A, where r = p 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.
Disciplines :
Mathematics
Author, co-author :
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)
Language :
English
Title :
Derivative relationships between volume and surface area of compact regions in Rd
Publication date :
21 October 2003
Event name :
Séminaire de Mathématique de l'Université du Luxembourg
Event place :
Luxembourg, Luxembourg
Event date :
21-10-2003
Audience :
International
Name of the research project :
F2R-SMA-PUL-03AADC > Aide à la décision / classification > 01/01/2003 – 31/12/2004 > BISDORFF Raymond
