Title :
Some Results on Monotonicity of Volume and Surface Area of Objects in K Dimensions
Author :
Loskot, Pavel ; Beaulieu, Norman C.
Author_Institution :
Univ. of Wales Swansea, Swansea
Abstract :
Hypergeometry of objects in K dimensions is considered. In particular, the K dimensional sphere, polytope, cube, scaled polytope and the scaled cube are studied. The volume and the surface area of these objects are shown to reach a maximum for a particular value of dimension. The dimension corresponding to the maximum volume and to the maximum surface area is derived as a function of the radius. Furthermore, the p-norm in K dimensions is shown to be monotonically increasing in K, and monotonically decreasing in p.
Keywords :
computational geometry; K dimensional sphere; maximum object surface area; maximum object volume; monotonicity; object hypergeometry; scaled cube; scaled polytope; Communication channels; Digital communication; Diversity reception; Error analysis; Estimation error; Frequency diversity; Information theory; Laboratories; Throughput; Wireless communication;
Conference_Titel :
Information Theory, 2007. CWIT '07. 10th Canadian Workshop on
Conference_Location :
Edmonton, AB
Print_ISBN :
1-4244-0769-9
Electronic_ISBN :
1-4244-0769-9
DOI :
10.1109/CWIT.2007.375732
