Concise formulas for the area and volume of a hyperspherical cap.
Asian J Math Stat 2011 Jan; 4(1):66-70
Spherical caps in hyperspace have found applications in stochastic optimizations and software engineering. However, there is a need for concise formulas for surface area and volume that are easy to express and compute. In this note, concise formulas are given in closed-forms. These formulas are obtained by integrating the area/volume of an (n-1)-sphere over a great circle arc in hyperspherical coordinates.
Author Keywords: Hyperspace; hyperspherical cap; hyperspherical sector; hyperspherical cone; area; volume
Shengqiao Li, 1095 Willowdale Road, MS 4050, Morgantown, WV 26505, USA
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Asian Journal of Mathematics & Statistics