Unit ball in high dimensions

Athreya, K. B. (2008) Unit ball in high dimensions Resonance - Journal of Science Education, 13 (4). pp. 334-342. ISSN 0971-8044

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Official URL: http://www.ias.ac.in/resonance/April2008/p334-342....

Related URL: http://dx.doi.org/10.1007/s12045-008-0014-0


In this article, we compute the volume V n of the unit ball in an n-dimensional space. For n = 1, 2, 3, the volumes are respectively 2, π 4π /3, which are the length of interval [-1,1], area of a unit circle and volume of the unit sphere. The numbers V n 'appear' to increase. But in fact this not so. In fact V n tends to zero as n tends to infinity!.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Euclidean Space; Unit Ball; Riemann Integral; Standard Normal Probability Density; Bell Curve; Gaussian Probability Density; Cesaro Average
ID Code:1135
Deposited On:05 Oct 2010 12:53
Last Modified:16 May 2016 12:17

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