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September, 1950 The Distribution of Distance in a Hypersphere
J. M. Hammersley
Ann. Math. Statist. 21(3): 447-452 (September, 1950). DOI: 10.1214/aoms/1177729805


Deltheil ([1], pp. 114-120) has considered the distribution of distance in an $n$-dimensional hypersphere. In this paper I put his results (17) in a more compact form (16); and I investigate in greater detail the asymptotic form of the distribution for large $n$, for which the rather surprising result emerges that this distance is almost always nearly equal to the distance between the extremities of two orthogonal radii. I came to study this distribution by the need to compute a doubly-threefold integral, which measures the damage caused to plants by the presence of radioactive tracers in their fertilizers; for the distribution affords a method of evaluating numerically certain multiple integrals. I hope to describe elsewhere this application of the theory.


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J. M. Hammersley. "The Distribution of Distance in a Hypersphere." Ann. Math. Statist. 21 (3) 447 - 452, September, 1950.


Published: September, 1950
First available in Project Euclid: 28 April 2007

zbMATH: 0039.39301
MathSciNet: MR37481
Digital Object Identifier: 10.1214/aoms/1177729805

Rights: Copyright © 1950 Institute of Mathematical Statistics

Vol.21 • No. 3 • September, 1950
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