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Biometrika 1979 66(1):158-162; doi:10.1093/biomet/66.1.158
© 1979 by Biometrika Trust
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Miscellanea

The closest pair of N random points on the surface of a sphere

P. A. P. MORAN

Department of Statistics, Australian National University Canberra

Consider N points distributed independently and uniformly on the surface of a sphere. Exact upper and lower bounds are found for the distribution of the smallest angular distance between pairs of the points. Similar methods can be used for analogous problems. The present problem arose in the study of the way in which antibodies attack red blood cells.

Key Words: Geometries probability • Nearest neighbour • Points on a sphere


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