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Some Problems Involving Circular and Spherical Targets

George Marsaglia
Operations Research
Vol. 13, No. 1 (Jan. - Feb., 1965), pp. 18-27
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/167951
Page Count: 10
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Some Problems Involving Circular and Spherical Targets
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Abstract

This article is concerned with some problems that occur in certain tactical considerations: how should one place k circles [spheres] in the plane [3-space] so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles [spheres]. For k>3 the problem seems hopeless, (except for certain special situations); the case for k=3 is still unresolved and is being worked on by a number of investigators, and the case for k=2 is solved completely in this paper. The results for k=2 have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for k≥ 3.

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