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A Variant of the Problem of the Thirteen Spheres
Published online by Cambridge University Press: 20 November 2018
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We use the term balls for congruent, closed spheres no two of which have interior points in common. In Euclidean n-space let Nn be the maximal number of balls which can touch a ball. Obviously, N2 = 6. R. Hoppe (see (1)) proved that N3 = 12, settling thereby a famous point of controversy between Newton and David Gregory, known as the problem of the thirteen spheres (see (3)). Simpler proofs were given by Günter (6), Schütte and van der Waerden (10), and Leech (7).
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- Copyright © Canadian Mathematical Society 1967
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