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A Variant of the Problem of the Thirteen Spheres

Published online by Cambridge University Press:  20 November 2018

L. Fejes Tóth  and
A. Heppes
L. Fejes Tóth
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences
A. Heppes
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences
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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).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1092 - 1100
Copyright
Copyright © Canadian Mathematical Society 1967

References

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