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The problem of the thirteen spheres

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Proofs from THE BOOK

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Abstract

A famous controversy between David Gregory and Isaac Newton in 1694 concerned the following question:

How many unit spheres can simultaneously touch a given sphere of the same size?

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References

  1. C. Bender: Bestimmung der grüssten Anzahl gleicher Kugeln, welche sich auf eine Kugel von demselben Radius, wie die übrigen, auflegen lassen, Archiv Math. Physik (Grunert) 56 (1874), 302–306;

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  4. J. H. Conway, N. J. A. Sloane: Sphere Packings, Lattices and Groups, Grundlehren der mathematischen Wissenschaften Vol. 290, Springer-Verlag New York, Second ed. 1993.

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  5. S. Günther: Ein stereometrisches Problem, Archiv Math. Physik (Grunert) 57 (1875), 209–215.

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  6. J. Leech: The problem of the thirteen spheres, The Mathematical Gazette 40 (1956), 22–23.

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  7. K. Schütte, B. L. van der Waerden: Das Problem der dreizehn Kugeln, Math. Annalen 53 (1953), 325–334.

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Author information

Authors and Affiliations

  1. Institut für Mathematik II (WE2), Freie Universität Berlin, Arnimallee 3, D-14195, Berlin, Germany

    Martin Aigner

  2. Fachbereich Mathematik, MA 7-1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Günter M. Ziegler

Authors
  1. Martin Aigner
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  2. Günter M. Ziegler
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© 1998 Springer-Verlag Berlin Heidelberg

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Aigner, M., Ziegler, G.M. (1998). The problem of the thirteen spheres. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22343-7_12

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  • DOI: https://doi.org/10.1007/978-3-662-22343-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-22345-1

  • Online ISBN: 978-3-662-22343-7

  • eBook Packages: Springer Book Archive

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