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The status of the kepler conjecture

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References

  1. B. Cipra, Gaps in a sphere-packing proof?,Science 259 (1993), 895.

    Google Scholar 

  2. L. Fejes Tóth,Regular Figures, New York: MacMillan, 1964.

    MATH  Google Scholar 

  3. L. Fejes Tóth,Lagerungen in der Ebene auf der Kugel und im Raum, Berlin: Springer-Verlag, 1953.

    Book  MATH  Google Scholar 

  4. David H. Freedman, Round things in square spaces,Discover, 13(1) (January 1992), 36.

    Google Scholar 

  5. S. Günther, Ein stereometrisches Problem,Arch. Math. Phys. 57 (1875), 209–215.

    MATH  Google Scholar 

  6. W.-Y. Hsiang, On the density of sphere packings inE 3, II — The proof of Kepler’s conjecture, Center for Pure and Appl. Math. University of California, Berkeley, preprint PAM-535, September, 1991.

    Google Scholar 

  7. W.-Y. Hsiang, On the sphere packing problem and the proof of Kepler’s conjecture,Int. J. Math. 4(5) (1993), 739–831.

    Article  MATH  MathSciNet  Google Scholar 

  8. W.-Y. Hsiang, personal communication, Letter to T. Hales, March 3, 1992.

  9. I. Stewart, The kissing number,Scientific American 256(2) (Feb. 1992), 112–115.

    Article  Google Scholar 

  10. I. Stewart, Mathematics, 1992Yearbook to the Encyclopædia Britannica, 1992.

  11. I. Stewart, Has the sphere packing problem been solved?,New Scientist 134 (2 May 1992), 16.

    Google Scholar 

  12. I. Stewart,The Problems of Mathematics, 2nd ed., New York: Oxford University Press, 1992.

    MATH  Google Scholar 

Bibliography

  1. C. Bender, Bestimmung der grössten Anzahl gleich grosser Kugeln, welche sich auf eine Kugel von demselben Radius, wie die übrigen, auflegen lassen,Arch. Math. Phys. 56 (1874), 302–306.

    MATH  Google Scholar 

  2. A. H. Boerdijk, Some remarks concerning close-packing of equal spheres,Philips Res. Rep. 7 (1952), 303–313.

    MATH  MathSciNet  Google Scholar 

  3. B. Cipra, Music of the spheres,Science 251 (1991), 1028.

    Article  Google Scholar 

  4. J. H. Conway and N. J. A. Sloane,Sphere Packings, Lattices and Groups, 2nd ed., New York: Springer-Verlag, 1993.

    Book  MATH  Google Scholar 

  5. L. Fejes Tóth, Über die dichteste Kugellagerung,Math. Z. 48 (1942–13), 676–684.

    Article  Google Scholar 

  6. R. Hoppe, Bemerkung der Redaction,Arch. Math. Phys. 56 (1874), 307–312.

    Google Scholar 

  7. W.-Y. Hsiang, On the density of sphere packings inE 3, I, preprint, 1990.

  8. W.-Y. Hsiang, On the density of sphere packings inE 3 — Kepler’s conjecture and Hilbert’s 18th problem, preprint, 1990.

  9. W.-Y. Hsiang, Sphere packings and spherical geometry — Kepler’s conjecture and beyond, Center for Pure and Appl. Math. University of California, Berkeley, preprint PAM-528, July 1991.

    Google Scholar 

  10. W.-Y. Hsiang, On the density of sphere packings inE 3, I, Center for Pure and Appl. Math. University of California, Berkeley, preprint PAM-530, August 1991.

    Google Scholar 

  11. J. Leech, The problem of the thirteen spheres,The Mathematical Gazette 40(331) (Feb. 1956), 22–23.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. J. Muder, A new bound on the local density of sphere packings,Discrete Comp. Geom. 10 (1993), 351–375.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Schütte and B. L. van der Waerden, Das Problem der dreizehn Kugeln,Math. Annalen 125 (1953), 325–334.

    Article  MATH  Google Scholar 

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Hales, T.C. The status of the kepler conjecture. The Mathematical Intelligencer 16, 47–58 (1994). https://doi.org/10.1007/BF03024356

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