A formulation of the Kepler conjecture

Discrete and Computational Geometry

Volumn 36, Issue 1, 2006, Pages 21-69

  Hales, Thomas C ^a   Ferguson, Samuel P ^b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744734284     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-005-1211-1     Document Type: Article

References (14)

1. [CS2] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, third edition, Springer-Verlag, New York, 1998.
2. [Fej8] L. Fejes Töth, Lagerungen in der Ebene auf der Kugel und im Raum, second edition, Springer-Varlag, Berlin, 1972.
3. [Ha1] T. C. Hales, The sphere packing problem, J. Comput. Appl. Math. 44 (1992), 41-76.
4. [Ha2] T. C. Hales, Remarks on the density of sphere packings in three dimensions, Combinatorica 13 (1993), 181-187.
5. [Ha5] T. C. Hales, A reformulation of the Kepler conjecture, Unpublished manuscript, Nov. 1996.
6. [Ha6] T. C. Hales, Sphere packings, I, Discrete Comput. Geom. 17 (1997), 1-51.
7. [Ha7] T. C. Hales, Sphere packings, II, Discrete Comput. Geom. 18 (1997), 135-149.
8. [Ha12] Thomas C. Hales, Cannonballs and honeycombs, Notices Amer. Math. Soc. 47(4) (2000), 440-449.
9. [Ha13] T. C. Hales, Sphere Packings in 3 Dimensions, Arbeitstagung, 2001.
10. [Ha14] T. C. Hales, Some algorithms arising in the proof of the Kepler conjecture, in Discrete and Computational Geometry, Algorithms and Combinatorics, vol. 25, Springer-Verlag, Berlin, 2003, pp. 489-507.
11. [Ha16] T. C. Hales, Computer Resources for the Kepler Conjecture, http://annals.math.princeton.edu/keplerconjecture/. (The source code, inequalities, and other computer data relating to the solution are also found at http://xxx.lanl.gov/abs/math/9811078v1.)
12. [Hi] D. Hilbert, Mathematische Probleme, Archiv Math. Phys. 1 (1901), 44-63,
13. also in Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, vol. 28, 1976, pp. 1-34.
14. [Ro1] C. A. Rogers, The packing of equal spheres, Proc. London Math. Soc. (3) 8 (1958), 609-620.