Discrete-geometry

  1. The sphere packing problem. J. Comput. Appl. Math. 44 (1992), no. 1, 41–76, pdf-link. {D}
  2. Remarks on the density of sphere packings in three dimensions. Combinatorica 13 (1993), no. 2, 181–197 pdf-link. {D}
  3. The status of the Kepler conjecture. Math. Intelligencer 16 (1994), no. 3, 47–58, springer-link. {D}
  4. Sphere packings I. Discrete Comput. Geom. 17 (1997), no. 1, 1–51, arXiv:math/9811073. {D}
  5. Sphere packings II. Discrete Comput. Geom. 18 (1997), no. 2, 135–149, arXiv:math/9811074. {D}
  6. Cannonballs and honeycombs. Notices Amer. Math. Soc. 47 (2000), no. 4, 440–449, AMS-link. {D}
  7. (with P. Sarnak and M. C. Pugh) Advances in random matrix theory, zeta functions, and sphere packing. Proc. Natl. Acad. Sci. USA 97 (2000), no. 24, 12963–12964, pdf-link. {D}
  8. Sphere packings in 3 dimensions, Arbeitstagung proceedings, June 2001, arXiv:math/0205208. {D}
  9. The honeycomb conjecture. Discrete Comput. Geom. 25 (2001), no. 1, 1–22, arXiv:math/9906042. {D}
  10. A computer verification of the Kepler conjecture. Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), 795–804, Higher Ed. Press, Beijing, 2002, arXiv:math/0305012. {D}
  11. The honeycomb problem on the sphere, preprint 2002, arXiv:math/0211234. {D}
  12. Some algorithms arising in the proof of the Kepler conjecture. Discrete Comput. Geom., 489–507, Algorithms Combin., 25, Springer, Berlin, 2003, arXiv:math/0205209. {D}
  13. A proof of the Kepler conjecture. Ann. of Math. 162 (2005), no. 3, 1065–1185, Annals-link. {D}
  14. Introduction to the Flyspeck project. Mathematics, Algorithms, Proofs, 05021, Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, 2006, pdf-link. {F}{D}
  15. (with S. P. Ferguson) A formulation of the Kepler conjecture. Discrete Comput. Geom., 36 (2006), 21–70, arXiv:math/9811072. {D}
  16. Historical overview of the Kepler conjecture. Discrete Comput. Geom., 36 (2006), 5–20, arXiv:math/9811071. {D}
  17. Sphere packings III: extremal cases. Discrete Comput. Geom., 36 (2006), 71–110, arXiv:math/9811076. {D}
  18. Sphere packings IV: detailed bounds. Discrete Comput. Geom., 36 (2006), 111–166, arXiv:math/9811076. {D}
  19. Sphere packings VI: tame graphs and linear programs. Discrete Comput. Geom., 36 (2006), 205–266, arXiv:math/9811078. {D}
  20. The Jordan curve theorem, formally and informally. Amer. Math. Monthly 114 (2007), no. 10, 882–894, MAA-link. {D}
  21. Jordan’s proof of the Jordan curve theorem. From Insight to Proof: Festscrift in Honour of Andrzej Trybulec, Studies in Logic, Grammar and Rhetoric 10 (23) 2007, 45–60, pdf-link. {D}
  22. Equidecomposable quadratic regions. Automated Deduction in Geometry, Lecture Notes in Computer Science 4869, Springer, 2007, pdf-link. {D}
  23. Some methods of problem solving in elementary geometry. LICS ’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science, IEEE Society Press, (2007), 35–40, –not-online–. {D}
  24. (with J. Harrison, S. McLaughlin, T. Nipkow, S. Obua, R. Zumkeller) A revision of the proof of the Kepler conjecture. Discrete Comput. Geom., (2009), arXiv:0902.0350. {D}
  25. (with S. McLaughlin) A proof of the dodecahedral conjecture. J. Amer. Math. Soc, 23 (2010), 299–344, arxiv-link. {D}
  26. Computational Discrete Gemetry, extended abstract in Mathematical Software — ICMS 2010, Proc. Third International Congress on Mathematical Software, 2010, LNCS 6327, pp. 1-3, Springer, 2010, pdf-link. {D}{F}
  27. Linear Programs for the Kepler Conjecture, extended abstract in Mathematical Software — ICMS 2010, Proc. Third International Congress on Mathematical Software, 2010, LNCS 6327, pp. 149–151, Springer, 2010, pdf-link. {D}{F}
  28. Dense Sphere Packings: a blueprint for formal proofs, Cambridge University Press, LMS volume 400, 2012, pdf-link. {F}{D}
  29. On the Reinhardt Conjecture, Vietnam Journal of Mathematics, 39(3), 2012, arxiv:1103.4518. {D}
  30. The Strong Dodecahedral Conjecture and Fejes Toth’s Contact Conjecture, in Discrete Geometry and Optimization Series: Fields Institute Communications, Vol. 69 Bezdek, Karoly; Deza, Antoine; Ye, Yinyu (Eds.) 2013, arxiv:1110.0402. {D}
  31. A Proof of Fejes Toth’s Conjecture on Sphere Packings with Kissing Number Twelve, preprint 2012, arxiv:1209.6043. {D}
  32. (with 21 other coauthors) A Formal proof of the Kepler conjecture, preprint 2014, arxiv:1501.02155. {D}{F}
  33. (with W. Kusner) Packings of Regular Pentagons in the Plane, preprint 2016, arxiv:1602.07220. {D}
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