Dodecahedral conjecture

The dodecahedral conjecture in geometry is intimately related to sphere packing.

László Fejes Tóth, a 20th century Hungarian geometer, considered the Voronoi decomposition of any given packing of unit spheres. He conjectured in 1943 that the minimal volume of any cell in the resulting Voronoi decomposition was at least as large as the volume of a regular dodecahedron circumscribed to a unit sphere.^[1]

Thomas Callister Hales and Sean McLaughlin proved the conjecture in 1998,^[2] following the same strategy that led Hales to his proof of the Kepler conjecture. The proofs rely on extensive computations. McLaughlin was awarded the 1999 Morgan Prize for his contribution to this proof.

References

1. ^ Fejes Tóth, L. (1943). "Über die dichteste Kugellagerung". Mathematische Zeitschrift 48 (1): 676–684. doi:10.1007/BF01180035. .
2. ^ Hales, Thomas C.; McLaughlin, Sean (2010). "The Dodecahedral Conjecture". Journal of the American Mathematical Society 23 (2): 299–344. arXiv:math.MG/9811079. doi:10.1090/S0894-0347-09-00647-X. .

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Conjectures Theorems in geometry Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Eoin Brosnan Anadarko Basin Look at other dictionaries: Conjecture de géométrisation — En mathématiques, et plus précisément en géométrie, la conjecture de géométrisation de Thurston affirme que les variétés compactes de dimension 3 peuvent être décomposées en sous variétés admettant l une des huit structures géométriques appelées… …   Wikipédia en Français Geometrization conjecture — Thurston s geometrization conjecture states that compact 3 manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3 manifolds of the uniformization theorem for… …   Wikipedia Rhombic dodecahedral honeycomb — The rhombic dodecahedra honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space. It is the Voronoi diagram of the face centered cubic sphere packing, which is believed to be the densest possible packing of equal spheres in… …   Wikipedia List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… …   Wikipedia List of conjectures — This is an incomplete list of mathematical conjectures. They are divided into four sections, according to their status in 2007. See also: * Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators * Unsolved problems in… …   Wikipedia Liste de conjectures mathématiques — Ce qui suit est une liste de conjectures mathématiques, non exhaustive. Elles sont divisées en quatre sections, en accord avec leur état en 2011. Voir aussi : Conjecture d Erdős (en), qui liste des conjectures de Paul Erdős et de ses… …   Wikipédia en Français Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student — The Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student is an annual award given to an undergraduate student in the US, Canada, or Mexico who demonstrates superior mathematics research. The $1,000… …   Wikipedia Morgan Prize — Distinguish from the De Morgan Medal awarded by the London Mathematical Society. The Morgan Prize (actually Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student) is an annual award given to an… …   Wikipedia Sean McLaughlin — may refer to: Sean McLaughlin (meteorologist) Sean McLaughlin (media activist educator) Sean C. McLaughlin, (Geologist and GIS Specialist) Sean J. McLaughlin, United States federal judge Sean McLaughlin, winner of the 1999 Frank and Brennie… …   Wikipedia 3-manifold — In mathematics, a 3 manifold is a 3 dimensional manifold. The topological, piecewise linear, and smooth categories are all equivalent in three dimensions, so little distinction is usually made in whether we are dealing with say, topological 3… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”