A084829 - OEIS

%I #44 Mar 22 2024 11:40:53

%S 2,3,4,6,8,9,11,12,18,21,25,30,31,32,33,34,35,36,38,49,51,53,56,59,60,

%T 61

%N Best packing of m>1 equal spheres in a sphere setting a new density record.

%C All terms beyond m=9 are only conjectures found by numerical experimentation. The density is defined as the fraction of the volume of the large sphere occupied by the small spheres. For 2 spheres the density is 0.25. The first known configuration with density exceeding 0.5 occurs for 31 spheres.

%C See the E. Specht link for latest results. - _Eduard Baumann_, Jan 03 2024

%H Dave Boll, <a href="http://web.archive.org/web/20121213221349/https://home.comcast.net/~davejanelle/packing.html">Optimal Packing of Circles and Spheres</a>.

%H WenQi Huang and Liang Yu, <a href="http://arxiv.org/abs/1202.4149">Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem</a>, arXiv:1202.4149 [cs.DM], 2012.

%H Eckard Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/ssp/ssp.html">The best known packings of equal spheres in a sphere</a>, July 2023.

%H Hugo Pfoertner, <a href="/A084827/a084827.txt">Numerical results for best packing of spheres in sphere</a>.

%H Hugo Pfoertner, <a href="/A084829/a084829.txt">Densest Packings of n Equal Spheres in a Sphere of Radius 1</a> Largest Possible Radii.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpherePacking.html">Sphere Packing</a>.

%H Jianrong Zhou, Shuo Ren, Kun He, Yanli Liu, and Chu-Min Li, <a href="https://arxiv.org/abs/2305.10023">An Efficient Solution Space Exploring and Descent Method for Packing Equal Spheres in a Sphere</a>, arXiv:2305.10023 [cs.CG], 2023.

%Y Cf. A084827, A084826, A084644, A084828, A121346.

%K hard,more,nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 12 2003

%E Inserted missing term 30, added comment with conjectured next terms and updated links by _Hugo Pfoertner_, Jun 24 2011

%E More terms from _Hugo Pfoertner_, Aug 25 2013