A084829 Best packing of m>1 equal spheres in a sphere setting a new density record.

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, 61

Offset: 1

Author

Hugo Pfoertner, Jun 12 2003

Keywords

• hard
• more
• nonn

Comments

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.

See the E. Specht link for latest results. - Eduard Baumann, Jan 03 2024

Links

• Dave Boll, Optimal Packing of Circles and Spheres.
• WenQi Huang and Liang Yu, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, arXiv:1202.4149 [cs.DM], 2012.
• Eckard Specht, The best known packings of equal spheres in a sphere, July 2023.
• Hugo Pfoertner, Numerical results for best packing of spheres in sphere.
• Hugo Pfoertner, Densest Packings of n Equal Spheres in a Sphere of Radius 1 Largest Possible Radii.
• Eric Weisstein's World of Mathematics, Sphere Packing.
• Jianrong Zhou, Shuo Ren, Kun He, Yanli Liu, and Chu-Min Li, An Efficient Solution Space Exploring and Descent Method for Packing Equal Spheres in a Sphere, arXiv:2305.10023 [cs.CG], 2023.

Crossrefs

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

Extensions

Inserted missing term 30, added comment with conjectured next terms and updated links by Hugo Pfoertner, Jun 24 2011

More terms from Hugo Pfoertner, Aug 25 2013