Talk:Sphere packing
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This page conflicts with kissing number problem where it claims that the densest packings are known up to 8-D. They are known for 1, 2, 3, 8, and 24 dimensions, but not others. -- Taral 21:33, 16 Aug 2004 (UTC)
- I don't think there is a conflict here. Kissing number problem is a different problem from sphere/hypersphere packing. The kissing number problem depends on local packing properties whereas sphere/hypersphere packing concerns the global property of average density. Also note that the sphere packing article says "the densest regular packings of hyperspheres are known up to 8 dimensions" - regular packings are sometimes called lattice packings. It is possible that denser irregular packings may exist in some dimensions - indeed the major difficulty in solving the 3D case is in ruling out the existence of an irregular packing with an average density that is higher than that of the cubic/hexagonal close packing (see Kepler conjecture). See MathWorld for more details. Gandalf61 09:15, Aug 17, 2004 (UTC)
I have to question the sanity of saying that spheres in the corners of a hypercube have their size determined by hamming distance. At the very least, the article on hamming distance seems to be the wrong topic. I'm very familiar with digital signal processing, but I don't know much about 4D geometry, so I am unwilling to make an edit. Still, someone should check this - and if they are related somehow, I would love to know! --Ignignot 20:23, Nov 19, 2004 (UTC)
i think the picture of the oranges is a bad example because it barely shows sphere packing.
[edit] and on a sphere?
Is there an article on arrangements of nodes on a sphere, including packing, covering, and the Thomson problem? —Tamfang 00:33, 26 June 2006 (UTC)
[edit] Current known packing inefficient?
The current known packing for three dimensions has density of about .74 and it was suggested that there might be a denser packing allowing a thirteenth sphere to be added. Can someone confirm this? —The preceding unsigned comment was added by 24.149.204.116 (talk • contribs) 16:29, 30 July 2006.
- When two spheres of the same radius are tangent, each, as seen from the centre of the other, fills less than 1/13 of the "sky"; for this reason it was long believed by some eminent mathematicians that a "kissing" arrangement of 13 around 1 must be possible, but 12 was eventually proven to be the limit. —Tamfang 01:03, 31 July 2006 (UTC)
