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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 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.
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)
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? —Preceding unsigned comment added by 24.149.204.116 ( talk • contribs) 16:29, 30 July 2006
The animated image was removed in a bold edit. However, the removal was reverted. An editor should not revert a revert until consensus has been established to remove the image. I think it's fine, and there is no absolute law against allegedly "distracting" images - it's still very illustrative and relevant to this article. I would ask that the user who is removing this image not engage in edit warring and instead discuss his changes instead of forcing them onto the article. This runs contrary to how Wikipedia is meant to function - collaboratively and through consensus-building. -- Cheeser1 16:55, 21 September 2007 (UTC)
The image displayed in the still frame and in the animation is a tetrahedron, not a pyramid. A pyramid has a four-sided, square base and four three-sided walls (like the pyramids in Egypt). A tetrahedron has a equilateral triangle for a base and three equilateral triangles for walls, giving the shape four equal sides (i.e. tetra- (four) hedron). I suggest renaming it. I'd do it myself, but the process looks complicated.
Tdbostick (
talk)
13:00, 5 May 2011 (UTC)Tim Bostick
H. S. M. Coxeter remarks that there are arrangements of equal spheres in both positively and negatively curved space that exceed the Kepler density. I think it's in The Beauty of Geometry; will look for it later. — Tamfang ( talk) 01:45, 29 February 2008 (UTC)
I'm not a mathematician, but these two seem to overlap to a fair extent. Shouldn't they be merged? dorftrottel ( talk) 20:53, 30 May 2008 (UTC)
It was recently found that sphere packing has direct, although still unexplained, connection to the arrangement of the elements in the periodic table, as shown here. It is thought provoking and fascinating. My view is that it would be benefitial for atracting more attention to the field of Sphere Packing if this web site is listed among the external links. What do you think? Drova ( talk) 13:29, 24 December 2008 (UTC)
If it is proven that the 24-dimensional regular sphere packing has the highest density, is the actual (numerical) density known? If it is, that certainly should be in the article. Eebster the Great ( talk) 07:17, 17 February 2009 (UTC)
I propose to merge the page Packing problem into Sphere packing. This shouldn't be too difficult as the second article is written beautifully whereas the first one contains lots of numbers (without citations) that don't tell you anything. And the style in the first one is quite relaxed (eg., "Packing problems are one area where mathematics meets puzzles (recreational mathematics)"). There is a second reason I want to cleanup Packing problem: In computer science, packing problems are combinatorial optimization problems (eg., the set packing problem) and they are LP-dual to covering problems. Of course, the combinatorial meaning is related to sphere packing, and there will be a disambiguation at the top of the page. I want to extend the article packing problem to the combinatorial and computational aspects and before I can do that, it needs a cleanup of experts in sphere packing. ylloh ( talk) 22:49, 11 March 2009 (UTC)
It would be nice to have a simple discussion and formula for how many small spheres of diam D1 can pack on the surface of a larger sphere diam D2 65.220.64.105 ( talk) 18:06, 12 May 2009 (UTC)
At the top of section 3 Hypersphere Packing, there are two edit links. The second is for the previous subsection 2.2 Irregular Packing. Obviously this is incorrect, but I don't know how it was caused or how to fix it. Any ideas? Anywhere else that this could be asked? Elroch ( talk) 09:02, 18 November 2010 (UTC)
Shouldn't Close-packing of spheres be merged into this article? Toshio Yamaguchi ( talk) 14:21, 8 May 2011 (UTC)
Is anyone interested in collaborating with me for a drive to get this article to GA quality? -- 99of9 ( talk) 11:47, 24 November 2011 (UTC)
In the section on irregular packing ( Sphere packing#Irregular packing), it says, "This irregular packing will generally have a density of about 64%." But then in the next sentence it says, "Recent research predicts analytically that it cannot exceed a density limit of 63.4%". This seems contradictory. Shouldn't the first number be at most 63% (if we are rounding)? Even then, it looks odd to me that the general packing density is so close to the upper bound. 130.66.206.111 ( talk) 15:03, 17 March 2014 (UTC)
I once saw a table providing the number of different regular close-packs in various dimensions. If I recall correctly, it was 1 in most dimensions, except its 2 in 3D (fcc and hcp), some number in 6 and a bigger number in 10 dimensions, and an explosion in 24 due to leech lattice, and then back to 1 for the rest. Is my memory faulty? Where can this table be found? 67.198.37.16 ( talk) 17:13, 22 September 2015 (UTC)
The article states that "In dimensions higher than three, the densest regular packings of hyperspheres are known up to 8 dimensions.[8] " . But the optimal (i.e. densest) packings for dimensions higher than 3 are only postulated and not known, as [8] clearly states. — Preceding unsigned comment added by 2A02:168:7406:0:A544:DB60:A8BB:3AEF ( talk) 15:20, 27 June 2018 (UTC)
Ok thanks — Preceding unsigned comment added by 2A02:168:7406:0:A544:DB60:A8BB:3AEF ( talk) 16:48, 27 June 2018 (UTC)
4D sphere packing = doughnut packing! ~ JasonCarswell (talk) 21:29, 28 August 2018 (UTC)
1 center circle ringed by 6, then those now 7 center circles fenced in by 9 around the border, then those 16 ringed by 18, then those 34 ringed by 24, then those 58 ringed by ---,... This 2D hexagonal circle packing ratio/equation must have a name as well as versions for 3D and higher. Please link to it here and/or try to include some of it on these "packing" pages. Thanks in advance. ~ JasonCarswell (talk) 21:26, 28 August 2018 (UTC)
The article currently states "Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face-centred cubic, "FCC")—where the layers are alternated in the ABCABC... sequence. The other is called hexagonal close packing ("HCP")—where the layers are alternated in the ABAB... sequence." I have tagged that statement as dubious. Sloane, N. (2003). "The proof of the packing". Nature. 425: 126-127. doi: 10.1038/425126c. says on page 127 "The f.c.c. and h.c.p. packings have the same density, but they are different: one is a lattice, the other is not." So the article currently seems to be wrong in stating both arrangements correspond to lattices. Toshio Yamaguchi ( talk) 12:04, 13 April 2022 (UTC)
This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
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 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.
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)
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? —Preceding unsigned comment added by 24.149.204.116 ( talk • contribs) 16:29, 30 July 2006
The animated image was removed in a bold edit. However, the removal was reverted. An editor should not revert a revert until consensus has been established to remove the image. I think it's fine, and there is no absolute law against allegedly "distracting" images - it's still very illustrative and relevant to this article. I would ask that the user who is removing this image not engage in edit warring and instead discuss his changes instead of forcing them onto the article. This runs contrary to how Wikipedia is meant to function - collaboratively and through consensus-building. -- Cheeser1 16:55, 21 September 2007 (UTC)
The image displayed in the still frame and in the animation is a tetrahedron, not a pyramid. A pyramid has a four-sided, square base and four three-sided walls (like the pyramids in Egypt). A tetrahedron has a equilateral triangle for a base and three equilateral triangles for walls, giving the shape four equal sides (i.e. tetra- (four) hedron). I suggest renaming it. I'd do it myself, but the process looks complicated.
Tdbostick (
talk)
13:00, 5 May 2011 (UTC)Tim Bostick
H. S. M. Coxeter remarks that there are arrangements of equal spheres in both positively and negatively curved space that exceed the Kepler density. I think it's in The Beauty of Geometry; will look for it later. — Tamfang ( talk) 01:45, 29 February 2008 (UTC)
I'm not a mathematician, but these two seem to overlap to a fair extent. Shouldn't they be merged? dorftrottel ( talk) 20:53, 30 May 2008 (UTC)
It was recently found that sphere packing has direct, although still unexplained, connection to the arrangement of the elements in the periodic table, as shown here. It is thought provoking and fascinating. My view is that it would be benefitial for atracting more attention to the field of Sphere Packing if this web site is listed among the external links. What do you think? Drova ( talk) 13:29, 24 December 2008 (UTC)
If it is proven that the 24-dimensional regular sphere packing has the highest density, is the actual (numerical) density known? If it is, that certainly should be in the article. Eebster the Great ( talk) 07:17, 17 February 2009 (UTC)
I propose to merge the page Packing problem into Sphere packing. This shouldn't be too difficult as the second article is written beautifully whereas the first one contains lots of numbers (without citations) that don't tell you anything. And the style in the first one is quite relaxed (eg., "Packing problems are one area where mathematics meets puzzles (recreational mathematics)"). There is a second reason I want to cleanup Packing problem: In computer science, packing problems are combinatorial optimization problems (eg., the set packing problem) and they are LP-dual to covering problems. Of course, the combinatorial meaning is related to sphere packing, and there will be a disambiguation at the top of the page. I want to extend the article packing problem to the combinatorial and computational aspects and before I can do that, it needs a cleanup of experts in sphere packing. ylloh ( talk) 22:49, 11 March 2009 (UTC)
It would be nice to have a simple discussion and formula for how many small spheres of diam D1 can pack on the surface of a larger sphere diam D2 65.220.64.105 ( talk) 18:06, 12 May 2009 (UTC)
At the top of section 3 Hypersphere Packing, there are two edit links. The second is for the previous subsection 2.2 Irregular Packing. Obviously this is incorrect, but I don't know how it was caused or how to fix it. Any ideas? Anywhere else that this could be asked? Elroch ( talk) 09:02, 18 November 2010 (UTC)
Shouldn't Close-packing of spheres be merged into this article? Toshio Yamaguchi ( talk) 14:21, 8 May 2011 (UTC)
Is anyone interested in collaborating with me for a drive to get this article to GA quality? -- 99of9 ( talk) 11:47, 24 November 2011 (UTC)
In the section on irregular packing ( Sphere packing#Irregular packing), it says, "This irregular packing will generally have a density of about 64%." But then in the next sentence it says, "Recent research predicts analytically that it cannot exceed a density limit of 63.4%". This seems contradictory. Shouldn't the first number be at most 63% (if we are rounding)? Even then, it looks odd to me that the general packing density is so close to the upper bound. 130.66.206.111 ( talk) 15:03, 17 March 2014 (UTC)
I once saw a table providing the number of different regular close-packs in various dimensions. If I recall correctly, it was 1 in most dimensions, except its 2 in 3D (fcc and hcp), some number in 6 and a bigger number in 10 dimensions, and an explosion in 24 due to leech lattice, and then back to 1 for the rest. Is my memory faulty? Where can this table be found? 67.198.37.16 ( talk) 17:13, 22 September 2015 (UTC)
The article states that "In dimensions higher than three, the densest regular packings of hyperspheres are known up to 8 dimensions.[8] " . But the optimal (i.e. densest) packings for dimensions higher than 3 are only postulated and not known, as [8] clearly states. — Preceding unsigned comment added by 2A02:168:7406:0:A544:DB60:A8BB:3AEF ( talk) 15:20, 27 June 2018 (UTC)
Ok thanks — Preceding unsigned comment added by 2A02:168:7406:0:A544:DB60:A8BB:3AEF ( talk) 16:48, 27 June 2018 (UTC)
4D sphere packing = doughnut packing! ~ JasonCarswell (talk) 21:29, 28 August 2018 (UTC)
1 center circle ringed by 6, then those now 7 center circles fenced in by 9 around the border, then those 16 ringed by 18, then those 34 ringed by 24, then those 58 ringed by ---,... This 2D hexagonal circle packing ratio/equation must have a name as well as versions for 3D and higher. Please link to it here and/or try to include some of it on these "packing" pages. Thanks in advance. ~ JasonCarswell (talk) 21:26, 28 August 2018 (UTC)
The article currently states "Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face-centred cubic, "FCC")—where the layers are alternated in the ABCABC... sequence. The other is called hexagonal close packing ("HCP")—where the layers are alternated in the ABAB... sequence." I have tagged that statement as dubious. Sloane, N. (2003). "The proof of the packing". Nature. 425: 126-127. doi: 10.1038/425126c. says on page 127 "The f.c.c. and h.c.p. packings have the same density, but they are different: one is a lattice, the other is not." So the article currently seems to be wrong in stating both arrangements correspond to lattices. Toshio Yamaguchi ( talk) 12:04, 13 April 2022 (UTC)