Talk:Packing problems

VfD results
This article was nominated for deletion. The result was no consensus, but some merging/redirecting might be in order. For details, please see Votes for deletion/MoreKarlScherer. -- BD2412 talk 00:36, July 14, 2005 (UTC)

This article was nominated for deletion a second time, this time kept outright, See Votes for deletion/KarlSchererRevisited1. Sjakkalle (Check!)  09:16, 27 July 2005 (UTC)

Dubious-ness
Could someone with a large (by number of edits, not by time) edit history (so that it is obviously not Karl Scherer or friends) verify the maths examples in this article. They strike me as inaccurate and/or non-noteworthy and/or presented with Weasel words

21:15, 20 July 2005 (UTC)


 * Why are you disputing these? Weren't they there a long time ago? Charles Matthews 10:05, 27 July 2005 (UTC)

Correct me if I'm wrong,


 * Maybe I did not find the best packing but the first box I could put an extra disc is 2x238 after that each extra 238 gives me extra two balls...

This is very different from numbers in the article, could anyone provide a ref? Tosha 23:24, 18 October 2005 (UTC)

Fiction? in article
I am a Maths Graduate and teacher, and yet I cannot see any possible way to pack more than 2n circles in an n X 2cm strip. To do so, essentially you would have either fit more circles (or part circles) vertically (there's no room) or horizontally. To benefit from hexagonal packing you would have to have a wider strip, and hexagonal packing is the most efficient way of packing circles. Furthermore, the article talks about a classic problem, and yet that problem is not mentioned on this article in Math World about circle packing.

As citations were asked for a long time ago, and have not been provided, I will now change the article and remove contentious references (they can be restored if citations are found).

Captainj 17:29, 22 May 2006 (UTC)


 * OK, I think I can posted the answer to your problem. Stand by... Michael Hardy 20:15, 22 May 2006 (UTC)



Maybe I'll return to this later. For now I'll just suggest thinking about how many circles in the figure above should be "centered" and how many should not be. Michael Hardy 20:38, 22 May 2006 (UTC)

I still can't make this work. If we use the packing method in the picture, and have 2 circles (in a vertical line) followed by a centered circle followed by another two circles, you get a total area of 3.92 for the five circles. The length of the strip that they occupy is $$1 + \sqrt(5) \approx 6.47$$. This means the area of the strip they occupy is approximately 8.47, giving an efficiency of 60.7%%. But the "standard efficiency" (all the circles two "neat" lines) is 78.5%. Therefore every time a centered circle is but between two standard packed circles, you lose area. So there doesn't seem to be any benefit in doing it that way.

If the circles were only put at then end, this wouldn't help either, because, in any case, the length of the strip is an integer.

Sorry I haven't drawn all the diagrams etc, but I don't have the software to do it easily. (I did all the working out back of the envelope). I hope my above Maths is correct, its clear I am going rusty in places.Captainj 21:28, 22 May 2006 (UTC)


 * You can do better than this. First lay a layer on the bottom.  Then lay a layer above it, touching it, but offset by half a ball.  Now notice that there is a gap at the top.  Therefore this whole structure can be zigzagged a bit to compact it.99of9 (talk) 02:01, 1 September 2009 (UTC)


 * So you can pack two rows of circles whose diameter is a bit greater than half the width of the strip; that's an answer to a question other than what was asked here, I think. —Tamfang (talk) 02:49, 1 September 2009 (UTC)


 * Well I meant you could zigzag the bottom row a bit (and the top row would still fit), increasing the lineal density, rather than expanding the circles. --99of9 (talk) 05:52, 10 May 2010 (UTC)


 * How does that increase the density? —Tamfang (talk) 16:37, 10 May 2010 (UTC)


 * Easier to explain with an image. I'm impressed that you're still watching the page - I almost didn't bother replying when I saw how long it had been! --99of9 (talk) 00:26, 11 May 2010 (UTC)


 * [[Image:Circle-strip.svg|frameless|500px|Packing on a strip with density 1.006046496.]]


 * Ah! —Tamfang (talk) 02:46, 11 May 2010 (UTC)
 * Well, you've convinced me. But it should really still be sourced.  — Preceding unsigned comment added by Captainj (talk • contribs) 23:16, 4 January 2012 (UTC)
 * That's easy. See Fig. 1.2 (c) on page 4 of the PDF Leob (talk) 21:05, 11 March 2016 (UTC)

Walter Stromquist
Where did the fact about Walter Stromquist proving something come from? I can't find it in the sources given. Leon math 23:44, 14 December 2006 (UTC)

Other known results
Not a single reference or proof for any of these. —Preceding unsigned comment added by 84.92.32.151 (talk) 21:09, 26 November 2007 (UTC)

balls inside a ball?
After noticing some interest at the RD/M I have added a short description about the case of packing few balls into a ball (of whom I don't have references)... I thought it could be nice to have a complete description of an easy packing problem. NOw I wonder if maybe it should better be shortened...--pma (talk) 09:12, 30 April 2009 (UTC)

de Bruijn's theorem: neccessary condition?
De Brujin's theorem, as stated, de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) is obvious. Perhaps what is really meant is "if and only if?" —Preceding unsigned comment added by 92.193.118.17 (talk) 09:59, 4 October 2009 (UTC)

"Klarner's" theorem
The article says:


 * Klarner's theorem: An a &times; b rectangle can be packed with 1 &times; n strips iff n | a or n | b.

No cite is given for the name "Klarner's theorem". Is "Klarner" David A. Klarner?

I added a citation of this theorem:. But Wagon does not refer to the theorem as Klarner's; he cites it as a special case of a theorem of N. G. de Bruijn which may be the de Bruijn's theorem mentioned in this wikipedia article just after "Klarner's".

cites to a book by Ross Honsberger. Can someone confirm that this book really calls the theorem "Klarner's"? Or is this just another Mathworld oddity?

—Dominus (talk) 16:19, 6 January 2010 (UTC)


 * The cited source does not bear out the attribution.  Honsberger credits Klarner, but does not refer to the result as "Klarner's theorem". I think this is a Mathworld neologism.  Klarner is indeed David A. Klarner.  Honsberger's cite is:  —Mark Dominus (talk) 07:16, 5 January 2012 (UTC)

Same problem in 3D
Does wikipedia have any references to this same problem in 3d, and for arbitrary shapes?

Is there any algorithm to solve these problems, other than just "try all possibilities"? 87.194.84.113 (talk) 23:35, 9 May 2010 (UTC)
 * Tetrahedron packing is one article I know of. I know a lot about binary sphere packing (in Euclidean space), but haven't written anything for wiki.  What shapes are you interested in? --99of9 (talk) 05:54, 10 May 2010 (UTC)

Rectangle Packing
This section is particularly sparse, and only talks about one special case. Could it possibly be fleshed out?Samineru (talk) 22:01, 1 March 2011 (UTC)

No techniques, no proofs
I believe the topic is important to have a wiki article on. I also believe the implementation is unsatisfactory in part because: 1) no word in it of how the packings presented were found;2) how they were proven (if at all). Both items, especially, 2 are hard to present fully and they may be connected. (The article has some names of people who prove optimalitry of some packings). I would not expect any complete description on these, but no word at all... that is too much to not have (or too little to have) in a good article. As to how some of the packings were found, I may suggest an item on which I've just written a wiki article Lubachevsky-Stillinger algorithm. This is certainly not the only one in existence, so go ahead and put a list of other techniques. But, as a matter of fact, I know that many of the optimal (proven or conjectured) packings, e.g., of 91 congruent circles in a circle, were found first with this very algorithm (and then confirmed with other algorithms, which is usually much easier, than to discover; some recent proof techniques are based on knowing the packing with high precision, so discovering the packing numerically becomes, essentially, a first step of the proof). See Curved Hexagonal Packings of Equal Disks in a Circle http://www.math.ucsd.edu/~ronspubs/95_02_dense_packings.pdf It was also fun to read a comment and its resolution above on packing more than 2n unit diam circles in 2 times n rectangles. That problem was one of many by Erdos. Does this article mention that name? Yes, but not emphatically enough for a math genius of the 20th century. (Remember notability requirement of wiki). The mentioned above algorithm produces the required packings (for some smaller n of course). If I remember it correctly, for n=1000 you can exceed 2n by 7.

Lsalgo (talk) 04:18, 23 May 2011 (UTC)

Finite uniform 3D sphere packing
There does not seem to be any discussion of uniform 3D sphere packing on the English Wikipedia; as "sited" here it is only discussed on the German Wikipedia here, even though there is an English summary of research as of 1999 by Conway and Sloane here. Mark Hurd (talk) 07:54, 28 August 2012 (UTC)


 * Sphere packing? Close-packing of equal spheres? —Tamfang (talk) 08:01, 28 August 2012 (UTC)
 * Yeah "not ... any" is a little strong. Specifically nothing seems to mention the "sausage collapse" after 55 spheres. Mark Hurd (talk) 13:00, 28 August 2012 (UTC)

unequal-sphere dimmers
What is unequal-sphere dimmer? Where I can read about it? Jumpow (talk) 13:11, 8 June 2016 (UTC)

May be it is misspelling and must be dimer? Jumpow (talk) 14:45, 8 June 2016 (UTC)

Again, what means woodpulp stowage in context of packing of a single rectangle? Woodpulp refers to article Pulp (paper): Pulp is a lignocellulosic fibrous material prepared by chemically or mechanically separating cellulose fibres from wood, fiber crops or waste paper. Jumpow (talk) 16:31, 8 June 2016 (UTC)

What means pack one of each n-omino into a rectangle? Pack set of n-omino into a single rectangle (each only ones)? Into given single rectangle? Into minimal single rectangle? Not all n-omino? Jumpow (talk) 17:12, 8 June 2016 (UTC)

Is the puzzle template appropriate?
The first line of the article reads

"Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers."

Given the technical nature of the article, is it appropriate to have a template with links such as Optical illusion and Thinking outside the box?

104.228.101.152 (talk) 05:04, 16 March 2017 (UTC)

Untitled
O(a7/11) is not consistent with Wikipedia's other pages. It changed several decades ago. Thanks Paul Erdös — Preceding unsigned comment added by 1.136.109.183 (talk) 09:22, 20 October 2021 (UTC)