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 Wikipedia: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 Wikipedia:Votes for deletion/KarlSchererRevisited1. Sjakkalle (Check!) 09:16, 27 July 2005 (UTC)[reply]

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)[reply]

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

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)[reply]

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)[reply]

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

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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

Every second one is closer together. Hard to explain without a picture, sorry. 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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

"Klarner's" theorem

The article says:

Klarner's theorem: An a × b rectangle can be packed with 1 × 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: Wagon, Stan (1987). "Fourteen Proofs of a Result About Tiling a Rectangle" (PDF). The American Mathematical Monthly. 94 (7): 601-617. Retrieved 6 Jan 2010. {{cite journal}}: Unknown parameter |month= ignored (help). 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".

(Weisstein, Eric W. "Klarner's Theorem". MathWorld.) 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)[reply]

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)[reply]

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)[reply]