Talk:Paper bag problem

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Votes for deletion This article was the subject of a previous vote for deletion.
An archived record of the discussion can be found here.

There's a good article to be written about paper bags (think recycling, paper engineering, drinking in public in the U.S., paper vs. plastic bags, TetraPaks, etc. etc.) This isn't it.

This is a very poor article, which goes into great mathematical detail (without justification or proof) about unreal "paper bag problem" model situations involving "idealized" paper bags that are shaped like envelopes.

Real paper bags (for example, the one in the picture that illustrates the article) have folded, glued bases designed to give them a flat base to avoid exactly the problems cited in the article, by allowing them to take on a roughly cuboid shape when unfolded.

Can we have an article about real paper bags here, and write a new article about the "paper bag problem" elsewhere? -- The Anome 15:25, Jun 21, 2005 (UTC)


re the comment above... "This is a very poor article, which goes into great mathematical detail (without justification or proof) about unreal "paper bag problem" model situations involving "idealized" paper bags that are shaped like envelopes."

It may be true that paper bags used in some regions are pleated. Here in the UK simple flat paper bags as described in the article are still very much available. This cannot be used as a reason for deleting the article. I cannot comment about the maths.

I have removed the "formulae from nowhere", and trimmed the article right down, whilst adding more extlinks to the other statement of the problem as the "teabag problem". This leaves the paper bag link available for discussion of real paper bags. -- The Anome 16:06, Jun 21, 2005 (UTC)

[edit] Mathematical constant

This actually seems like an interesting problem to me; however, I'm not sure how to formalise is to it becomes understandable to mathematicians with little knowledge of real paper bags :-)

It seems to me that the "paper" case can be formalised by choosing a simplicial structure on the unit square (not, of course, the most trivial one), and choosing a simplicial map that's locally an isometry and embeds that square into three-dimensional space. While that doesn't cover all possibilities, we should be able to approximate them. The volume of the convex hull of that embedding is half the volume of the paper cushion.

However, my intuition seems to claim that if I choose a decomposition of the unit square into smaller squares, I'm not going to get a nonzero volume by perturbing the map. Maybe the simplicial idea doesn't work at all?

I'm also not sure what's preventing us from just approximating a sphere, which would have larger volume than stated in the article as an upper bound. Do we require that some edge remains square?

Once those issues have been fixed, I believe this should be included as a mathematical constant - it nicely demonstrates that even for geometric constants, only rough bounds may be known.

RandomP 13:16, 18 June 2006 (UTC)