Talk:Paper bag problem

message: 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)
thread_title:  Mathematical constant 

message: "The problem is made even more difficult by assuming that the bag is made out of a material like paper or PET film which can neither stretch nor shear." Surely this makes the problem easier as it abstracts away from the properties of the material of which the bag is made? It would be much more difficult to have to take into account when the bag would burst or tear.  —Preceding unsigned comment added by 86.139.109.135 (talk) 09:38, 7 December 2008 (UTC)
replies: text: Agree, it doesn't make the problem more difficult, plus it essentially repeats what was said in the first sentence ("material which can bend but not stretch"). Removed. GregorB (talk) 22:12, 22 September 2013 (UTC)
thread_title:  More difficult? 

message: Hello fellow Wikipedians,
I have just added archive links to  on Paper bag problem. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive https://web.archive.org/20050410213151/http://www.dse.nl:80/%7Eandreas/teabag.html to http://www.dse.nl/~andreas/teabag.html
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Cheers.—cyberbot IITalk to my owner:Online 12:34, 13 February 2016 (UTC)
thread_title:  External links modified 

message: This article has a problem with verifiability. It appears to be entirely sourced on a single journal publication, which unfortunately I don't personally have access to. If somebody does indeed have access to this publication, it would be appreciated if this article could be improved with further explanations, proofs, etc. that would be expected to appear in a mathematical journal publication.
Furthermore, @David Eppstein, we appear to be at the impasse of an edit war. Can we have a discussion as to why you think this article shouldn't contain citation requests? Isn't the iterative edit improvement approach less objectionable than a full reversion?
I will say, that a full reversion is not appropriate, because I restored archive links in the reference section, prior to removing some of the seemingly unrelated references.
Let's work together.
JKVeganAbroad (talk) 20:57, 16 June 2023 (UTC)
thread_title:  Citation Problems