Talk:Moving sofa problem

Sofa Pop-Sci
Would it be appropriate to link to Dan Romik's Numberphile video where he explains the old Hammersley sofa, Gerver's sofa and his own ambidextrous sofa?

Existence of the sofa
Is it proven that the greatest sofa possessing the described properties exists? Suppose one proves that no such sofa has an area bigger than A and on the other hand one finds a sequence of sofa's with increasing area where the areas converge to A. Then it is proven that no largest sofa of this type exists. — Preceding unsigned comment added by 62.235.146.47 (talk) 11:39, 13 August 2012 (UTC)

In this link http://www.math.ucdavis.edu/~suh/gerver-moving_sofa.pdf, the author mentions that the existence of the sofa has indeed been proven. Being no specialist, I'll leave further research on this issue to someone else. (Notice however that uniqueness of the sofa seems to be an open problem too) — Preceding unsigned comment added by 193.190.253.144 (talk) 11:15, 21 August 2012 (UTC)

Douglas Adams
it's necessary to insert a reference to Dirk Gently !


 * Again a great graphics addition. Thanks Rocchini! Don't understand your last remark (Dirk Gently). JocK 17:21, 15 June 2007 (UTC)


 * Aha... this link was more informative about the connection between Dirk Gently and the problem of moving sofas. Indeed deserves a link from the article! ;) JocK 22:43, 4 August 2007 (UTC)

Other languages
I added a reasonable interpretation of your nice page in Russian. http://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D0%B8_%D0%B4%D0%B8%D0%B2%D0%B0%D0%BD%D0%B0

Bounds
Also, I may suggest the (rather trivial) upper limit of the 'sofa constant' by 2√2 (2.828427124...) to be included. —The preceding unsigned comment was added by Special:Contributions/ (talk)
 * I don't see a reason for that being a trivial upper limit, unless you assume convexity; it does not need to be contained in a box of length 2√2 (indeed, the Hammersley sofa is longer than that). Still, I agree that the article should mention at least a trivial upper bound, and ideally the best known upper bound (with reference).  76.201.140.116 (talk) 22:19, 7 August 2008 (UTC)

Users PrimeHunter, 146.151.84.226, and David Eppstein disagree on the meanings of Upper and Lower bounds. I am rewording the section to say that the upper bound is that of the shape that has the largest area that can still fit through the corner, as seems to be the consensus other than user 146.151.84.226. ETSkinner (talk) 13:59, 15 March 2016 (UTC)

Variants
Judging from a peek at Guy's book, even the restriction to convex sofas is an unsolved problem; I find this surprising. If true, then it might be worth mentioning this variant of the problem, along with known bounds. Joule36e5 (talk) 21:59, 21 August 2008 (UTC)