Talk:Kawasaki's theorem

DYK
There were 10.3 thousand = 4.7 + 5.6 thousand viewers for this DYK, in the two days in which this article appeared (in different time zones). Kiefer .Wolfowitz 23:21, 26 April 2011 (UTC)
 * Thanks, but where did you get these numbers? When I try it I get 4.7k + 5.6k. Still, well over the threshold of 5k for listing in WP:DYKSTATS. —David Eppstein (talk) 23:39, 26 April 2011 (UTC)
 * I added this DYK to WP:DYKSTATS. (I corrected my error. My long-term memory is better ....) Kiefer .Wolfowitz 17:58, 27 April 2011 (UTC)
 * Unfortunately this is not eligible for WP:DYKSTATS. It was on the Main page on April 22, from 18:00 to midnight (UTC). It wasn't on the Main page on April 23, so the additional 5.6k hits don't count (see rule 1). Sorry. —Bruce1eetalk 05:20, 28 April 2011 (UTC)
 * Bruce, I don't understand your comment. Rule 1 states that both days count, if the article appeared over two days (because of different time zones): The "two-day period after the article's DYK appearance if the article was featured on the next day as well".
 * I couldn't check the queuing information, now, to specify the exact incidence of its main-page appearance. Thanks, Kiefer .Wolfowitz 09:17, 29 April 2011 (UTC)
 * The article appeared on the Main page here on April 22 at 18:00 (UTC) until here on April 23 at 00:00 (UTC). It might have also featured on April 23 in other time zones, but the times used here are UTC. Rule 1 says the page views from the next day can be added "if the article was featured on the next day as well", which it wasn't – it was only on the Main page on April 22. I hope I've explained this properly. —Bruce1eetalk 09:57, 29 April 2011 (UTC)
 * Hi David & Kiefer, there has been an update of the DYKSTATS rules that point out that hooks exiting the Main page around 00:00 UTC get extra DYK views the next day (see DYKSTATS rule 1). What this means is that I got it wrong, and that the next day's views for Kawasaki's theorem should have been counted as stated above. I've added the 10.3k views to DYKSTATS/Archive 2011#April 2011. I'm sorry I messed you guys around, but I wasn't aware of this at the time. —Bruce1eetalk 15:07, 26 May 2011 (UTC)

proof against global flat-foldability
"Tom Hull (1994) conjectured that global flat-foldability could be tested by checking Kawasaki's theorem at each vertex of a crease pattern, and then also testing bipartiteness of an undirected graph associated with the crease pattern, but this conjecture was disproven by Bern & Hayes (1996), who showed that the problem of testing global flat-foldability is NP-complete."

The conjecture is not disproven through the fact that the problem is NP-complete. As the P=NP-Problem is not yet solved, it might be that all NP-problems are solvable in polynomial time. --Mathmensch (talk) 15:40, 25 May 2013 (UTC)
 * The conjecture was disproved, *and* they showed that it was NP-complete. In any case NP-completeness makes simple polynomial-time characterizations such as the conjectured one highly unlikely.—David Eppstein (talk) 15:46, 25 May 2013 (UTC)
 * That bit was about checking the flat-foldability of any particular crease pattern, he conjectured passing those two simple tests would ensure it but that's not true, it is a lot more complicated. You can make a crease pattern the flat foldability of which is equivalent to solving a particular logic problem that is NP-complete. Dmcq (talk) 16:21, 25 May 2013 (UTC)

Total confusion
Nothing can be undesrtood from this page. All the material was mixed up so badly that one is not sure if this is the asked page. What is the Kawasaki theorem? Where exactly is the body of it? Is it about angles or folding valleys and mountains, or maybe about all. Put this together and let away the history. — Preceding unsigned comment added by 79.113.124.72 (talk) 19:35, 3 November 2016 (UTC)
 * Your English is (perhaps ironically) ungrammatical and difficult to understand. In any case, the theorem is the one found in the section "Statement of the theorem", in the sentence that begins "Then Kawasaki's theorem is the statement that...". —David Eppstein (talk) 20:13, 3 November 2016 (UTC)

External links modified
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 * Added archive https://web.archive.org/web/20071012093200/http://kahuna.merrimack.edu/~thull/papers/origamimath.pdf to http://kahuna.merrimack.edu/~thull/papers/origamimath.pdf
 * Added archive https://web.archive.org/web/20071012093106/http://kahuna.merrimack.edu/~thull/papers/countingfolds.pdf to http://kahuna.merrimack.edu/~thull/papers/countingfolds.pdf

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