Talk:Lazy caterer's sequence

I don't know if "lazy caterer's sequence" is the best name for this article. It is the second name given in the OEIS, the first being "central polygonal numbers." Anton Mravcek 21:43, 14 Jun 2005 (UTC)


 * The only thing I have against the term "central polygonal number" is that is could easily be confused with centered number. PrimeFan 23:11, 14 Jun 2005 (UTC)


 * I never heard of "lazy cater's sequence" until now, despite working with various sequences. That name sounds unprofessional to me.  I guess that, historically, the name must be "central polygonal numbers", with "lazy cater's sequence" a catchy pop name made up later.  If so, I'd prefer to rename the article; except that I don't think it's important enough to bother with!  (I did make a link from "central polygonal numbers".)  Zaslav 04:27, 8 November 2007 (UTC)


 * Kimberling and Brown J. Int. Seq. 2004 do use the "lazy caterer" name. In general, I prefer a little whimsy in the nomenclature to the stuffy insistance that everything must be professional and serious, but I don't feel strongly about it in this case. —David Eppstein 04:38, 8 November 2007 (UTC)
 * Per WP:NAME, "Names of Wikipedia articles should be optimized for readers over editors; and for a general audience over specialists." Given a choice between an established popular name and a more professional one, I'd go for the popular name in the title. I'm moving mention of central polygonal number to the article lede, however.--agr 12:16, 8 November 2007 (UTC)

Importance
I'm dropping the rating to "mid" again. The evidence cited by Anton Mravcek (that OEIS calls it "core" and "nice") is enough to give it high importance within its own category of integer sequences, but that's not the same as its importance in mathematics more generally. Compared to most of the other "high" articles listed at WikiProject Mathematics/Wikipedia 1.0/Basics (where it is listed now) or at WikiProject Mathematics/Wikipedia 1.0/Number_theory (where it could plausibly be relisted) I think it just doesn't fit. I'm leaving the field alone for now, since the article's in the fuzzy area between number theory and geometry, but I wouldn't object if someone else thinks that should be changed. —David Eppstein 06:45, 28 May 2007 (UTC)


 * I'm dropping this further to low-priority. It is a nice sequence, but it is related straightforwardly to another more basic sequence. Geometry guy 20:55, 10 June 2007 (UTC)
 * I agree with the mid importance rating. Note that there is some consensus to take context into account when assessing importance, but even in the context of Integer sequences, this article is not as important as triangle number. Geometry guy 10:45, 28 May 2007 (UTC)


 * I guess I overcompensated. Yes, triangular numbers are more important: they turn up in all sorts of places, including the computation of these central polygonal numbers. Anton Mravcek 22:11, 29 May 2007 (UTC)

Just because people forgot to look in the box here doesn't mean it's any less important. The concensus here is for "mid," with only Anton advocating "high" and only Geometry guy advocating "low." Everyone else agrees this is "mid" (and if you don't and I haven't already mentioned you, speak up). Concepts like this are far more important to a general encyclopedia than mathematical masturbations like impossible topologies. Knodeltheory (talk) 22:11, 31 March 2008 (UTC)

Much easier proof
Make n straight cuts in a disk, none of them horizontal, no three cuts through a single point, and no cut through the bottom point of the disk. Each piece is convex, hence has a unique bottom point. This bottom point is either the meeting point of two out of the n+1 curves from the set (n cuts + the circle bounding the disk), or is the bottom point of the circle, and each two curves that cross form the bottom point of exactly one piece. Therefore, the maximum number of pieces occurs when all curves cross each other; there are (n + 1 choose 2) meeting points of two curves and one bottom point of the circle so there are (n + 1 choose 2) + 1 pieces.

If this proof can be sourced, I think it would be an improvement on the one in the article because it gives an explanation for why the formula is what it is rather than being just another boring induction proof.

By the way, there was a typo in the formula in the article for a long time: it said, incorrectly, that the number of pieces was (n + 2 choose 2) + 1. I just fixed it. —David Eppstein (talk) 22:42, 31 March 2008 (UTC)

A mistake
Notice that the formula is no more than an estimate for the number of parts. Prove that for any n, this estimate can be reached. — Preceding unsigned comment added by 160.114.140.17 (talk) 11:02, 1 April 2013 (UTC)
 * The proof is there since at least 9 November 2007: https://en.wikipedia.org/w/index.php?title=Lazy_caterer%27s_sequence&oldid=170243715#Proof --CiaPan (talk) 22:04, 27 January 2016 (UTC)

There's another mistake. The graphic showing the circles maximum cuts for n = 1 through 6 has f(n) = 23. But f(n) = 22. — Preceding unsigned comment added by 24.205.95.195 (talk) 08:39, 24 February 2015 (UTC)
 * Commons:User:AnonMoos fixed f(6) value in this upload on  19 January 2016. --CiaPan (talk) 21:54, 27 January 2016 (UTC)