Talk:Happy Ending problem

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Mathematics rating:	B Class	Low Priority	Field: Discrete mathematics
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 21:42, 9 June 2007 (UTC)

[edit] General position

Brendan: is it really necessary to say no two points coincident, in the general position footnote? I'd think that would be covered by calling them a set. —David Eppstein 16:21, 7 October 2006 (UTC)

It's not mathematically necessary, and in fact it is also covered by "no three points are collinear". So it can be removed. On the other hand, this article is aimed at general readers, who might find some redundancy helpful. I'm happy either way. McKay 04:41, 15 November 2006 (UTC)

[edit] Name

Why is it named the 'happy ending' problem? Thanks! - Fasrad 04:03, 15 November 2006 (UTC)

See the first sentence of the article. McKay 04:36, 15 November 2006 (UTC)

Thanks! I need to stop reading Wikipedia late at night. Fasrad 19:57, 19 January 2007 (UTC)

My recollection is that the HEP is the general statement, that is, for every n there is an f(n) such that it is true that among f(n) points some n form a convex polygon (and not the special case f(4)=5 proved by Ms Klein). Kope 16:24, 16 June 2007 (UTC)

[edit] Another reference

In hopes of convincing Tompw (talk · contribs) that the importance is more than low, here's an application of closely related ideas to an important open problem in algorithms: arXiv:cs.CG/0610092. But I'm not going to do more than mention this here for fear of violating WP:OR. —David Eppstein 19:10, 4 January 2007 (UTC)

Updated citation: Eppstein, D. (2007). "Happy endings for flip graphs". 23rd Annual Symposium on Computational Geometry, Gyeongju, South Korea: 92–101. doi:10.1145/1247069.1247084. arXiv:cs.CG/0610092.  So no longer any danger of being original research, but I'll let someone else mention it in the article here or not as they see fit as I think adding it myself would be too much of a conflict of interest. I've added self-refs to other articles, but only when they're more central to the topic; this one isn't so much about the happy ending problem itself as an application of related ideas to a different problem. It does, though, include a more efficient new algorithm for finding empty pentagons when they exist. —David Eppstein 16:58, 16 June 2007 (UTC)