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Can we prove or disprove this?

For a sufficiently large $n$, every set of at least $ n$ points in the plane with no three collinear has a subset that form the vertices of a convex $2012$-gon.

Gerry mentions the Happy Ending theorem but I don't see how it relates. If someone could show me the steps in the proof or disproof, that would be nice.

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1 Answer 1

up vote 1 down vote accepted

This follows from the theorem of Erdos and Szekeres (sometimes known as "The Happy Ending Theorem").

The statement of the theorem, with some discussion, is here. There is also a link there to the original paper.

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Could you show how? –  Xuan Huang Jul 11 '12 at 7:05
    
Are you familiar with the theorem? Have you tried to find it and read it and see what it says? –  Gerry Myerson Jul 11 '12 at 7:28
    
Yes, but I don't quite see how it relates. –  Xuan Huang Jul 12 '12 at 2:08
1  
Quoting from the paper: "Can we find for a given $n$ a number $N(n)$ such that from any set containing at least $N$ points it is possible to select $n$ points forming a convex polygon? There are two particular questions: (1) does the number $N$ exist? (2) If so, how is the least $N(n)$ determined? We give two proofs that the first question is to be answered in the affirmative. Both of them will give definite values for $N(n)$." How can you read that, and still ask how it relates to your question? It is your question! –  Gerry Myerson Jul 12 '12 at 7:18

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