The Erdős-szekeres Theorem: a Geometric Application of Ramsey’s Theorem
نویسنده
چکیده
In this paper, we examine Ramsey’s theorem, originally a combinatorial result, and use it to prove a result of a geometric nature, the ErdősSzekeres theorem on convex polygons: given any positive integer k, it is possible to find a least positive integer, ES(k), such that any set of at least ES(k) points is guaranteed to contain the vertex set of a convex k-gon. We generalize the problem to higher dimensions and examine a better upper bound on the the Erdős-Szekeres numbers ES(k).
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