I wonder if there are any is at least one proof of any mathmatical fact that would use convex hull or convex envelope as mathmatical object valuable for that proof?
What proofs are based/use/depend on existance convex hull or convex envelope?
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convex-analysis
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1Also [Newton polygon](http://en.wikipedia.org/wiki/Newton_polygon), but the Wikpedia article does not do it justice. See also http://mathoverflow.net/questions/15703/newton-and-newton-polygon. – 2011-12-17