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?
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1Gauss-Lucas? – J. M. ain't a mathematician Dec 17 '11 at 16:40
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1Also Newton polygon, but the Wikpedia article does not do it justice. See also http://mathoverflow.net/questions/15703/newton-and-newton-polygon. – lhf Dec 17 '11 at 18:43