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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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    Also [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

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