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Lower Bound for Convex Hull Area and Universal Cover Problems

Published 28 Jan 2011 in math.MG | (1101.5638v1)

Abstract: In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.

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