Lower Bound for Convex Hull Area and Universal Cover Problems

Details Lower Bound for Convex Hull Area and Universal Cover Problems Lower Bound for Convex Hull Area and Universal Cover Problems

2011-01-28

arxiv.org/abs/1101.5638v1

Mathematics

Metric Geometry

12 pages, 9 figures

Scientific paper

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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