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Combinatoral Geometry

Source: 2016 Korea Winter Camp 1st Test #8

January 25, 2016
geometryKorea

Problem Statement

There are nn lattice points in a general position. (no three points are collinear) A convex polygon PP covers the said nn points. (the borders are included) Prove that, for large enough nn and a positive real ϵ\epsilon, the perimeter of PP is no less than (2+ϵ)n(\sqrt{2}+\epsilon)n.
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