Technical Report CS0241

Title: On the Densest Packing of Circles in Convex Figures
Authors: Shlorno Moran
Abstract: Let the term "unit circle" mean a circle of radius 1. The main result of this paper is:

Theorem 1: Let C1,...,Cn be n>=2 disjoint unit circles in the plane and let B be the smallest convex figure containing them. Then the area of B is greater than n*sqrt(12). This generalizes a similar well known result, in which B is assumed tci Be a convex hexagon. It is also indicated how the proof of Theorem 1 can extended to prove that the area of the smallest convex figure B contain1ng n disjoint unit circles is n*sqrt(12)+Omega(sqrt(n)).

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