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Licensed Unlicensed Requires Authentication Published by De Gruyter October 13, 2016

Optimal cover of a disk with three smaller congruent disks

  • Balázs Szalkai EMAIL logo
From the journal Advances in Geometry

Abstract

In 2008 R. Connelly asked how one should place n small disks of radius r to cover the largest possible area of a disk of radius R > r. More specifically, is there always an optimal configuration with n-fold rotational symmetry for small values of n? The answer is known to be positive for n = 2, negative for n = 5, and it has been conjectured to be positive for n = 3 and 4. In this paper, we present a systematic way to list all possible combinatorial structures of optimal configurations, and we prove that for n = 3 there is always an optimal configuration with rotational symmetry of order three.

MSC 2010: 05B40; 52C15

Communicated by: G. Korchmáros


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Received: 2013-10-14
Revised: 2015-4-1
Published Online: 2016-10-13
Published in Print: 2016-10-1

© 2016 by Walter de Gruyter Berlin/Boston

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