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Multi-Level Regular Coverings of the Plane by Disks

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We study the problem of finding the least dense regular covering of a plane by disks of different radii. We introduce k-level regular coverings that generalize some known models. We obtain a bound for the density of multi-level coverings and construct a three-level covering of density ≈ 1.083. Bibliography: 14 titles. Illustrations: 11 figures.

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References

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Authors and Affiliations

  1. Novosibirsk State University, 2, ul. Pirogova, Novosibirsk, 630090, Russia

    I. I. Takhonov

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  1. I. I. Takhonov
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Correspondence to I. I. Takhonov.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 1, 2014, pp. 112-128.

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Takhonov, I.I. Multi-Level Regular Coverings of the Plane by Disks. J Math Sci 211, 886–901 (2015). https://doi.org/10.1007/s10958-015-2642-8

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