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Simultaneous Packing and Covering in the Euclidean Plane

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Abstract.

 In this article we study the simultaneous packing and covering constants of two-dimensional centrally symmetric convex domains. Besides an identity result between translative case and lattice case and a general upper bound, exact values for some special domains are determined. Similar to Mahler and Reinhardt’s result about packing densities, we show that the simultaneous packing and covering constant of an octagon is larger than that of a circle.

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Authors and Affiliations

  1. Peking University, Beijing, People’s Republic of China, , , , , , CN

    Chuanming Zong

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  1. Chuanming Zong
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(Received 17 January 2001; in revised form 13 July 2001)

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Zong, C. Simultaneous Packing and Covering in the Euclidean Plane. Mh Math 134, 247–255 (2002). https://doi.org/10.1007/s605-002-8260-3

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  • DOI: https://doi.org/10.1007/s605-002-8260-3

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