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Covers for closed curves of length two

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Abstract

The least area α 2 of a convex set in the plane large enough to contain a congruent copy of every closed curve of length two lies between 0.385 and 0.491, as has been known for more than 38 years. We improve these bounds by showing that 0.386 < α 2 < 0.449.

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Authors and Affiliations

  1. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O. Box 127, Hungary, H-1364

    Zoltán Füredi

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA

    Zoltán Füredi & John E. Wetzel

Authors
  1. Zoltán Füredi
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  2. John E. Wetzel
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Correspondence to Zoltán Füredi.

Additional information

Communicated by Imre Bárány

Research supported in part by the Hungarian NFSR under grants OTKA 69062 and 60427 and by the National Science Foundation under grant NSF DMS 09-01276 ARRA.

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Füredi, Z., Wetzel, J.E. Covers for closed curves of length two. Period Math Hung 63, 1–17 (2011). https://doi.org/10.1007/s10998-011-7001-z

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  • DOI: https://doi.org/10.1007/s10998-011-7001-z

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