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The Smallest Convex Cover for Triangles of Perimeter Two

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Abstract

We find the unique smallest convex region in the plane that contains a congruent copy of every triangle of perimeter two. It is the triangle ABC with AB=2/3, ∠ B=60°, and BC≈1.00285.

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Authors and Affiliations

  1. Mathematics Institute, Hungarian Academy of Sciences, POB 127, 1364, Budapest, Hungary

    Zoltan Füredi

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

    John E. Wetzel

Authors
  1. Zoltan Füredi
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  2. John E. Wetzel
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Füredi, Z., Wetzel, J.E. The Smallest Convex Cover for Triangles of Perimeter Two. Geometriae Dedicata 81, 285–293 (2000). https://doi.org/10.1023/A:1005298816467

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  • DOI: https://doi.org/10.1023/A:1005298816467

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