Covers for closed curves of length two

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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Published in:Periodica mathematica Hungarica 2011-09, Vol.63 (1), p.1-17
Main Authors: Füredi, Zoltán, Wetzel, John E.
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Language:English
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Mathematics
Mathematics and Statistics
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description 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.
doi_str_mv 10.1007/s10998-011-7001-z
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title Covers for closed curves of length two
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