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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Bibliographic Details
Published in:Periodica mathematica Hungarica 2011-09, Vol.63 (1), p.1-17
Main Authors: Füredi, Zoltán, Wetzel, John E.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-011-7001-z