On the exact constant in the quantitative Steinitz theorem in the plane |
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Authors: | I Bárány A Heppes |
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Institution: | 1. Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary 2. Hungaria Computing Ltd, Dózsa Gy?rgy u. 150, 1134, Budapest, Hungary
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Abstract: | We determine the maximal value ofr with the following property. If the convex hull of a set inR
2 contains a unit circleB, then a subset of at most four points can be selected so that the convex hull of this subset contains the circle of radiusr concentric withB. That the result is sharp is shown by the example when the original set is the set of vertices of a regular pentagon circumscribed
aroundB.
Imre Bárány was partially supported by Hungarian National Science Foundation Grant Nos. 1907 and 1909. Aladár Heppes was partially
supported by Hungarian National Science Foundation Grant No. 2583. |
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Keywords: | |
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