On one extremal problem on the Euclidean plane (Q2746892)
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scientific article; zbMATH DE number 1656825
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On one extremal problem on the Euclidean plane |
scientific article; zbMATH DE number 1656825 |
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11 October 2001
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overlapping congruent convex bodies
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isoperimetric inequality
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0.9999998
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On one extremal problem on the Euclidean plane (English)
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In the book [\textit{H. T. Croft}, \textit{K. J. Falconer}, and \textit{R. K. Guy}, Unsolved problems in geometry, Springer-Verlag, New York, etc. (1991; Zbl 0748.52001)], we can find the following problem initially posed by J. W. Fickett: ``Let \(C\) and \(C'\) be the perimeters of overlapping congruent rectangles \(K\) and \(K'\). Is it true that for any relative positions \(1/3 \leq \text{length} (C \cap K') / \text{length} (C' \cap K) \leq 3\)?''NEWLINENEWLINENEWLINEIn the article under review, the author gives an affirmative answer to this question.
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