The ratio of the perimeter and the area of unions of copies of a fixed set (Q633213)
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scientific article; zbMATH DE number 5872630
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The ratio of the perimeter and the area of unions of copies of a fixed set |
scientific article; zbMATH DE number 5872630 |
Statements
The ratio of the perimeter and the area of unions of copies of a fixed set (English)
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31 March 2011
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The author considers a problem posed by \textit{T. Keleti} [Acta Univ. Carol., Math. Phys. 39, No. 1--2, 111--118 (1998; Zbl 1016.28003)]. He showed that if we take a finite union of unit squares, the ratio of the perimeter and area of the resulting figure cannot be arbitrarily large, and asked whether or not \(4\) is a good upper bound. The author improves the known bound, and shows that it is slightly less than \(5.6\). Several interesting comments are provided, and generalizations of the above problem are discussed
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extremal problems in discrete geometry
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integral geometry
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inverse isoperimetric inequality
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0.9107372164726256
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0.8012204170227051
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0.7785133123397827
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0.696803092956543
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0.696803092956543
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