Dido's problem in the plane for domains with fixed diameter (Q1345111)
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scientific article; zbMATH DE number 727300
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dido's problem in the plane for domains with fixed diameter |
scientific article; zbMATH DE number 727300 |
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Dido's problem in the plane for domains with fixed diameter (English)
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26 February 1995
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Let \(D\) be a compact connected domain in \(\mathbb R^ 2\) with diameter \(2a\) and area \(s\); \(a > 0\), \(s > 0\). The authors determine when \(D\) has minimum relative perimeter. In particular, \(D\) is a circular segment if \(0 < s < \pi a^ 2/2\), and \(D\) is defined by five circular arcs of \(\pi a^ 2/2 < s < \pi a^ 2\).
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Dido's problem
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minimum relative perimeter
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0.8233935832977295
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0.8162215352058411
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0.7810496687889099
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