Einschliessung ebener Kurven (Q1064544)
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scientific article; zbMATH DE number 3919211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Einschliessung ebener Kurven |
scientific article; zbMATH DE number 3919211 |
Statements
Einschliessung ebener Kurven (English)
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1985
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A curve in the Euclidean plane is said to enclose a set K if K lies in the convex hull of the curve. In the note the set K is taken to be a closed rectifiable curve of length L(K). The infimum \(L^*(K)\) of the lengths of all curves which enclose such K is shown to satisfy the inequality \(L^*(K)\leq (1/2\pi)(2+\pi)L(K).\) The equality holds if and only if K is a circle.
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length of curves
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convex hull of a curve
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curve in the Euclidean plane
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closed rectifiable curve
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circle
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