Lower bound of length of triangle inscribed in a circle on non-Euclidean spaces (Q2911462)
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scientific article; zbMATH DE number 6074796
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower bound of length of triangle inscribed in a circle on non-Euclidean spaces |
scientific article; zbMATH DE number 6074796 |
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31 August 2012
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spherical geometry
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hyperbolic geometry
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covering ball
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minimum chord
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Lower bound of length of triangle inscribed in a circle on non-Euclidean spaces (English)
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\textit{J. E. Wetzel} proved that, if \(\Gamma\) is a closed curve of length \(L\) in \(E^n\), then \(\Gamma\) lies in some ball of radius \(L/4\) [Enseign. Math., II. Sér. 17, 275--277 (1971; Zbl 0223.52010)]. The authors extend Wetzel's result to the spherical and hyperbolic geometries. Namely, it is shown that a triangle inscribed in a circle on \(S^2\) (or on \(H^2\)) having a given point \(P\) in its interior has length at least twice the minimum chord through \(P\).
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0.7502428293228149
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0.7231557369232178
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0.7219712734222412
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0.7193688750267029
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