On a question of Makai and Martini on bodies of~constant width (Q464818)
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scientific article; zbMATH DE number 6362520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a question of Makai and Martini on bodies of~constant width |
scientific article; zbMATH DE number 6362520 |
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On a question of Makai and Martini on bodies of~constant width (English)
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30 October 2014
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The author proves that, for any \(n\geq 3\), the following properties are not equivalent in case of a convex body \(B\subseteq \mathbb{R}^{n}\) with diameter \(1\): ``Any \(n\) mutually perpendicular non-degenerate chords with a common point have total length at least \(1\)'' and ``B is a body of constant width \(1\)''. The paper solves a problem formulated by \textit{E. Makai jun.} and \textit{H. Martini} [Geom. Dedicata 34, No. 2, 199--209 (1990; Zbl 0688.52002)].
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convex geometry
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bodies of constant width
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discrete geometry
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