Abstract
We prove that the Euclidean ball is the unique convex body with the property that all its sections through a fixed point are convex bodies of constant width. Furthermore, we characterize those convex bodies which are sections of convex bodies of constant width.
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Chakerian, G. D. and Groemer, H., ‘Convex bodies of constant width’, in Convexity and its Application (ed. Gruber and Wills), Birkhauser, Basel, 1983, pp. 49–96.
Süss, W., ‘Eine charakteristische Eigenschaft der Kugel’, Jahresber. Deutsch. Math.-Verein. 34 (1926), 245–247.
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Research supported by the Alexander von Humboldt-Foundation.
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Montejano, L. A characterization of the Euclidean ball in terms of concurrent sections of constant width. Geom Dedicata 37, 307–316 (1991). https://doi.org/10.1007/BF00181407
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DOI: https://doi.org/10.1007/BF00181407