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A generalization of Jung's theorem

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Abstract

Jung's theorem establishes a relation between circumradius and diameter of a convex body. Half of the diameter can be interpreted as the maximum of circumradii of all 1-dimensional sections or 1-dimensional orthogonal projections of a convex body. This point of view leads to two series of j-dimensional circumradii, defined via sections or projections. In this paper we study some relations between these circumradii and by this we find a natural generalization of Jung's theorem.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen, Germany

    M. Henk

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  1. M. Henk
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Additional information

I would like to thank Prof. Dr J. M. Wills, who called my attention to these generalized circumradii.

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Henk, M. A generalization of Jung's theorem. Geom Dedicata 42, 235–240 (1992). https://doi.org/10.1007/BF00147552

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  • DOI: https://doi.org/10.1007/BF00147552

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