A generalization of Jung's theorem | Zendy

Martin Henk | Zendy

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A generalization of Jung's theorem

Author(s) -

Martin Henk

Publication year - 1992

Publication title -

geometriae dedicata

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.746

H-Index - 43

eISSN - 1572-9168

pISSN - 0046-5755

DOI - 10.1007/bf00147552

Subject(s) - mathematics , generalization , convex body , hyperbolic geometry , differential geometry , projective geometry , regular polygon , algebraic geometry , combinatorics , pure mathematics , mathematical analysis , geometry , convex hull

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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