Abstract
The theorem of Steinhagen establishes a relation between inradius and width of a convex set. The half of the width can be interpreted as the minimum of inradii of all 1-dimensional orthogonal projections of a convex set. By considering i-dimensional projections we obtain series ofi-dimensional inradii. In this paper we study some relations between these inradii and by this we find a natural generalization of Steinhagen’s theorem.
Further we show in the course of our investigation that the minimal error of the triangle inequality for a set of vectors cannot be too large.
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Betke, U., Henk, M. A generalization of steinhagen’s theorem. Abh.Math.Semin.Univ.Hambg. 63, 165–176 (1993). https://doi.org/10.1007/BF02941340
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DOI: https://doi.org/10.1007/BF02941340