Abstract
The paper deals with the problem of approximating point sets byn-point subsets with respect to the minimal widthw. Let, in particular, ℋd denote the family of all convex bodies in Euclideand-space, letA ⊂ ℋd and letn be an integer greater thand. Then we ask for the greatest number μ=Λ n (A) such that everyA εA contains a polytope withn vertices which has minimal width at least μw(A). We give bounds for Λ n (ℋd), for Λ n (ℳ2133;d), and for Λ n (W d), where ℳ2133;d,W d denote the families of centrally symmetric convex bodies and of bodies of constant width, respectively.
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Dedicated to Professor L. danzer on the occasion of his sixtieth birthday
Research for this paper was conducted in the academic year 1986/87 while both authors were visiting the University of Washington, Seattle. P. Gritzmann was supported by the Alexander von Humboldt Foundation.
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Gritzmann, P., Lassak, M. Estimates for the minimal width of polytopes inscribed in convex bodies. Discrete Comput Geom 4, 627–635 (1989). https://doi.org/10.1007/BF02187752
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DOI: https://doi.org/10.1007/BF02187752