
Journal of Convex Analysis 19 (2012), No. 3, 865874 Copyright Heldermann Verlag 2012 Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane Marek Lassak Institute of Mathematics and Physics, University of Technology and Life Sciences, al. Kaliskiego 7, Bydgoszcz 85789, Poland lassak@utp.edu.pl We prove that for every ε > 0 and for every convex body of constant width in a normed plane there exists a convex body of the same constant width whose boundary consists only of arcs of circles in the sense of the norm such that the Hausdorff distance between the two bodies is at most ε. This generalizes the Euclidean case proved by Blaschke. We also present a more general theorem about approximation of reduced bodies. Keywords: Reduced convex body, body of constant width, normed plane, Hausdorff distance, approximation. MSC: 52A10, 52A21, 52A27, 46B25 [ Fulltextpdf (121 KB)] for subscribers only. 