Abstract
A convex bodyR of Euclideand-spaceE d is called reduced if there is no convex body properly contained inR of thickness equal to the thickness Δ(R) ofR. The paper presents basic properties of reduced bodies inE 2. Particularly, it is shown that the diameter of a reduced bodyR⊂E 2 is not greater than √2Δ(R), and that the perimeter is at most (2+½π)Δ(R). Both the estimates are the best possible.
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Lassak, M. Reduced convex bodies in the plane. Israel J. Math. 70, 365–379 (1990). https://doi.org/10.1007/BF02801470
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DOI: https://doi.org/10.1007/BF02801470