A characterization of sets of constant width
โ Scribed by P. R. Goodey; M. M. Woodcock
- Publisher
- Springer
- Year
- 1978
- Tongue
- English
- Weight
- 425 KB
- Volume
- 238
- Category
- Article
- ISSN
- 0025-5831
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๐ SIMILAR VOLUMES
In this paper we prove the following result: THEOREM. Let K be a planar set of constant width 6; if {Bt, B2, B3} is a cover of K, in which the diameters d (Bi), where i = 1, 2, 3, are smaller than ~, then d(nl The proof is an immediate consequence of the three lemmas of Section 2. 1. NOTATION
A convex plate D c R 2 of diameter 1 is of constant width 1 if and only if any two perpendicular intersecting chords have total length => 1. . Let D c R", n > 2, be a convex body of diameter 1. We say that D has the property (P) if any n mutually perpendicular chords, having a common point, have to
We prove that the Euclidean ball is the unique convex body with the properly that all its sections through a fixed point are convex bodies of constant width. Furthermore, we characterize those convex bodies which are sections of convex bodies of constant width. ## 1. INTRODUCTION AND NOTATION The