Geodesic
A Note on Sets of Constant Width
Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 289 
Siniša Vrećica. A Note on Sets of Constant Width. Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 289 . http://geodesic.mathdoc.fr/item/PIM_1981_N_S_29_43_a31/
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     title = {A {Note} on {Sets} of {Constant} {Width}},
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We prove here that each convex set in Euclidean space can be extended to a set of constant width having the same diameter and being contained in same Jung's ball. We also prove a characterization of the sets of constant width, which gives the answer to a problem of F. A. Valentine.