On a question of Makai and Martini on bodies of constant width

Original Paper


We aim to answer the following question from Makai Jr and Martini (1990): QuestionAre the following properties equivalent for a convex body\(B\)in\({\mathbb R}^n\)with diameter\(1\):

1. Any\(n\)mutually perpendicular non-degenerate chords, having a common point,have total length at least\(1\).

2.\(B\)is a body of constant width\(1\).


Convex geometry Bodies of constant width Discrete geometry 

Mathematics Subject Classification



  1. Alonso, J., Martini, H., Mustafaev, Z.: On orthogonal chords in normed planes. Rocky Mountain J. Math. 41, 23–35 (2011)MathSciNetCrossRefMATHGoogle Scholar
  2. Bonnesen, T., Fenchel, W.: Theorie der konvexen Körper, Ergebn. d. Math. u. ihrer Grenzgeb. Springer, Berlin (1934)CrossRefGoogle Scholar
  3. Makai Jr, E., Martini, H.: A new characterization of convex plates of constant width. Geometriae Dedicata 34, 199–209 (1990)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Managing Editors 2014

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyMoscowRussia

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