Let Φ a three-dimensional body of constant width B. Then the geodesic diameter G of the surface of Φ is estimated via B from above and from below. It is proved that \( G \leqslant \frac{\pi }{2}B \), where an equality occurs and only if Φ is a body of revolution. Bibliography: 3 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Springer-Verlag, Berlin (1934).
Yu. D. Burago and V. A. Zalgaller, “Isoperimetric problem under restriction of the width of a region on a surface,” Trudy Matem. Inst. Steklov. LOMI, 76, 81–87 (1965).
E. Meissner, “Über Punktmengen konstanter Breite,” Wissensch. Naturforsch. Ges. Zürich, 56, 42–50 (1911).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 353, 2008, pp. 35–38.
Rights and permissions
About this article
Cite this article
Zalgaller, V.A. Geodesic diameter of bodies of constant width. J Math Sci 161, 373–374 (2009). https://doi.org/10.1007/s10958-009-9561-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-009-9561-5