Some geometric properties of convex bodies. II
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V. V. Makeev
Translated by: N. Yu. Netsvetaev - St. Petersburg Math. J. 15 (2004), 867-874
- DOI: https://doi.org/10.1090/S1061-0022-04-00836-2
- Published electronically: November 16, 2004
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Abstract:
Topological means are used for the study of approximation of $2$-dimensional sections of a $3$-dimensional convex body by affine-regular pentagons and approximation of a centrally symmetric convex body by a prism. Also, the problem of estimating the relative surface area of the sphere in a normed $3$-space, the problem on universal covers for sets of unit diameter in Euclidean space, and some related questions are considered.References
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Bibliographic Information
- V. V. Makeev
- Affiliation: Universitetskiĭ Pr. 27, St. Petersburg 190000, Russia
- Received by editor(s): December 25, 2002
- Published electronically: November 16, 2004
- Additional Notes: The paper was revised by the author for the English edition.
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 867-874
- MSC (2000): Primary 52A10, 52A15
- DOI: https://doi.org/10.1090/S1061-0022-04-00836-2
- MathSciNet review: 2044632