Inscribed and circumscribed polyhedra for a convex body and continuous functions on a sphere in Euclidean space
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V. V. Makeev
Translated by: B. M. Bekker - St. Petersburg Math. J. 18 (2007), 997-1009
- DOI: https://doi.org/10.1090/S1061-0022-07-00979-X
- Published electronically: October 2, 2007
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Abstract:
Two related problems concerning continuous functions on a sphere $S^{n-1}\subset {\mathbb {R}}^n$ are studied, together with the problem of finding a family of polyhedra in ${\mathbb {R}}^n$ one of which is inscribed in (respectively, circumscribed about) a given smooth convex body in ${\mathbb {R}}^n$. In particular, it is proved that, in every convex body $K\subset {\mathbb {R}}^3$, one can inscribe an eight-vertex polyhedron obtained by “equiaugmentation” of a similarity image of any given tetrahedron of class $T$.References
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Bibliographic Information
- V. V. Makeev
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospect 28, Staryĭ Peterhof, St. Petersburg 198904, Russia
- Email: mvv57@inbox.ru
- Received by editor(s): May 20, 2005
- Published electronically: October 2, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 997-1009
- MSC (2000): Primary 52A10, 52A15
- DOI: https://doi.org/10.1090/S1061-0022-07-00979-X
- MathSciNet review: 2307358