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This article is cited in 2 scientific papers (total in 2 papers)
Research Papers
Inscribed and circumscribed polyhedra for a convex body and continuous functions on a sphere in Euclidean space
V. V. Makeev St. Petersburg State University, Department of Mathematics and Mechanics
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 $T$.
Received: 20.05.2005
Citation:
V. V. Makeev, “Inscribed and circumscribed polyhedra for a convex body and continuous functions on a sphere in Euclidean space”, Algebra i Analiz, 18:6 (2006), 187–204; St. Petersburg Math. J., 18:6 (2007), 997–1009
Linking options:
https://www.mathnet.ru/eng/aa97 https://www.mathnet.ru/eng/aa/v18/i6/p187
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Abstract page: | 1058 | Full-text PDF : | 352 | References: | 42 | First page: | 11 |
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