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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 353, Pages 116–125
(Mi znsl1635)
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This article is cited in 2 scientific papers (total in 2 papers)
Polygons inscribed in a closed curve and a three-dimensional convex body
V. V. Makeev Saint-Petersburg State University
Abstract:
Here are samples of results obtained in the paper. Let $\gamma$ be a centrally symmetric closed curve in $\mathbb R^n$ that does not contain its center of symmetry, $O$. Then $\gamma$ is circumscribed about a square (with center $O$), and about a rhombus (also with center $O$) whose vertices split $\gamma$
into parts of equal length. If $n$ is odd, then there is a centrally symmetric equilateral $2n$-link polyline inscribed in $\gamma$ and lying in a hyperplane. Let $K\subset\mathbb R^3$ be a convex body, $x\in(0;1)$. Then $K$ is circumscribed about an affine-regular pentagonal prism $P$ such that the ratio of the lateral edge $l$ of $P$ to the longest chord of $K$ parallel to $l$ is equal to $x$. Bibl. – 7 titles.
Received: 25.12.2005
Citation:
V. V. Makeev, “Polygons inscribed in a closed curve and a three-dimensional convex body”, Geometry and topology. Part 10, Zap. Nauchn. Sem. POMI, 353, POMI, St. Petersburg, 2008, 116–125; J. Math. Sci. (N. Y.), 161:3 (2009), 419–423
Linking options:
https://www.mathnet.ru/eng/znsl1635 https://www.mathnet.ru/eng/znsl/v353/p116
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Abstract page: | 222 | Full-text PDF : | 70 | References: | 45 |
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