|
Zapiski Nauchnykh Seminarov POMI, 1999, Volume 261, Pages 198–203
(Mi znsl1098)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
On common sections with given properties for finite set of convex compacts
V. V. Makeev, A. S. Mukhin Saint-Petersburg State University
Abstract:
The general theorem below is proved.
Theorem. {\it Let $O$ be the interior point for $n-2$ convex compacts $K_1,\dots,K_{n-2}$ in $\mathbb R^n$. There exists such two-dimensional plane $H$, passing through the point $O$, that for $i\le n-2$ some affine image of the given centrally-summetric hexagon is inscribed in $K_i\cap H$ and has the center at point $O$. There exist such $n-3$ two-dimensional planes $H_1,\dots,H_{n-3}$, passing through the point $O$, and laying at the same time in three-dimensional plane, that for $i\le n-3$ some affine image of regular octagon us inscribed in $H_i\cap K_i$ and has the center at point $O$.}
Received: 28.06.1999
Citation:
V. V. Makeev, A. S. Mukhin, “On common sections with given properties for finite set of convex compacts”, Geometry and topology. Part 4, Zap. Nauchn. Sem. POMI, 261, POMI, St. Petersburg, 1999, 198–203; J. Math. Sci. (New York), 110:4 (2002), 2868–2871
Linking options:
https://www.mathnet.ru/eng/znsl1098 https://www.mathnet.ru/eng/znsl/v261/p198
|
Statistics & downloads: |
Abstract page: | 201 | Full-text PDF : | 46 |
|