|
Zapiski Nauchnykh Seminarov POMI, 1995, Volume 231, Pages 286–298
(Mi znsl3757)
|
|
|
|
This article is cited in 15 scientific papers (total in 15 papers)
Topological methods in geometry
Affine-inscribed and affine-circumscribed polygons and polytopes
V. V. Makeev Saint-Petersburg State University
Abstract:
Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point $O$ of a convex compact set in $\mathbb R^3$, there exists a two-dimensional section through $O$ circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in $\mathbb R^3$ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram $P$ and contained in a cylinder with directrix $P$. Bibl. 29 titles.
Received: 17.04.1995
Citation:
V. V. Makeev, “Affine-inscribed and affine-circumscribed polygons and polytopes”, Investigations in topology. Part 8, Zap. Nauchn. Sem. POMI, 231, POMI, St. Petersburg, 1995, 286–298; J. Math. Sci. (New York), 91:6 (1998), 3518–3525
Linking options:
https://www.mathnet.ru/eng/znsl3757 https://www.mathnet.ru/eng/znsl/v231/p286
|
Statistics & downloads: |
Abstract page: | 275 | Full-text PDF : | 127 |
|