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Common Sections with Given Properties for a Finite Set of Convex Compacta

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Abstract

Let \(K_1,\ldots,K_{n-2} \subset \mathbb{R}^n\) be convex compacta and let O be their common interior point. It is proved that there exists a 2-plane H through O such that for i≤n−2 an affine image of a given centrally symmetric hexagon is inscribed in Ki⋂H and has center at O. Furthermore, there exist n−3 2-planes H1,...,Hn-3 through O lying at the same time in a 3-plane such that for i≤n−3 an affine image of a regular octagon is inscribed in Hi⋂Ki and has center at O. Bibliography: 9 titles.

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Authors and Affiliations

  1. St.Petersburg State University, Russia

    V. V. Makeev & A. S. Mukhin

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  1. V. V. Makeev
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  2. A. S. Mukhin
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Makeev, V.V., Mukhin, A.S. Common Sections with Given Properties for a Finite Set of Convex Compacta. Journal of Mathematical Sciences 110, 2868–2871 (2002). https://doi.org/10.1023/A:1015366732332

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