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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 329, Pages 92–106
(Mi znsl299)
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This article is cited in 8 scientific papers (total in 8 papers)
Theorems on equipartition of a continuous mass distribution
V. V. Makeev Saint-Petersburg State University
Abstract:
Here are three samples of results.
Let $\mathbf m$ be a finite continuous mass distribution (an FCMD) in $\mathbb R^2$, and let $\ell=\{\ell_1,\dots,\ell_5\subset\mathbb R^2\}$ be 5 rays with common endpoint such that
the sum of any two adjacent angles between them is at most $\pi$. Then $\mathbf m$ can be sibdivided into 5 parts at any prescribed ratio by an affine image of $\ell$.
For each FCMD $\mathbf m$ in $\mathbb R^n$ there exist $n$ mutually orthogonal hyperplanes
any two of which subdivide $\mathbf m$ into 4 equal parts.
For any two FCMD's $\mathbf m_1$ and $\mathbf m_2$ in $\mathbb R^n$
with common center of symmetry $O$ there exist $n$ hyperplanes through $O$
any two of which subdivide both $\mathbf m_1$ and $\mathbf m_2$ into 4 equal parts.
Received: 01.03.2005
Citation:
V. V. Makeev, “Theorems on equipartition of a continuous mass distribution”, Geometry and topology. Part 9, Zap. Nauchn. Sem. POMI, 329, POMI, St. Petersburg, 2005, 92–106; J. Math. Sci. (N. Y.), 140:4 (2007), 551–557
Linking options:
https://www.mathnet.ru/eng/znsl299 https://www.mathnet.ru/eng/znsl/v329/p92
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