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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 580–593
DOI: https://doi.org/10.4213/mzm7698 (Mi mzm7698) 		 
This article is cited in 30 scientific papers (total in 30 papers)

On a Property of $n$-Dimensional Simplices

M. V. Nevskij

P. G. Demidov Yaroslavl State University
Full-text PDF (496 kB) Citations (30)
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DOI: https://doi.org/10.4213/mzm7698
Abstract: Suppose that $n\in\mathbb N$ and $S$ is a simplex in $\mathbb R^n$, containing the cube $[0,1]^n$. It is proved that, for some $i=1,\dots,n$, the simplex $S$ contains an interval of length $n$ parallel to the $i$th coordinate axis. The relationship with questions arising in linear interpolation of continuous functions of $n$ variables is noted.
Keywords: $n$-dimensional simplex, polytope, barycentric coordinates, axial diameter, interpolation projection operator, Steiner symmetrization, Hadamard number.
Received: 22.04.2009
Revised: 03.07.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 543–555
DOI: https://doi.org/10.1134/S0001434610030326
Bibliographic databases:
Document Type: Article
UDC: 517.51+514.17
Language: Russian
Citation: M. V. Nevskij, “On a Property of $n$-Dimensional Simplices”, Mat. Zametki, 87:4 (2010), 580–593; Math. Notes, 87:4 (2010), 543–555
Citation in format AMSBIB
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    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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