On a property of \(n\)-dimensional simplices (Q1957087)
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scientific article; zbMATH DE number 5791083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a property of \(n\)-dimensional simplices |
scientific article; zbMATH DE number 5791083 |
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On a property of \(n\)-dimensional simplices (English)
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24 September 2010
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The main result states that if an \(n\)-dimensional simplex \(S\subset \mathbb R^n\) contains a unit cube \([0,1]^n\) then, for some \(i=1,\dots, n\), the simplex \(S\) contains a line segment of length \(n\) parallel to the \(x_i\)-axis. Relationships with the linear interpolation of continuous functions of \(n\) variables are discussed [cf. \textit{M. Nevskii}, Model. Analiz Inform. Sistem 16, 24--43 (2009)].
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\(n\)-dimensional simplex
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polytope
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barycentric coordinates
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axial diameter
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interpolation projection operator
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Steiner symmetrization
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Hadamard number
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