Schranken für längste Tetraederkanten. (Estimates for the longest edges of tetrahedra) (Q1093910)
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scientific article; zbMATH DE number 4024178
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Schranken für längste Tetraederkanten. (Estimates for the longest edges of tetrahedra) |
scientific article; zbMATH DE number 4024178 |
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Schranken für längste Tetraederkanten. (Estimates for the longest edges of tetrahedra) (English)
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1987
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The author proves the following sharp inequalities for the volume V, the surface area S and the diameter D \((= longest\) edge) of a tetrahedron: \[ 6\sqrt{6} V/S \leq D < S^ 2/9\sqrt{3} V. \] A general inequality for V, S, and D for arbitrary convex bodies conjectured by Rieger was recently proved by \textit{P. Gritzmann}, the reviewer and \textit{D. Wrase} in J. Reine Angew. Math. 379, 22-30 (1987; Zbl 0611.52009).
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isoperimetric problems
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inequalities
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volume
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surface area
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diameter
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tetrahedron
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0.8024238348007202
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0.7693486213684082
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0.7658807039260864
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0.7655014991760254
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