Inradii of Simplices |
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| Authors: | U. Betke M. Henk L. Tsintsifa |
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| Affiliation: | Fachbereich Mathematik, Universit?t Siegen, H?lderlinstrasse 3, 57068 Siegen, Germany betke@mathematik.uni-siegen.d400.de, DE
Konrad-Zuse-Zentrum für Informationstechnik (ZIB) Berlin, Takustra? e 7, D-14195 Berlin, Germany ,henk@zib.de, DE
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| Abstract: | We study the following generalization of the inradius: For a convex body K in the d-dimensional Euclidean space and a linear k-plane L we define the inradius of K with respect to L by , where r(K;x+L) denotes the ordinary inradius of with respect to the affine plane x+L. We show how to determine for polytopes and use the result to estimate for the regular d-simplex T_r d . These estimates are optimal for all k in infinitely many dimensions and for certain k in the remaining dimensions. Received July 5, 1996, and in revised form August 8, 1996. |
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