1Institut für Diskrete Mathematik und Geometrie Technische Universität Wien Wiedner Hauptstraße 8-10/104 1040 Wien, Austria 2Mathematisches Seminar Christian Albrechts Universität D-24098 Kiel, Germany 3Department of Mathematics Case Western Reserve University Cleveland, OH 44106, U.S.A. and Université de Lille 1 UFR de Mathématique 59655 Villeneuve d'Ascq, France
Studia Mathematica, Tome 173 (2006) no. 1, pp. 1-18
There is a constant $c$ such that for every $n\in\mathbb N$,
there is an $N_{n}$ so that for
every $N\geq N_{n}$ there is a polytope $P_{}$ in $\mathbb R^{n}$
with $N$ vertices and
$$
\mathop{\rm vol}\nolimits _{n}(B_{2}^{n}\mathbin{\triangle} P)
\leq c \mathop{\rm vol}\nolimits _{n}(B_{2}^{n})N^{-\frac{2}{n-1}}
$$
where $B_{2}^{n}$ denotes the Euclidean unit ball of dimension $n$.
Keywords:
there constant every mathbb there every geq there polytope mathbb vertices mathop vol nolimits mathbin triangle leq mathop vol nolimits frac n where denotes euclidean unit ball dimension
Affiliations des auteurs :
Monika Ludwig
1
;
Carsten Schütt
2
;
Elisabeth Werner
3
1
Institut für Diskrete Mathematik und Geometrie Technische Universität Wien Wiedner Hauptstraße 8-10/104 1040 Wien, Austria
2
Mathematisches Seminar Christian Albrechts Universität D-24098 Kiel, Germany
3
Department of Mathematics Case Western Reserve University Cleveland, OH 44106, U.S.A. and Université de Lille 1 UFR de Mathématique 59655 Villeneuve d'Ascq, France
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author = {Monika Ludwig and Carsten Sch\"utt and Elisabeth Werner},
title = {Approximation of the {Euclidean} ball by polytopes},
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Monika Ludwig; Carsten Schütt; Elisabeth Werner. Approximation of the Euclidean ball by polytopes. Studia Mathematica, Tome 173 (2006) no. 1, pp. 1-18. doi: 10.4064/sm173-1-1
