Approximating the ball by a Minkowski sum of segments with equal length
type: Item
instance of: scholarly article
title: Approximating the ball by a Minkowski sum of segments with equal length
zbMATH Open document ID: 0770.52005
DOI: 10.1007/BF02189313
author: Jean Bourgain
author: J. Lindenstrauss
published in: Discrete \& Computational Geometry
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/131239
review text: The following theorem is proved. For every \(n\in\mathbb{N}\), there is a constant \(c(n)\) so that the \(n\)-dimensional Euclidean ball can be approximated up to \(\varepsilon>0\) in the Hausdorff metric by a sum of \[ N\leq c(n)(\varepsilon^{-2}|\log\varepsilon|)^{(n- 1)/(n+2)} \] segments of equal length. For \(n\leq 6\), this was proved by \textit{G. Wagner} [Discrete Comput. Geom. 9, 111-129 (1993)]. The authors use a different method, in part also related to numerical integration with equal weights. The same result, but with sums of segments of not necessarily equal lengths, had been obtained earlier by the same authors [Isr. J. Math. 64, No. 1, 25-31 (1988; Zbl 0667.52001)].
reviewed by: Rolf Schneider
Mathematics Subject Classification ID: 52A21
Mathematics Subject Classification ID: 52A27
zbMATH DE Number: 168597
zbMATH Keywords: zonotope
zbMATH Keywords: approximation
zbMATH Keywords: dimensional Euclidean ball
MaRDI profile type: Publication
cites work: Distribution of points on spheres and approximation by zonotopes
cites work: Approximation of zonoids by zonotopes
cites work: Estimating the Sizes of Convex Bodies from Projections
cites work: On a new method for constructing good point sets on spheres
description: scientific article; zbMATH DE number 168597