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Umbrellas and Polytopal Approximation of the Euclidean Ball

✍ Scribed by Yehoram Gordon; Shlomo Reisner; Carsten Schütt

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
335 KB
Volume
90
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

There are two positive, absolute constants c 1 and c 2 so that the volume of the difference set of the d-dimensional Euclidean ball B d 2 and an inscribed polytope with n vertices is larger than

for n (c 2 d) (d&1)Â2 .

1997 Academic Press

We study here the approximation of a convex body in R d by a polytope with at most n vertices. There are many means to measure the approximation, the two most common are the Hausdorff distance or the symmetric article no. AT963065 9 0021-9045Â97 25.00

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