Umbrellas and polytopal approximation of the euclidean ball

Details Umbrellas and polytopal approximation of the euclidean ball Umbrellas and polytopal approximation of the euclidean ball

1996-03-18

arxiv.org/abs/math/9603208v1

Mathematics

Metric Geometry

Scientific paper

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 and an
inscribed polytope with n vertices is larger than $$ c_{2}\ d\
{n}^{-\frac{2}{d-1}}vol_d(B^d_2) $$ for $n \geq (c_{1}\ d)^{\frac{d-1}{2}}$.

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