The plank problem for symmetric bodies

Details The plank problem for symmetric bodies The plank problem for symmetric bodies

1990-09-25

arxiv.org/abs/math/9201218v1

Mathematics

Metric Geometry

Scientific paper

10.1007/BF01245089

Given a symmetric convex body $C$ and $n$ hyperplanes in an Euclidean space,
there is a translate of a multiple of $C$, at least ${1\over n+1}$ times as
large, inside $C$, whose interior does not meet any of the hyperplanes. The
result generalizes Bang's solution of the plank problem of Tarski and has
applications to Diophantine approximation.

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