The plank problem for symmetric bodies

Research paper by Keith Ball

Indexed on: 25 Sep '90Published on: 25 Sep '90Published in: Mathematics - Metric Geometry


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.