Small holding circles

摘要

A circle C holds a convex body K if C does not meet the interior of K and ifthere does not exist any euclidean displacement which moves C as far as desiredfrom K, avoiding the interior of K. The purpose of this note is to explore howsmall can be a holding circle. In particular it is shown that the diameter ofsuch a holding circle can be less than the width w of the body but is alwaysgreater than 2w/3.