Covering a plane convex body by its negative homothets
The author proves specific results about covering a planar convex body by negative homothets of itself. Namely, let \(\lambda_k\) denote the smallest positive number such that every planar convex body can be covered by \(k\) homothetic copies of itself with homothety ratio \(-\lambda_k\). Confirming a conjecture of Januszewski and Lassak, it is shown that \(\lambda_7=\frac {10}{17}\). Also an estimate on \(\lambda_6\) is given, and the following conjecture is posed: Every planar convex body \(C\) can be covered by five translates of \(-\frac 57C\).
scientific article; zbMATH DE number 5562639