Covering a plane convex body with five smaller homothetical copies
A conjecture of Marek Lassak (1986) concerning Hadwiger's covering problem is solved: For a convex body C in the Euclidean plane, let \(h_ k(C)\) be the smallest positive ratio of k homothetical copies of C whose union covers C. Define \(h_ k=\inf \{h_ k(C): C\) is a plane convex body\(\}\). Then \(h_ 5=1/2\). Lassak also formulated the conjecture that \(h_ 6=1/2\), but this is still unsolved.
scientific article; zbMATH DE number 4005046