Translative packing of a convex body by sequences of its positive homothetic copies (Q955193)

Let \(C\) be a planar convex body. A finite or infinite sequence \((C_i)\) of positive homothetic copies of \(C\) is said to be transitively packed in \(C\) if there exists translations \(\sigma_i\) such that the sequence \((\sigma_i C)\) is packed in \(C\). In the paper under review the author proves that if the total area of \((C_i)\) does not exceed a quarter of the area of \(C\) then \((C_i)\) can be transitively packed in \(C\). This improves the earlier lower bound of \((1/8)\) the area of \(C\).