Translative covering by homothetic copies
The authors prove the following nice theorem using elementary geometry only: For every convex disc \(K\) in the Euclidean plane there are homothetic triangles \(T\) and \(\lambda T\) with \(T\subseteq K\subseteq \lambda T\) and \(\lambda = 3(\sqrt{17}-1)/4\). As a corollary the authors give the sufficient condition \(\sum V(K_ i) \geq 9(9-\sqrt{17})/4\) for the existence of a translative covering of \(K\) with area \(V(K) = 1\) by any sequence \((K_ i)\) of homothetic copies of \(K\).
scientific article; zbMATH DE number 205530
scientific article