On the Multiple Packing Densities of Triangles

Abstract

Given a convex disk $K$ and a positive integer $k$, let ${\delta }_T^k(K)$ and ${\delta }_L^k(K)$ denote the $k$-fold translative packing density and the $k$-fold lattice packing density of $K$, respectively. Let $T$ be a triangle. In a very recent paper, K. Sriamorn proved that ${\delta }_L^k(T)=\frac{2k^2}{2k+1}$. In this paper, I will show that ${\delta }_T^k(T)={\delta }_L^k(T)$.

arXiv admin note: text overlap with arXiv:1412.5391

References in corpus (3)

• On the Covering Densities of Quarter-Convex Disks
• Multiple Lattice Packings and Coverings of the Plane with Triangles
• On the Multiple Covering Densities of Triangles