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 $\delta_T^k(T)=\delta_L^k(T)$.