On the Multiple Covering Densities of Triangles

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