On the Multiple Covering Densities of Triangles

Abstract

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, Sriamorn (http://arxiv.org/abs/1412.5096, 2014) proved that $\vartheta _L^k(T)=\frac{2k+1}{2}$. In this paper, we will show that $\vartheta _T^k(T)=\vartheta _L^k(T)$.