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An opaque set (or a barrier) for $U \subseteq \mathbb{R}^2$ is a set $B$ offinite-length curves such that any line intersecting $U$ also intersects $B$.In this paper, we consider the lower bound for the shortest barrier when $U$ isthe unit equilateral triangle. The known best lower bound for triangles is theclassic one by Jones [Jones,1964], which exhibits that the length of theshortest barrier for any convex polygon is at least the half of its perimeter.That is, for the unit equilateral triangle, it must be at least $3/2$. Veryrecently, this lower bounds are improved for convex $k$-gons for any $k\geq 4$[Kawamura et al. 2014], but the case of triangles still lack the bound betterthan Jones' one. The main result of this paper is to fill this missing piece:We give the lower bound of $3/2 + 5 \cdot 10^{-13}$ for the unit-sizeequilateral triangle. The proof is based on two new ideas, angle-restrictedbarriers and a weighted sum of projection-cover conditions, which may be ofindependently interest.

Improving Lower Bound on Opaque Set for Equilateral Triangle