Illuminating Rectangles and Triangles in the Plane

A set S of light sources, idealized as points, illuminates a collection F of convex sets if each point in the boundary of the sets of F is visible from at least one point in S. For any n disjoint plane isothetic rectangles, ⌊(4n + 4)/3⌋ lights are sufficient to illuminate their boundaries. If, in addition, the rectangles have equal width, then n + 1 lights always suffice and n − 1 are occasionally necessary. For any family of n plane triangles, ⌊(4n + 4)/3⌋ light sources are sufficient and n − 1 are occasionally necessary.