Illumination of polygons by 45°-floodlights Original Research Article

What is the minimal number of floodlights that can illuminate the interior of any polygon with n vertices, provided that every floodlight has an α, α∈(0°,360°], range of illumination? This question is answered in this paper for α∈[45°,60°), stating that this number is n−1, if n is odd, and n−2, if n is even. We show also that every simple polygon with 2ℓ+2 vertices can be partitioned into ℓ quadrilaterals using at most ℓ−1 Steiner points.