Illuminating triangles, quadrilaterals and convex polygons with vertex floodlights.

Abstract

This work presents the solution to three problems in Computational Geometry. First we introduce a theorem to illuminate every triangle with three p6 vertex-floodlights and we provide three proofs. Secondly we show that three p4 vertex-floodlights suffice to illuminate every quadrilateral. Finally we provide a theorem for illuminating a cocircular convex n-gon P of n vertices with a set of k vertex-floodlights, (k ≤ n) whose total sum is pi.