We know on e camera suffices to guard any convex polygon. The triangle is a convex polygon, thus if we triangularize the polygon into say n triangles, we are sure that it can be guarded by n cameras. To use this technique we must be sure that any simple polygon can be triangularized. We will prove this is true. Any simple polygon can be triangulated This proof uses another theorem about polygons which is called the Two Ears Theorem .This theorem states that any simple polygon must have at least two ears .
Any simple polygon has two ears.
Of course to be clear we must define what is a polygonal ear. We say that a Polygon P has an ear at vertex V if the triangle formed by V and its two adjacent vertices lies inside P and does not contain a piece of the polygon. To be precise, there are no vertices of P inside the triangle formed by V and its 2 adjecent vertices. This does not hold if P is a triangle. A triangle has only one ear.