There are different ways to solve the art gallery problem. We explained the solution to the problem of the art gallery, which is based on the monotony of polygons and triangulation. Arriving at the final polygon triangulation algorithm, we encountered various solutions. As a first solution to the problem, we triangulated the triangle. Each triangulation of a simple polygon with n vertices consists of exactly n-2 triangles. Placing a camera inside each triangle seemed excessive, so we placed the camera on a diagonal that would guard two triangles, reducing the number of cameras to approximately n/2. Placing cameras on the vertices seemed like an even better solution. We solved the problem of vertex selection by 3-coloring the triangulated polygon. By choosing the smallest color class to place the cameras, we can preserve P using at most ⌊n/3⌋ cameras. The strategy for triangulating a polygon P is to first divide P into y-monotone parts and then triangulate the parts. We have described the algorithms needed to divide a polygon into monotone parts, as well as the algorithm for triangulating a simple polygon.