Editing Art gallery problem (section)

=== Illustration of the proof ===
To illustrate the proof, we consider the polygon below. The first step is to triangulate the polygon (see ''Figure 1''). Then, one applies a proper <math>3</math>-colouring (''Figure 2'') and observes that there are <math>4</math> red, <math>4</math> blue and <math>6</math> green vertices. The colour with the fewest vertices is blue or red, thus the polygon can be covered by <math>4</math> guards (''Figure 3''). This agrees with the art gallery theorem, because the polygon has <math>14</math> vertices, and <math>\left\lfloor \frac{14}{3} \right\rfloor = 4</math>.
<gallery mode="nolines" class="center">
File:Triangulation of polygon.png|Figure 1
File:3-coloring of the polygon.png|Figure 2
File:Least color of 3-coloration.png|Figure 3
</gallery>