section_path: Properties/Triangulation of a polygon
section_name: Triangulation of a polygon
paragraph_text: Triangulation of a polygon
  
  Triangulation means the partition of any planar object into a collection of triangles. For example, in polygon triangulation, a polygon is subdivided into multiple triangles that are attached edge-to-edge, with the property that their vertices coincide with the set of vertices of the polygon. In the case of a simple polygon with n {\displaystyle n} sides, there are n − 2 {\displaystyle n-2} triangles that are separated by n − 3 {\displaystyle n-3} diagonals. Triangulation of a simple polygon has a relationship to the ear, a vertex connected by two other vertices, the diagonal between which lies entirely within the polygon. The two ears theorem states that every simple polygon that is not itself a triangle has at least two ears.