Polygons have Ears . By definition of x, P must be a simple polygon. Remove an ear of P that does not contain c 2 or x. An ear of P is a triangle such that one of its edges is a diagonal of P and the remaining two edges are edges of P . The new chain C 0 from c 2 to x contains one fewer vertex.
Polygons have ears .
We call p i 1 the top of ear p i . Except for triangles every simple polygon has at least two non overlapping ears. This theorem forms the basis of the ear cutting algorithm for triangulation. Except for triangles every simple polygon P has at least two non overlapping ears. Meisters proof by induction is both elegant and concise.