Ear

A Principal Vertex $x_i$ of a Simple Polygon $P$ is called an ear if the diagonal $[x_{i-1}, x_{i+1}]$ that bridges $x_i$ lies entirely in $P$. Two ears $x_i$ and $x_j$ are said to overlap if

$$\mathop{\rm int}[x_{i-1}, x_i, x_{i+1}]\cap \mathop{\rm int}[x_{j-1}, x_j, x_{j+1}]\not=\emptyset.$$

The Two-Ears Theorem states that, except for Triangles, every Simple Polygon has at least two nonoverlapping ears.

See also Anthropomorphic Polygon, Mouth, Two-Ears Theorem

References

Meisters, G. H. ``Polygons Have Ears.'' Amer. Math. Monthly 82, 648-751, 1975.

Meisters, G. H. ``Principal Vertices, Exposed Points, and Ears.'' Amer. Math. Monthly 87, 284-285, 1980.

Toussaint, G. ``Anthropomorphic Polygons.'' Amer. Math. Monthly 122, 31-35, 1991.