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
| int[x_(i-1),x_i,x_(i+1)] intersection int[x_(j-1),x_j,x_(j+1)]!=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 TheoremExplore with Wolfram|Alpha
References
Meisters, G. H. "Polygons Have Ears." Amer. Math. Monthly 82, 648-651, 1975.Meisters, G. H. "Principal Vertices, Exposed Points, and Ears." Amer. Math. Monthly 87, 284-285, 1980.Toussaint, G. "Anthropomorphic Polygons." Amer. Math. Monthly 98, 31-35, 1991.Referenced on Wolfram|Alpha
EarCite this as:
Weisstein, Eric W. "Ear." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Ear.html