The One-Mouth Theorem

The One-Mouth Theorem was developed and proven by Godfried T. Toussaint at McGill University in 1991 [7].

Construct the
convex hull *CH*(*P*) where *P* is a non-convex
simple polygon. Since *P* is non-convex there must exist edges on the boundary
*bd*(*CH*(*P*)) that are not edges of *P*. Each such edge
forms the "lid" of a "pocket" of *CH*(*P*). We shall prove that in
fact every such pocket yields a
mouth. Let *K _{ij}*
denote the pocket of

Q.E.D.

Anthropomorphic polygons are simple polygons that contain precisely two ears and one mouth [7].

`This page was last updated on Wednesday, December 10 ^{th},
1997.`

`©` `1997 Ian Inc.`