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The Two-Ears Theorem


The Two-Ears Theorem was developed and proven by Gary H. Meisters at the University of Nebraska in 1975 [4].

The Two-Ears Theorem:


Proof #1: By Gary H. Meisters

The proof by Meisters is by induction on the number of vertices, n, in the simple polygon P.   It is quite elegant.

Base Case:

Induction:

Case 1:

Case 2:

Case 2a:

Case 2b:

Q.E.D.

Proof #2: By Joseph O'Rourke [6]

It is known that a simple polygon can always be triangulated. Leaves in the dual-tree of the triangulated polygon correspond to ears and every tree of two or more nodes must have at least two leaves.

Q.E.D.

Some Examples:











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This page was last updated on Wednesday, December 10th, 1997.

© 1997 Ian Inc.