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Polygonal Ears

A convex polygon with n sides can be dissected (triangulated) into triangles by drawing a certain number of non-crossing diagonals.

  1. How many diagonals are needed?
  2. How many triangles result?
  3. A triangle in the triangulation consisting of two consecutive edges of the boundary together with one internal diagonal is called an ear of the triangulation. Prove that if tex2html_wrap_inline771 then every triangulation has at least two ears.

Carl Lee
Wed Apr 21 08:26:07 EDT 1999