1. Math
  2. Advanced Math
  3. problem 4 20 pts let pn be an nsided regular...

Question: problem 4 20 pts let pn be an nsided regular...

Question details

Problem 4. (20 pts) Let P(n) be an n-sided regular polygon in the plane. A trian gulation of the polygon is a decomposition of the interior of the polygon into triangles, such that each triangle only intersects another triangle along one of its three sides. In Figure I have depicted the different possible triangulations for the triangle P(3), the square P(4), the pentagon P(5) and the hexagon P(6) Show that a triangulation of P(n) must have exactly (n - 2) triangles. 8938888 FIGURE 1. The triangle, the square with its two possible triangulations, the pentagon with its five possible triangulations and the hexagon with its fourteen possible triangulations.
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution