The word triangulation has two definitions. The first, and most common, is the use of trigonometry ...

  

In this assignment, you examine a practical procedure used in computer-aided design and computational fluid dynamics. You will make some assessments regarding this procedure.

The word triangulation has two definitions. The first, and most common, is the use of trigonometry to establish the position of an object relative to two or more fixed, known locations. This is common in navigation. The second definition is the decomposition of a polygon into triangles. This provides a convenient representation of a polygon that can be used in a variety of computational contexts, such as those mentioned above. For this assignment you will not be concerned about computer science; rather, you will study the variety of ways in which polygons may be triangulated.

Questions

A. Determine T(n) for n = 6, 7, & 8.

B. Do you detect a pattern to these numbers? This pattern may arise out of the numbers or the manner in which you generated triangulations. (A closed-form function for T(n) is relatively straightforward, but is fairly nontrivial to construct; you will not have to explore that here.)