Week 3 Practical Problem. a+ Essay
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 …show more content…
The pattern is contained in the formula. When you carry out numerator you find that the next number in sequence is always an increase of 4. This seems to work for all polynomials.
C. How would T(n) change if you ignored the vertices’ distinctness? That is, if you remove the labels, and say two triangulations are identical if one can be transformed into the other via a rotation or a reflection, how does this change T(n) for n = 4, 5, 6, 7, & 8?
Using the formula given below, which I believe is designed to eliminate duplication, we would find that T(4) would still be 2, T(5) would still be 5, but the pattern would end there. T(6) = 9, T(7)= 14, and T(8) = 20.
There is a definite pattern to the numbers. Each additional vertex increases the number of triangle by the n-2. That is, when figuring a hexagon, where we had 5 sides with a pentagon, that number is increased by (6-2) for a total of 9 sides. 9 sides plus (7-2) totals 14, and this pattern seems to continue.
If I understand this right, by ignoring the distinctness and using the explanation given in the