With MATLAB We are looking for an algorithm to estimate the value of . One method is based on the fact that the perimeter of a circle of radius 1/2 is . To estimate the value of , it then suffices to estimate the perimeter of a circle of radius 1/2. So the idea is to register regular polygons in the circle and calculate the perimeter of the polygon. By increasing the number of sides of the polygon, we get closer and closer to the perimeter of the circle and therefore to . We will note pn the perimeter of the polygon having 2n sides (for example, p2 = 22) and we will assume that the following recurrence formula is true:

Write a Matlab program which will calculate pn for n = 3, 4, ..., 30 using the algorithm (3). The program must present using the fprintf command the results in a table of three columns containing the values of n, pn as well as the absolute error committed. What do you notice abnormal?

Find: the Matlab program, the table, the number of significant digits of p15 and p24 produced by this program and the discussion.

Pn+1 = 2" 21-11 Pus=z-J3(1-va-(53*), pour n-2,3.. pour n = 2, 3, ... e (3)