Problems
Use the following problems to test your geometric programming skills. Give each problem a try before you turn to the solutions and download the example programs. If you have trouble with the graphical part, try to implement the non-graphical pieces. Then, you can download the example solutions and replace the key parts of the program with your code.
20. Monte Carlo π
A Monte Carlo algorithm uses randomness to approximate the solution to a problem. Often, using more random samples gives you a more accurate approximated solution or gives a greater probability that the solution is correct.
For this problem, use a Monte Carlo algorithm to approximate π. To do that, generate random points in the square (0 ≤ X, Y ≤ 1) and then see how many fall within a circle centered in that square.
21. Newton's π
Various mathematicians have developed many different ways to approximate π over the years. Sir Isaac Newton devised the following formula to calculate π:
Use Newton's method to approximate π. Let...
