The resulting approximate value of Pi = 4*I/N is calculated on line 16. On line 6 we define a counter for the points lying inside the quarter-circle, and this counter is increased on line 14 whenever the random point lies inside. The number N on line 4 defines the number of random points we want to use.
Here, the function random() imported from the “random” library generates a random number between 0 and 1. You can easily run it using the Python app in the Creative Suite – it only has 10 lines not counting comments: The corresponding Python program is presented below. And that’s all! From the equation I / N = A / S we can easily express that Pi = 4 * I / N. By I we will denote the number of points lying inside the quarter-circle.Īs you will certainly agree, with large N the ratio I / N must be very similar to the ratio of A / S. To calculate it, we will generate a large number N of random points in the unit square. Let’s pretend that we don’t know the value of Pi. The area of the quarter-circle is A = Pi*S/4. Obviously, the area of the square is S = 1. Let’s start by drawing a quarter-circle in the unit square. Let us show an example of how this method works – we will calculate the value of Pi. It performs many (thousands of) trials to infer results such as areas or volumes of complex objects, and many other types of problems that often could not be solved otherwise. It uses the “brute force” of computing to solve a wide range of problems. This method is very simple in its nature. In the article about John von Neumann we mentioned that he invented the Monte Carlo method.
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