Monte Pi

Set Framerate

Start

Enter the number of times you want the experiment in the box above and click on Simulate

Method

The Monte Carlo method relies on repeated random sampling to simulate some process or compute a value.

Pi can be computed using Monte Carlo simulation through a series of experiments. Here is a single experiment:

Choose a pair of random floating point numbers between 0 and 1

Call the numbers x and y, think of (x,y) as a point on the plane in the unit square

Test whether the point falls within the unit circle by measuring the distance from the point to the origin

Now suppose you do m experiments and in n of those experiments, the random point chosen falls within the upper right quarter of the unit circle. Since the area of a circle is known to be pi * r^2 and the area of a square is r^2 (and here we are dealing with a radius/square side of length 1), the following equations hold:

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