Estimating PI using the monte carlo method

      • Number of points

by Thoralf Möbius

 

 

Why do I make an estimate of PI instead of calculating PI or taking PI directly from a computer? The answer is simple: It would be boring :).

Simulating PI is relatively easy.
It is based on a square containing a circle.The circle has a size that fits exactly into the square. So far, so good. Now it needs random points, which are drawn into the square with the circle. The points are drawn randomly (as gambling in Monte Carlo).

How do we get to PI ?
Quite simply, we relate the number of points inside the circle to the number of points outside the circle. The result is (more or less) PI.

Experimental setup
This experiment uses only a quarter of the square and the circle, but ends up with the same result as a full square and a full circle.

How to get results ?
The easiest way is to click the Estimating – PI button and see what happens. If the button is clicked several times, the newly generated points are added to the existing ones.

What can be seen with this experiment ?
In order to simulate PI relatively well, you don’t need many of the random points, because most of them end with quite a good result. Further is shows, that after a certain number of random points the result will not change significantly when we focus on the first 10 digits after the comma. PI is an irrational number and therefor it can’t be reached either with a calculation or with a simulation.