My first three.js app

Explanation code by Danijel

Computing Pi by a Monte Carlo Method Explained by Danijel Ivanovic

you are ever stranded on a desert l island and cannot remember the value of PI, all you need to compute it is a random number generator.

This program will show you how. The method used in this assignment is called a "Monte Carlo" method because it is based on probability.

Here are some useful facts:

The area of a circle is equal to PI times the square of the radius.
The area of a square is equal to the square of the length of the side.
The distance from a point (x1, y1) to a point (x2, y2) is equal to the square root of
(x2 – x1)^2 + (y2 – y1)^2.

Imagine a circle inscribed inside a square.

Since the radius of the circle is R, its area is PI*R^2. Since the side of the square is 2*R, its area is 4*R^2. Therefore the ratio of the area of the circle to the area of the square is PI/4.

Using a random number generator, you can "throw" random points at the square.

The ratio between the number of points that fall inside the circle and the total number of points that fall inside the square is an approximation to the value of PI/4.

Points inside Circle (inside):

Points outside Circle:

Total random points on square (total):

Projected PI value(inside / total * 4):

Math Library PI value:

Difference in values:

MONTE CARLO SIMULATION