Estimating the value of PI

Assuming a circle with radius r fitted inside a square with sides of 2r in length.

If we randomly generate points within the square, the ratio of

"points inside the circle" : "total number of the points"
= "area of the circle" : "area of the square"
= pi * r^2 : 4 * r^2

So pi can be estimated by:

pi = 4 * "points inside the circle" / "total number of points"

For ease of calculation, we can just consider a quarter of the circle with r = 1 and the enclosing square with sides of 1.

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