TWT department of MPEI: Live Calculations by MAS

Approximation of p with the Monte Carlo Method
Prof. Massimo Priano and Dr. Valery Ochkov
(see too http://en.wikipedia.org/wiki/Monte_Carlo_method )

If a circle of radius r = 1 is inscribed inside a square whit side length L = 2, then we obtain

So the ratio of the area of the circle to the area of the square will be

Inside the square, we can put n points at random
with uniform distribution with (x,y) coordinates.
In Mathcad we can define (x, y) as follows:

We obtain

Now, we can to count how many points have fallen in the circle :

The result is:

If n is large enough, we can think that the ratio

is approximately equal to

and so

is approximately equal to

We have obtained one approximation for p

with error

	This web page generated by Mathcad Application Server
	You can also visit our products site at http://www.trie.ru
	This web page can use the WaterSteamPro functions
	Softline is MAS/MPEI partner