Monte Carlo (idea)

A classic Monte Carlo simulation is to approximate pi. Take a 2 unit square, its area is 4. Within this square, a circle of radius 1 can be inscribed. The area of this circle is pi. So, for the approximation...

1. Take two 10, 20, or 100 sided dice.
   One for X, one for Y.
   For future reference, the number of sides is called N
2. Draw a one quadrant of the 2 unit square.
3. Divide this quadrant up into the number of sides on the selected dice.
4. Roll the two dice and plot this spot on the paper
5. Calculate if its a hit or miss:
   If X² + Y² < N², it is a "hit".
   Otherwise its a "miss".
6. Repeat Z times.
   Higher values of Z result in increased precision
7. 4 * (number of hits)/Z is approximately pi.

Monte Carlo simulations are also used in climatology. One example of a SETI@Home like project that plans to use Monte Carlo simulations can be found at http://www.climate-dynamics.rl.ac.uk/. Because of the number of variables in climate dynamics, you select one set of variables, run it and see if its right. In this model, the data is started at 1950, and run for 50 years to see if it matches present conditions. If it does, it is then run for another 50 years to form an approximation of what 2050 will be like.