Monte Carlo Method and pi

[Jeff Epler]

Others spotted the problem with your implementation of the approximatoin
method.

You can greatly speed things up with numarray. It gets "3.141..." as
the approximation using n=2000000 in about 4 seconds on this sub-GHz
laptop.  Of course, a method with faster convergence would get to 3.141
in a lot less than 4 seconds, even if written in pure Python.

Jeff

import numarray
import numarray.random_array

def approx_pi(n):
    a = numarray.random_array.uniform(0, 1, n)
    return 4 * numarray.sum(numarray.sqrt(1 - a**2)) / n

if __name__ == '__main__':
    n = int(raw_input("Please enter the number of iterations: "))
    print approx_pi(n)
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