Monte Carlo Method and pi

[Robert Brewer]

Karl Pech wrote:
> import random
> import math
> 
> n = long(raw_input("Please enter the number of iterations: "))
> sy = 0                                   # sum of the function-values
> 
> for i in range(0, n):
>   x = random.random()                    # coordinates
>   sy += math.sqrt(1-math.sqrt(x))        # calculate y and add to sy
> 
> print 4*sy/n                             # compute pi
> ---
> 
> Unfortunately, even for n = 2000000 the result is ~2,13... .
> It converges very slow to pi and I don't know why.

Start by localizing the functions and using xrange...

random = random.random
sqrt = math.sqrt

for i in xrange(n):
  x = random()                    # coordinates
  sy += sqrt(1-sqrt(x))        # calculate y and add to sy


Robert Brewer
MIS
Amor Ministries
fumanchu at amor.org