gistfile1.py

# Adapted from a friend's alternative solution to the Madhava implementation problem
# from question 16 in the Interactive Python Textbook problem set:
# http://interactivepython.org/runestone/static/thinkcspy/Functions/thinkcspyExercises.html
# Original gist: https://gist.github.com/anonymous/2f78d796e965d6abcaec/321252a19d85aebca2359188d9991f7472e9f786
 
def myPi(tolerance=0.01):
    """Compute Pi by Madhava's technique, to specified tolerance, default .01."""
    accumulator = 0
    n = 0
    newvalue = abs(tolerance) + 1
    while abs(newvalue) > tolerance:
        newvalue = ( ( (-1) ** n) / ((2 * n) + 1) )
        n += 1
        accumulator += newvalue
        # Show the newvalue formula result for each step in the loop:
        print(n, accumulator*4)
    return (accumulator * 4)
 
if __name__ == "__main__":
    print(myPi())