python_pi.py

# Uses Python 3.x
from decimal import Decimal, getcontext
from time import time, strftime
import datetime

"""
Machin's Formula as:
4(4(arccot(5))-arccot(239))

or expanded as:

4(4(1/5 - 1/3(5)^3) + 1/5(5)^5 + 1/7(5)^7) - (1/239 - 1/3(239)^3 + 1/5(239)^5 + 1/7(239)^7))

of course a lot longer
"""

def arccot(x, digits):
    # set precision and starting values
    getcontext().prec = digits
    
    total = 0
    n = 1
    
    # loop while new term is large enough to actually change the total
    while Decimal((2 * n - 1) * x ** (2 * n - 1)) < Decimal(10 ** digits):
        # find value of new term
        term = ((-1)**(n - 1)) * 1 / Decimal((2 * n - 1) * x ** (2 * n - 1))
        
        # add the new term to the total
        total += term
        
        # next n
        n += 1
    
    # return the sum
    return total

# pi function
def pi(decimals):
    # start timer
    timestart = time()
    
    # find pi using Machin's Formula pi = 4 * (4 * arccot(5) - arccot(239))
    
    #  and the power formula for arccot (see arccot function above)
    print("pi = " + str(Decimal(4 * (4 * arccot(5, decimals + 3) - arccot(239, decimals + 3))).quantize(Decimal(10) ** (-decimals))))
    
    # display elapsed time
    timeelapsedint = round(time() - timestart, 2)
    timeelapsedstr = str(datetime.timedelta(seconds = round(timeelapsedint, 0)))
    
    print("runtime: " + timeelapsedstr + " or " + str(timeelapsedint) + " seconds.")

if __name__ == "__main__":
    n = input("How many digits of pi would you like to know? ")
    pi(int(n))