Approximation of Pi using the Leibniz and the Nilkantha series, implemented in Python.

pi_approx.py

from decimal import *


getcontext().prec = 1000

# simple and beautiful but diverges slowly.
def leibniz():
    prefactor = -1
    pre_result = 1
    current_index = 3
    while True:
        pre_result = Decimal(pre_result) + (Decimal(prefactor) * (Decimal(1)/Decimal(current_index)))
        current_index += 2
        prefactor *= -1
        print("Current approximation: π = " + str(Decimal(pre_result * 4)))


# Much, much faster than Leibniz
def nilakantha():
    prefactor = 1
    pre_result = 3
    index = 2
    while True:
        pre_result = Decimal(pre_result) + (Decimal(prefactor) * Decimal(Decimal(4)/Decimal(Decimal(index) * Decimal((index+1)) * Decimal((index+2)))))
        index += 2
        prefactor *= -1
        print("Current approximation: π = " + str(pre_result))


# leibniz()
nilakantha()