Python script that computes successive iterations of an infinite product that converges to π

infinite_product_to_pi.py

# Computes the value of pi by iteratively evaluating the infinite product:
# 4 * (8/9) * (24/25) * (48/49) * (80/81) * (120/121) * (168/169) * ...
# Each line of output shows the last denominator considered so far, and
# the value of the finite product at that point.
#
# As featured by Matt Parker: https://www.youtube.com/watch?v=8pj8_zjelDo

from decimal import *

def converge():
    area = Decimal(4)
    fraction = Decimal(3)
    while True:
        denominator = fraction * fraction
        numerator = denominator - 1
        area = (area / denominator) * numerator

        yield (fraction, area)
        fraction = fraction + 2

for (iteration, area_guess) in converge():
    iteration_text = str(iteration) + ': ' + str(area_guess)
    print iteration_text