Ways of computing the value of Pi in Python (Pithon. geddit?)

gregory-leibniz.py

#!/usr/bin/env python3

'''
the Gregory-Leibniz series
slower than Nilakantha's in terms of rate of convergence

pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 ...
'''

import math

denominator = 1
sum = 0
sign = 1
i = 1

while True:
    sum += sign * 1 / denominator
    sum_times_four = sum * 4
    error = str(abs(math.pi - sum_times_four) * 100) + "%"
    
    print("{i} | {sum} ({error})".format(i=i, sum=sum_times_four, error=error))
    
    denominator += 2
    if sign is 1:
       sign = -1
    else:
        sign = 1
    i += 1

math.pi.py

#!/usr/bin/env python3

'''
math.pi
not much to say about this
i swaer this isn't cheating
'''

import math

print("{i} | {val} ({error})".format(i=1, val=math.pi, error="0%"))

nilakantha.py

#!/usr/bin/env python3

'''
Nilakantha's series
faster than Gregory-Leibniz in terms of rate of convergence

pi = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) ...
'''

import math

sum = 3
dff = 2 # first factor of the denominator
sign = 1
i = 1

while True:
    sum += sign * 4 / (dff * (dff + 1) * (dff + 2))
    error = str(abs(math.pi - sum) * 100) + "%"
    print("{i} | {sum} ({error})".format(i=i, sum=sum, error=error))
    dff += 2
    if sign is 1:
        sign = -1
    else:
        sign = 1
    i += 1

PITHON.md

Ways of computing the value of Pi in Python (Pithon. geddit?)

Featuring:

• Gregory-Leibniz series
• Nilakantha's series
• math.pi (this counts, right?)
• possibly more in the future