naive.py

#!/usr/bin/env python3
#
#   naive.py  -  by Don Cross
#
#   Illustrates why 4*arctan(1) is not a good way to calculate pi.
#   Calculates the series 4*(1/1 - 1/3 + 1/5 - 1/7 + ...)

import math

n = 1
polarity = +4
x = 0.0
error = 1.0
while error >= 1.0e-6:
    x += polarity / n
    error = abs(math.pi - x)
    print('n={:15d}, x={:15.13f}, error={:10.6g}'.format(n, x, error))
    polarity *= -1
    n += 2