import math
"""Estimates the value of pi

Uses the secant of successivly smaller slices of a unit circle
as an estimate of the circumference
"""

# Initial value is the hypotenuse of a quarter of a circle
# 2pi ~ 4 * srt(2)
# pi ~ 2 * sqrt(2)
# x is the length of the secant
x = math.sqrt(2)
N = 2
print('The estimate of pi is')
for i in range(30):
  y = math.sqrt(1 - (x / 2)**2)
  z = 1 - y
  x = math.sqrt((x / 2)**2 + z**2)
  N *= 2
  pi = N * x
  print('{0:d}, {1:.20f}'.format(i, pi))