# archimedesPi.py
# https://code.activestate.com/recipes/578478-archimedes-method-for-pi-arbitrary-precision/

# Archimedes Method for PI
# FB - 200912082
# Revised by Bjorn.madsen AT operationsresearchgroup.com for Python3.3
# BHM - 20130302


import decimal


precision=99
# x: circumference of the circumscribed (outside) regular polygon
# y: circumference of the inscribed (inside) regular polygon

decimal.getcontext().prec = precision+1
D = decimal.Decimal

# max error allowed
eps = D(1)/D(10**precision)

# initialize w/ square
x = D(4)
y = D(2)*D(2).sqrt()

ctr = D(0)
while x-y > eps:
  xnew = 2*x*y/(x+y)
  y = D(xnew*y).sqrt()
  x = xnew
  ctr += 1
  

print(str((x+y)/D(2)))