Simple algorithm that calculates an approximation of pi. It is based on the idea that the area of a polygon with many sides circumscribed inside a unit circle approaches pi. In the example I test the algorithm with a polygon of 500 sides and the result of executing the code in my machine is 3.141592653589795Important Notes: The maximum length it…

gistfile1.py

import math
def calcSide(a):
     side = math.sqrt(2)
     H = math.sqrt(1/2)
     for x in range(1,a):
             b = side/2
             x = 1 - H
             side = math.sqrt(b**2+x**2)
             H = math.sqrt(1-(side/2)**2)
     r = {"side":side,"H":H}
     return r

def calcPi(a):
     r = calcSide(a)
     side = r["side"]
     H = r["H"]
     pi = (side*H*(2**(a+1)))/2
     return pi

calcPi(500)