from math import sqrt

def inscribedSemiperimeter(iterations):
    sides = 6
    sideSquared = 1
    for x in range (iterations):
        sideSquared = sideSquared/4 + (1- sqrt (1- sideSquared/4))**2
        sides=sides*2
    pi=sqrt(sideSquared)*(sides/2)
    return pi

def change(iterations):
    return inscribedSemiperimeter(iterations+1) - inscribedSemiperimeter(iterations)

def upperBound(iterations):
    return inscribedSemiperimeter(iterations) + change(iterations-1)