import math
import random

def EulerPi(n):
    sum = 0
    for i in range(1,n+1):
        term = 1/(i*i)
        sum = sum + term
    return(math.sqrt(sum*6))

def LeibnizPi(n):
    sum = 0
    for i in range(0,n+1):
        term = ((-1)**i)*(1/(2*i+1))
        sum = sum + term
    return(4*sum)

def WallisPi(n):
    prod = 1
    for i in range(0,n+1):
        num = (2*i+2)**2
        den = (2*i+1)*(2*i+3)
        term = num/den
        prod = prod*term
    return(2*prod)

def MonteCarloPi(n):
    m = 0
    for i in range(n):
        x = random.random()
        y = random.random()
        d = x**2+y**2
        if d<=1:
           m = m + 1
    return(4*m/n)

#------------------
for n in range(10,100,10):
    p0 = EulerPi(n)
    p1 = LeibnizPi(n)
    p2 = WallisPi(n)
    p3 = MonteCarloPi(n)
    print("n =          ",n)
    print("Euler:       ",p0)
    print("Leibniz:     ",p1)
    print("Wallis:      ",p2)
    print("Monte Carlo: ",p3)

#------------------