海龟模拟蒙特卡罗法求圆周率

import turtle as t
import random
t.speed(0)
t.up()
t.goto(-200,-200)
t.down()
for i in range(4):
    t.fd(400)
    t.lt(90)
t.up()
t.goto(0,-200)
t.down()
t.circle(200)

t.color("red")
for i in range(500):
    x = random.randint(-200,200)
    y = random.randint(-200,200)
    t.up()
    t.goto(x,y)
    t.dot(10)
    t.down()
pi = (cnt1/(cnt1+cnt2))*400*400/(200*200)
print(pi)

蒙特卡洛Python圆周率计算

import random
cnt1=0
for i in range(10000000):
    x = random.random()*2-1
    y = random.random()*2-1
    if (x*x+y*y)<=1:
        cnt1+=1
    if(i == 100 or i == 500 or i == 1000 or i == 10000 or i == 100000 or i == 1000000):
        print("n:",i,"pi:",cnt1/i*4)

import math
d = 2
for n in [3,4,5,10,100,1000,10000,100000]:
    r = d/2
    a = 360/n
    x = (2 * r**2 * (1 - math.cos(math.radians(a))))**0.5
    perimeter = x * n
    pi = perimeter / d
    print(n, "-->", pi)