【MOOC嵩天Python语言程序设计】4.5 实例6：圆周率的计算

一、公式法：
pi = 0
N = 100
for k in range(N):
    pi += 1/pow(16,k)*(\
        4/(8*k+1) - 2/(8*k+4) -\
        1/(8*k+5) - 1/(8*k+6))
print("圆周率是：{}".format(pi))


pi = 0
N = 100
for k in range(N):
    pi += 1/pow(16,k)*(4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6))
print("圆周率是：{}".format(pi))


圆周率是：3.141592653589793


二、蒙特卡罗方法：

from random import random
from time import perf_counter
DARTS =1000*1000
hits = 0.0
start = perf_counter()
for i in range(1,DARTS+1):
    x, y = random(), random()
    dist = pow(x ** 2 + y ** 2, 0.5)
    if dist <= 1.0:
        hits = hits +1
pi = 4* (hits/DARTS)
print("圆周率值是：{}".format(pi))
print("运行时间是：{:.5f}".format(perf_counter()-start))

圆周率值是：3.14018
运行时间是：1.09499