蒙特卡罗法近似求解圆周率πpythonMichael是个半路程序员-

1. 原理

• 给出
  $x in [0,1),yin[0,1)$

  x∈[0,1),y∈[0,1) 的均匀分布随机点，模拟
  $t$

  t 次，落在以
  $(0,0)$

  (0,0) 为圆心，半径
  $r=1$

  r=1 的圆以内的次数为
  $c$

  c

• 当模拟次数足够大时，可以看成面积比
  $frac{pi}{4} approx frac{c}{t}Rightarrow pi approx 4c/t$

  4π​≈tc​⇒π≈4c/t

2. 模拟代码

# -*- coding:utf-8 -*- # @Python Version: 3.7 # @Time: 2020/5/2 9:02 # @Author: Michael Ming # @Website: https://michael.blog.csdn.net/ # @File: monte_carlo_cal_pi.py # @Reference:  import random import matplotlib.pyplot as plt  simulations = [100, 1000, 10000] plt.figure() plt.rcParams['font.sans-serif'] = 'SimHei' # 消除中文乱码 plotid = 1 color = ['r', 'b'] for i in range(len(simulations)):     f = plt.subplot(1, 3, plotid)     plotid += 1     count = 0     t = simulations[i]     time = simulations[i] while time > 0:         time -= 1         x = random.random() # [0,1)         y = random.random() # [0,1)         val = x ** 2 + y ** 2         pos = 1 if (val < 1):             pos = 0             count += 1         f.scatter(x, y, c=color[pos])     pi = 4 * count / t     f.set_title("模拟次数{},pi的值{:.4f}".format(t, pi)) plt.suptitle("蒙特卡罗法近似求解圆周率pi") plt.show()