The Monte Carlo method solves the PI and draws points with turtle, and completes the progress bar problem

Use Monte Carlo method to solve the PI π

• Background of Monte Carlo method

'''

         Monte Carlo method in 20 century 40 In the s, the United States developed the atomic bomb in the Second World War “ Mann
Hatton plan ” Members of the program S.M. Ulam and J. feng · Neumann first proposed . Mathematician Feng · Neumann uses the world-famous gambling city — Monaco's Monte Carlo— To name this method , Give it a layer of mystery . before this , Monte Carlo method already exists .1777 year , French mathematician Buffon （Georges Louis Leclere de Buffon,1707—1788） It is proposed to calculate the circumference ratio by means of needle throwing experiment π. This is considered to be the origin of Monte Carlo method .

'''

• Subject requirements

The area of the unit circle is PI, The area of the circumscribed square of the unit circle is 4. therefore ,1/4 The area of a circle is PI/4, The area of the circumscribed square is 1 Use turtle library turtle.goto()、turtle.dot() Other methods , Complete the drawing as shown in the figure on the right ; And it is required that in the calculation process , Every time 10% When calculating the point of , Display the currently completed progress through console output .

This method is not difficult to understand , In fact, it's the probability problem learned in high school .

The code is as follows ：

import time
from random import random
from math import *
from time import clock
from time import sleep
import turtle
import sys
DARTS = 1000
hits = 0
clock()
turtle.setup(800, 800,startx=0,starty=0)
turtle.speed(0)
turtle.pensize(2)
for i in range(1, DARTS + 1):
    x, y = random(), random()
    dist = sqrt(x ** 2 + y ** 2)
    turtle.penup()
    turtle.goto(x*200,y*200)
    turtle.pendown()
    if dist <= 1.0:  #  Judge the point in the circle 
        hits += 1
        #turtle.color("red")  # You can also change the brush color , be not in dot Riga color 
        turtle.dot(6,"red")
    else:
        #turtle.color('blue')
        turtle.dot(6,'blue')
    j=int(i/10)
    if j%10==0:
        print("\r",end="")
        print("Download progress:{}%".format(j)," "*(j//2),end="")
        sys.stdout.flush()
        time.sleep(0.01)
pi = 4 * (hits / DARTS)
print("\n")
print("pi The value is {}.".format(pi))
print(" The running time is ：{:.5f}s".format(clock()))
turtle.done()

The operation results are as follows ：

The middle dynamic progress bar is as follows ：

Console ：

Upper figure pi I forgot the value of line feed , But the code has changed , In the process of running, there will be the problem of slow dot drawing speed , It may be related to computers , I haven't found the reason yet , If a friend knows , You can send me a private letter , I will correct it immediately . Thank you for your support .