用Monte Carlo方法计算Pi

Monte Carlo方法是计算Pi时我们经常会演示的一种算法，这种方法就是通过随机点的计数来得到Pi的值，如果用上Python中turtle包的图形绘制功能，会比较直观，最终执行的效果如下：

运行效果

具体代码如下：

import turtle
import random

myPen = turtle.Turtle()
myPen.hideturtle()
# If you feel the drawing process is too time lasting, conside to use either of the following sentances:
#myPen.getscreen().tracer(0)
#myPen.getscreen().delay(0)
myPen.getscreen().delay(0)
myPen.speed(500)

window = turtle.Screen()
window.bgcolor("#FFFFFF")

def drawSquare(x, y, width):
    myPen.penup()
    myPen.goto(x, y)
    myPen.pensize(3)
    myPen.color("#333333")
    myPen.pendown()
    for side in range(0, 4):
        myPen.forward(width)
        myPen.right(90)
    myPen.pensize(1)

def drawCircle(x, y ,radius):
    myPen.penup()
    myPen.goto(x, y-radius)
    myPen.pensize(2)
    myPen.color("#333333")
    myPen.pendown()
    myPen.circle(radius)
    myPen.pensize(1)

def drawDots(x, y, color):
    myPen.penup()
    myPen.goto(x, y-1)
    myPen.pendown()
    myPen.fillcolor(color)
    myPen.color(color)
    myPen.begin_fill()
    myPen.circle(1)
    myPen.end_fill()

radius = 180
color = "#000000"
total = 25000
totalIn = 0

drawSquare(-radius, radius, 2*radius)
drawCircle(0, 0, radius)

for dots in range(0, total):
    x = random.randint(-radius, radius)
    y = random.randint(-radius, radius)
    distance = (x**2 + y**2)**0.5
    if distance < radius:
        color = "#FF0000"
        totalIn += 1
    else:
        color = "#0000FF"
    drawDots(x, y, color)

myPen.getscreen().update()

pi = 4 * (totalIn / total)
print("Pi estimation:{}".format(pi))

这里打了25000个随机点，如果在教学中需要考虑时间，可以适当地改小。另外，如果只需要加速可以考虑取消代码中的两行注释中的任意一个，当然要是只在乎结果，那个整个绘图的过程都可以不要。