蟒蛇，烏龜，pi和蒙特卡洛

Question

我正在嘗試使用monte carlo和python中的海龜來近似pi。 代碼運行良好，但是我遇到了問題，我的“近似值”全都錯了。 我總是得到小於1的值，所以？？？ 我的代碼在這里

import turtle
import math
import random

fred = turtle.Turtle()
fred.speed(0)
fred.up()

wn = turtle.Screen()
wn.setworldcoordinates(-1,-1,1,1)

numdarts = int(input("How many darts will you throw"))
for i in range(numdarts):
x = random.random()
y = random.random()
numIncircle = 0

if i == 0 or i == 1:
    fred.up()
    fred.goto(x, y)


    if fred.distance(0, 0) <= 1:
        numIncircle += 1
        fred.color("Indianred")
        fred.stamp()
        fred.up()
    else:
        numIncircle += 0
        fred.color("cyan")
        fred.stamp()
        fred.up()


else:
    fred.goto(x, y)

    if fred.distance(0, 0) <= 1:
        numIncircle += 1
        fred.color("Indianred")
        fred.stamp()
        fred.up()
    else:
        numIncircle += 0
        fred.color("cyan")
        fred.stamp()
        fred.up()

piapproximation = float(float(numIncircle) / float(numdarts)) * 4

print piapproximation

wn.exitonclick()

Answer 1

你設置numIncircle = 0的內部 for循環，有效地失去每次計數。

有時它會計數最后一個，因此近似值為1 /飛鏢數*4。這將在頻率pi / 4≈0.78539816339時發生 。

這是我的建議：

import turtle
import math
import random

fred = turtle.Turtle()
fred.speed(0)
fred.up()

wn = turtle.Screen()
wn.setworldcoordinates(-1,-1,1,1)

numdarts = int(input("How many darts will you throw"))

// this MUST come before the for loop
numIncircle = 0

for i in range(numdarts):
x = random.random() * 2 - 1
y = random.random() * 2 - 1

if i == 0 or i == 1:
    fred.up()
    fred.goto(x, y)

    if fred.distance(0, 0) <= 1:
        numIncircle += 1
        fred.color("Indianred")
        fred.stamp()
        fred.up()
    else:
        numIncircle += 0
        fred.color("cyan")
        fred.stamp()
        fred.up()
else:
    fred.goto(x, y)

    if fred.distance(0, 0) <= 1:
        numIncircle += 1
        fred.color("Indianred")
        fred.stamp()
        fred.up()
    else:
        numIncircle += 0
        fred.color("cyan")
        fred.stamp()
        fred.up()

piapproximation = float(float(numIncircle) / float(numdarts)) * 4

print piapproximation

wn.exitonclick()