#Monte Carlo method to find pi using Python

at first

In this article This is an article that explains the program to find the pi using the Monte Carlo method written in the midnight tension as it is by watching Lambda's Video. Don't expect too much because it's midnight tension!

The code is terrible

import matplotlib.pyplot as plt
import random

Xlist=[]
Ylist=[]
Number_list=[]
pi=0
pi_list=[]

for i in range(15000):
    Xlist.append(random.uniform(0,1))
    Ylist.append(random.uniform(0,1))
    if (i+1)%10 == 0:
        Number_list.append(i+1)
        pi_list.append((pi/(i+1))*4)
    if Xlist[i]**2+Ylist[i]**2 <= 1 and (i+1)%10 == 0:
        Number_list.append(i+1)
        pi_list.append((pi/(i+1))*4)
        pi+=1
    elif Xlist[i]**2+Ylist[i]**2 <= 1:
        pi+=1

print((pi/(i+1))*4)
plt.plot(Number_list,pi_list)
plt.show()

What this is not dirty It works, but the same process is written many times and it's awkward, so I rewrote it in the morning.

import matplotlib.pyplot as plt
import random

Xlist=[]
Ylist=[]
Number_list=[]
pi=0
pi_list=[]

for i in range(15000):
    Xlist.append(random.uniform(0,1))
    Ylist.append(random.uniform(0,1))
    if (i+1)%10 == 0:
        Number_list.append(i+1)
        pi_list.append((pi/(i+1))*4)
    if Xlist[i]**2+Ylist[i]**2 <= 1:
        pi+=1

print((pi/(i+1))*4)
plt.plot(Number_list,pi_list)
plt.show()

It's a little better. Let's explain the code line by line.

import matplotlib.pyplot as plt
import random

In the first line, a library called ** matplotlib **, which is convenient for drawing graphs, is available under the name ** plt **. The second line imports a library that can generate a random value called ** random **.

Xlist=[]
Ylist=[]
Number_list=[]
pi=0
pi_list=[]

Here, the variables necessary for calculating various pis are declared. The coordinates of randomly generated points are stored in ** Xlist and Ylist **, and it is determined whether or not the points are inside the circle in a later calculation. ** Number_list ** creates the arithmetic progression required for graph creation. Actually, it is faster to make arithmetic progression first using numpy, but this time it was troublesome to find out the method, so I passed it (Saborima). ** pi ** is used to save the total number of points plotted inside the circle, and ** pi_list ** is used to save the calculated pi in list format.

for i in range(15000):
    Xlist.append(random.uniform(0,1))
    Ylist.append(random.uniform(0,1))
    if (i+1)%10 == 0:
        Number_list.append(i+1)
        pi_list.append((pi/(i+1))*4)
    if Xlist[i]**2+Ylist[i]**2 <= 1:
        pi+=1

Here, the for statement is used to repeat the following process 15,000 times (humans will die). Use the ramdom module to store the coordinates of points in ** Xlist and Ylist **. For convenience of explanation, I will explain the block of ** if Xlist [i] ** 2 + Ylist [i] ** 2 <= 1: **. I won't explain the annoying explanation here, x^2+y^2=r^2 For the time being, if the numbers stored at the end of Xlist and Ylist are squared and added, and the radius is less than the square, you can see that there is a point in the circle. The above if statement expresses this as a mathematical formula. Since this if statement shows that the point is inside the circle, add 1 to pi. Finally, about the block of ** if (i + 1)% 10 == 0: **. Here, the pi is calculated once every ten times and stored in pi_list, and then the number is added to make Number_list an arithmetic progression.

plt.plot(Number_list,pi_list) plt.show() This is a program that only creates graphs, so I will not explain it (cut out).

At the end

I don't think you need it, but I made it PDF and summarized the contents of this time. The program history is surprisingly short, so feel free to let us know in the comments if you make a mistake! !! Please leave a comment if you like.