The area of a circle is defined as πr^2. Estimate π to 3 decimal places using a Monte Carlo method.

Daily_coding_Problem_14.py

import numpy as np

def dst_to_origin(x,y):
    return np.sqrt(x*x + y*y)

def monte_carlo_pi():
    '''
    sq_area=(2*r)**2
    cir_area=pi*(r**2)
    
    pi*(r**2)     No.of Points inside Circle           (2*r)**2 
    ---------- == --------------------------   => pi = --------
    (2*r)**2      No.of Points inside Square           (r**2)
    
             4 * No.of Points inside circle
    ==> pi = ------------------------------
                 Total no.of Points
    '''
    x=np.random.rand(100000)
    y=np.random.rand(100000)
    circle=0
    for i,j in zip(x,y):
        if dst_to_origin(i,j) <=1 :
            circle+=1
    return (circle/100000)*4