Pi aproximation using the montecarlo approach written in python using numpy

pi-montecarlo-aprox.py

import numpy as np

class PiMontecarloEstimates:
  @staticmethod
  def area_method(iter):
    """Calculates an aproximation of the value of PI by the area method using `iter` random points.
    Area Method:
      Given that Y = sqrt(1 - x**2) in the range [0, 1] draws a quarter of a circle of radius 1,
      its area is PI/4.
      An estimate can be calculated by drawing N random points in the space [0,1][0,1] and counting how many lie
      under the curve drawn by Y. With this number and the total number of points, we can obtain a 
      ratio of points under the curve against total points, which is equivalent to the empiric probability of a 
      random point falling under the curve. If we multiply this ratio with the area of the space (1 x 1), we have 
      an aproximation of the area under the curve (PI/4). Finally, we multiply this value by 4 to get PI.
      
      
    Expects `iter` to be a positive integer.
    """
    
    # Uniformly distributed random values in range [0, 1].
    # They represent X and Y dimensions of the random points.
    x = np.random.rand(iter)
    y = np.random.rand(iter)
    
    # Function for 1/4 of a circle.
    f_y = np.sqrt(1 - x**2)
    
    # Ratio of random points that lie in the area of `f_y`.
    # We only check the Y values b/c the share X values.
    ratio_is_below = np.mean(y < f_y)
    
    # Multiply by 4 to get PI.
    return 4 * ratio_is_below
  
  @staticmethod
  def average_value_method(iter):
    """Calculates an aproximation of the value of PI by the average value method using `iter` random points.
    Average Value Method:
      Given that Y = sqrt(1 - x**2) in the range [0, 1] draws a quarter of a circle of radius 1,
      its area is PI/4.
      In this approach we generate N random samples of function Y to estimate the average value of the 
      continuous function on the interval [0, 1]. This average value approximates PI/4, so we finish by multiplying by 4.
    
    Expects `iter` to be a positive integer.
    """
    
    # Uniformly distributed random values in range [0, 1].
    x = np.random.rand(iter)
    
    y = np.sqrt(1 - x**2)
    quarter_pi_estimate = np.mean(y)
    return 4 * quarter_pi_estimate