Calculate pi using numeric integration

pi.py

# Calculate pi using numeric integration
# @autor Lukáš Plevač <xpleva07@vutbr.cz> (BUT FIT)
# @date 2.6.2021
# CC0 license - No Rights Reserved.
#
# taken from the relationship:
#
# pi * r ** 2     S of circle
# ------------ = --------------------------
#  (2r) ** 2      S of square around circle
#
# let r = 1
#
#   pi        SC
# -------  = ----
#    4        SS
#
# pi = SC / SS * 4
#

from numpy import arange

##
# Is point in circle with r = 1 and s = [0,0]
# @param point - array with x and y of point
# @return bool
def in_circle(point):
    return (point[0] ** 2 + point[1] ** 2) <= 1 # from distance of point and [0,0]

##
# Calculate pi using Numeric integral
# @param step - size of step for numeric integration
# @return float number near to pi number
def pi(step = 0.001):

    c_points = 0 # mumber of points in circle
    t_points = 0 # number of points in total (square)

    # Numeric integral of 1/4 circle and square 0 .. 1
    for y in arange(0,1,step):
        for x in arange(0,1,step):
            
            if in_circle([x,y]):
                c_points += 1
            
            t_points += 1

    # integration of circle can by calc as c_points * (step ** 2) and of square is t_points * (step ** 2)
    return c_points / t_points * 4 # (step ** 2) is in fraction in denominator and numerator


## test it
print(pi(0.0003)) # 3.1415396584750237