maths.pi_monte_carlo_estimation

Attributes

prompt

Classes

Point

Functions

estimate_pi(→ float)

Generates an estimate of the mathematical constant PI.

Module Contents

class maths.pi_monte_carlo_estimation.Point(x: float, y: float)
is_in_unit_circle() → bool

True, if the point lies in the unit circle False, otherwise

classmethod random_unit_square()

Generates a point randomly drawn from the unit square [0, 1) x [0, 1).

x
y
maths.pi_monte_carlo_estimation.estimate_pi(number_of_simulations: int) → float

Generates an estimate of the mathematical constant PI. See https://en.wikipedia.org/wiki/Monte_Carlo_method#Overview

The estimate is generated by Monte Carlo simulations. Let U be uniformly drawn from the unit square [0, 1) x [0, 1). The probability that U lies in the unit circle is:

P[U in unit circle] = 1/4 PI

and therefore

PI = 4 * P[U in unit circle]

We can get an estimate of the probability P[U in unit circle]. See https://en.wikipedia.org/wiki/Empirical_probability by:

  1. Draw a point uniformly from the unit square.

  2. Repeat the first step n times and count the number of points in the unit

    circle, which is called m.

  3. An estimate of P[U in unit circle] is m/n

maths.pi_monte_carlo_estimation.prompt = 'Please enter the desired number of Monte Carlo simulations: '