maths.pi_monte_carlo_estimation
===============================

.. py:module:: maths.pi_monte_carlo_estimation


Attributes
----------

.. autoapisummary::

   maths.pi_monte_carlo_estimation.prompt


Classes
-------

.. autoapisummary::

   maths.pi_monte_carlo_estimation.Point


Functions
---------

.. autoapisummary::

   maths.pi_monte_carlo_estimation.estimate_pi


Module Contents
---------------

.. py:class:: Point(x: float, y: float)

   .. py:method:: is_in_unit_circle() -> bool

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



   .. py:method:: random_unit_square()
      :classmethod:


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



   .. py:attribute:: x


   .. py:attribute:: y


.. py:function:: 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


.. py:data:: prompt
   :value: 'Please enter the desired number of Monte Carlo simulations: '