maths.pi_generator
==================

.. py:module:: maths.pi_generator


Functions
---------

.. autoapisummary::

   maths.pi_generator.calculate_pi
   maths.pi_generator.main


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

.. py:function:: calculate_pi(limit: int) -> str

   https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
   Leibniz Formula for Pi

   The Leibniz formula is the special case arctan(1) = pi / 4.
   Leibniz's formula converges extremely slowly: it exhibits sublinear convergence.

   Convergence (https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80#Convergence)

   We cannot try to prove against an interrupted, uncompleted generation.
   https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80#Unusual_behaviour
   The errors can in fact be predicted, but those calculations also approach infinity
   for accuracy.

   Our output will be a string so that we can definitely store all digits.

   >>> import math
   >>> float(calculate_pi(15)) == math.pi
   True

   Since we cannot predict errors or interrupt any infinite alternating series
   generation since they approach infinity, or interrupt any alternating series, we'll
   need math.isclose()

   >>> math.isclose(float(calculate_pi(50)), math.pi)
   True
   >>> math.isclose(float(calculate_pi(100)), math.pi)
   True

   Since math.pi contains only 16 digits, here are some tests with known values:

   >>> calculate_pi(50)
   '3.14159265358979323846264338327950288419716939937510'
   >>> calculate_pi(80)
   '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899'


.. py:function:: main() -> None