From 32ceec550f085439404fe1bbdc8d6e952a269595 Mon Sep 17 00:00:00 2001
From: MatteoRaso <33975162+MatteoRaso@users.noreply.github.com>
Date: Sat, 8 Feb 2020 15:47:11 -0500
Subject: [PATCH] Added a Monte Carlo simulation (#1723)

* Added montecarlo.py

This algorithm uses a Monte Carlo simulation to estimate the value of pi.

* Rename montecarlo.py to maths/montecarlo.py

* Add files via upload

* Delete montecarlo.py

* Rename montecarlo.py to maths/montecarlo.py

* Update montecarlo.py
---
 maths/montecarlo.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 maths/montecarlo.py

diff --git a/maths/montecarlo.py b/maths/montecarlo.py
new file mode 100644
index 000000000..903012429
--- /dev/null
+++ b/maths/montecarlo.py
@@ -0,0 +1,43 @@
+"""
+@author: MatteoRaso
+"""
+from numpy import pi, sqrt
+from random import uniform
+
+def pi_estimator(iterations: int):
+    """An implementation of the Monte Carlo method used to find pi.
+    1. Draw a 2x2 square centred at (0,0).
+    2. Inscribe a circle within the square.
+    3. For each iteration, place a dot anywhere in the square.
+    3.1 Record the number of dots within the circle.
+    4. After all the dots are placed, divide the dots in the circle by the total.
+    5. Multiply this value by 4 to get your estimate of pi.
+    6. Print the estimated and numpy value of pi
+    """
+
+
+    circle_dots = 0
+
+    # A local function to see if a dot lands in the circle.
+    def circle(x: float, y: float):
+        distance_from_centre = sqrt((x ** 2) + (y ** 2))
+        # Our circle has a radius of 1, so a distance greater than 1 would land outside the circle.
+        return distance_from_centre <= 1
+
+    circle_dots = sum(
+        int(circle(uniform(-1.0, 1.0), uniform(-1.0, 1.0))) for i in range(iterations)
+    )
+
+    # The proportion of guesses that landed within the circle
+    proportion = circle_dots / iterations
+    # The ratio of the area for circle to square is pi/4.
+    pi_estimate = proportion * 4
+    print("The estimated value of pi is ", pi_estimate)
+    print("The numpy value of pi is ", pi)
+    print("The total error is ", abs(pi - pi_estimate))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()