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

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+"""
+@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()