Function pi_estimator

maths/monte_carlo.py:11–39

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. a. Record the number of dots within the circle. 4. After all the dots are

(iterations: int)

def pi_estimator(iterations: int) -> None:
    """
    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.
       a. 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
    """

    # A local function to see if a dot lands in the circle.
    def is_in_circle(x: float, y: float) -> bool:
        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

    # The proportion of guesses that landed in the circle
    proportion = mean(
        int(is_in_circle(uniform(-1.0, 1.0), uniform(-1.0, 1.0)))
        for _ in range(iterations)
    )
    # The ratio of the area for circle to square is pi/4.
    pi_estimate = proportion * 4
    print(f"The estimated value of pi is {pi_estimate}")
    print(f"The numpy value of pi is {pi}")
    print(f"The total error is {abs(pi - pi_estimate)}")


def area_under_curve_estimator(