Pi Approximation in Python (Turtle Dartboard Monte Carlo Simulation)

montecarlopi.py

#!/usr/bin/python

"""
How to think like a computer scientist

Exercise: Approximating the value of Pi with Turtles!

Author: Adrian Arumugam
Date: 2016-01-10

"""

import turtle
import math
import random

# Instatiate Turtle and Screen
fred = turtle.Turtle()
wn = turtle.Screen()

# Dartboard coordinates
wn.setworldcoordinates(-1,-1,1,1)

# We don't want to leave lines by default
fred.up()

# Speed things up when placing darts on board.
fred.tracer(100)

# Highly accurate approximations with >= 1000 darts thrown
numdarts = 1000
insideCount = 0

for i in range(numdarts):
    # Generate random floating points within (-1, 1)
    # Figured out two methods of achieving this.
    
    # .uniform() allows a negative range, returns floating point ints.
    randx = random.uniform(-1, 1)
    # .random() * 2 = [0 ,2], -1 = [-1, 1]
    randy = random.random() * 2 - 1

    x = randx
    y = randy
    
    # Move to position
    fred.goto(x, y)
    
    # Determine how many darts actually fall within the dart board.
    # Dartboard is centred on 0,0 with radius of 1. Therefore need
    # to verify if dart is within 1 unit away from 0,0.
    #
    # Colour red if within dartboard and count. Otherwise colour blue.
    if fred.distance(0,0) <= 1.0:
        fred.color("red")
        insideCount += 1
    else:
        fred.color("blue")
    fred.dot()

fred.hideturtle()

# Consider the area of the circular dartboard. It has a radius of one so its area is pi. 
# The area of the square piece of wood is 4 (2 x 2). 
# The ratio of the area of the circle to the area of the square is pi/4. 
# If we throw a whole bunch of darts and let them randomly land on the square piece of wood, 
# some will also land on the dartboard. The number of darts that land on the dartboard, 
# divided by the number that we throw total, will be in the ratio described above (pi/4).
# Multiply by 4 and we have pi.

print('Percentage of darts inside dartboard: {}'.format(insideCount / numdarts)) # requires Python3
print('Pi Approximation: {}'.format(insideCount / numdarts * 4))                 # requires Python3
print('Ratio of area of cirle to area of square: %f' % (math.pi / 4))
    

wn.exitonclick()