# montePi.py - combined listings 2.5 and 2.6
# from Miller/Ranum text

import random
import math
import turtle

# montePi - approximates pi by Monte Carlo simulation
def montePi(numDarts):
    
    inCircle = 0       

    for i in range(numDarts):
    	x = random.random()
    	y = random.random()

    	d = math.sqrt(x**2 + y**2)   
	
    	if d <= 1:
    		inCircle = inCircle + 1
	
    pi = inCircle/numDarts * 4

    return pi

# showMontePi - same as montePi, but also shows
# the simulation with turtle graphics
def showMontePi(numDarts):
    wn = turtle.Screen()
    drawingT = turtle.Turtle()
    
    wn.setworldcoordinates(-2,-2,2,2)
    drawingT.hideturtle()
    
    drawingT.up()
    drawingT.goto(-1,0)
    drawingT.down()
    drawingT.goto(1,0)
    
    drawingT.up()
    drawingT.goto(0,1)
    drawingT.down()
    drawingT.goto(0,-1)
    
    circle = 0
    drawingT.up()

    for i in range(numDarts):
        x = random.random()
        y = random.random()

        d = math.sqrt(x**2 + y**2)

        drawingT.goto(x,y)
        
        if d <= 1:
            circle = circle + 1
            drawingT.color("blue")
        else:
            drawingT.color("red")
            
        drawingT.dot()

    pi = circle/numDarts * 4

    return pi