''' estimate pi by throwing darts at a board

    fill in all ??? with appropriate number or formula
    when you are done, run one of your functions! ( try forPi(100) or whilePi(0.001) )
'''

import random
import math

def forPi(n):
    '''forPi uses a for loop to return an estimate of pi for n darts thrown
        at a 2x2 square with a circle of radius 1 inside it by using the
        ratio of the areas and the ratio of the darts out of the total that
        land in the circle.'''
    inSoFar=0
    for i in range(n):
        total = i+1                             # counter for total number of points generated so far
        xCoord = random.uniform(-1.0,1.0)       # x coordinate of random point
        yCoord = random.uniform(-1.0,1.0)       # y coordinate of random point
        # use Pythagorean theorem to find rSq:
        rSq = ???                               # distance of random point from (0,0)
        # if the point is inside the circle (how dow we know???), add one to inSoFar
        if rSq <= ???:
            inSoFar+=1                          # counter for number of points inside the circle
        piEst = ???                             # our estimate for pi based on i+1 darts
        print(inSoFar,' hits out of ', total,' throws so that pi is ',piEst)
        
def whilePi(error):
    '''whilePi uses a while loop to return the number of darts thrown
        at a 2x2 square with a circle of radius 1 inside it that give an
        estimate of pi within the given error bound'''
    inSoFar = 0
    total = 0
    while True:
        xCoord = random.uniform(-1.0,1.0)
        yCoord = random.uniform(-1.0,1.0)
        rSq = ???                               # same formula as in the for loop!
        total+=1
        if rSq <= ???:
            inSoFar+=1
        piEst = ???
        print(inSoFar,' hits out of ', total,' throws so that pi is ',piEst)
        if abs(math.pi-piEst)<=error:
            break