quick hack for 10/12/18 Riddler Classic problem

graze.py

import random, math

# WLOG, we take the field radius R to be 1 and the stake for the goat's rope
# to be at (1,0).

# random point in the field; sqrt() gives uniformly distributed distance from
# the origin (see https://programming.guide/random-point-within-circle.html;
# thanks, David)
def randPoint():
    randr = math.sqrt(random.random())
    theta = random.random() * 2 * math.pi
    return randr * math.cos(theta), randr * math.sin(theta)

# generator of n random points in the field
def randSeq(n):
    return (randPoint() for i in range(n))

# return True iff (x, y) is within reach of the goat with rope length r
def grazeable(x, y, r):
    return (x - 1)**2 + y**2 <= r**2

# fraction of randomly selected points in field that are also grazeable
# should approximate the fraction of the field the goat can get to
def trial(n, r):
   grazeables = sum(1 for x, y in randSeq(n) if grazeable(x, y, r))
   return grazeables / n