def distance(x,y)
  Math.sqrt(x * x + y * y)
end

def in_circle(x,y)
  distance(x,y) < 1
end

def random_point
  rand * 2 - 1
end

def pi_from_proportion(nr_trials, nr_within_circle)
  # Square's area is 4, Circle's area is PI. So PI =
  (nr_within_circle / nr_trials.to_f) * 4
end

original_time = Time.now
nr_within_circle = 0

1.upto(100_000_000) do |nr|
  x,y = random_point, random_point
  nr_within_circle += 1 if in_circle(x,y)
  if nr % 1_000_000 == 0
    puts "After #{nr} trials: #{pi_from_proportion(nr, nr_within_circle)}"
  end
end

puts "Calculated in #{Time.now - original_time} seconds."