function pi_grid(r)
	r_squared = r^2
	inside = 0
	for i = 1:r 
		for j = 1:r
			if (i-0.5)^2 + (j - 0.5)^2 < r_squared
				inside +=1
			end
		end
	end
	4 * inside / r_squared
end

function pi_rand(n)
	inside = 0
	for i = 1:n
		if sum(rand(Float64, 2).^2) < 1
			inside += 1
		end
	end
	4 * inside / n
end

function pi_rect(n)
	dx = 1 / 2
	r = n * dx
	r_squared = r^2
	x = dx / 2
	sum = 0
	while x < r
		y = sqrt(r_squared - x^2)
		sum += y * dx
		x += dx
	end
	4 * sum / r_squared
end

for i in [10, 10^2, 10^3, 10^4, 10^5]
	println(i^2)
	println("Random    : ", pi_rand(i^2))
	println("Fixed     : ", pi_grid(i))
	println("Rectangles: ", pi_rect(i^2))
	println("===")
end