[xenophanes]

Worked out the math to get rid of the loop.

  def efficient(x)
    num = (Math.sqrt(2 * x + 0.25) - 0.5).floor
    num2 = (num**2 + num)/2
    [x-num2, num]
  end

Edit: Or:

  def efficient2(x)
    num = (Math.sqrt(2 * x + 0.25) - 0.5)
    num2 = ((num - num.floor) * num).round
    [num2, num.floor]
  end