How does this size have anything to do with the metric system, it could have been any units of length with same ratio.
As such A1 is 1/2 m², A2 is 1/4 m², A3 1/8 m², A4 is 1/16 m².
I would call this tied to the metrics system. It never occurred to me that I could approximate odd 1m² areas with 16 sheets of A4... I found this enlightening from the original article. TIL.