“This is something of a shock, if you ponder it, because rectangles do not normally behave like this.”
Cut an A4 sheet in half and you get two A5 sheets with the same shape. That only works with a side ratio of the square root of two. A0 is exactly one square meter, so an 80 gsm A4 sheet weighs 5 grams. Lichtenberg worked this out in 1786. America still uses Letter.