It has a very logical and elegant derivation; the ratio of height to width is 1 : √2, which is why two A4 sheets next to each other make an A3 sheet that has the same aspect ratio: 1 + 1 : √2 = 2 : √2 = √2 : 1

Given that √2 is irrational, at least one of the sides will always be irrational, so it was decided to standardise the area of A0 to be 1 m

^{2}. The inevitable irrational values for the height and width are then rounded to the nearest millimeter.

I take odd comfort from the aspect ratio being mathematical, as there is a good chance that it has been discovered by other civilisations across the cosmos.

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