I just thought I share something with you…
Have you ever noticed that if you fold a sheet of A3 paper in half it is the same size as a sheet of A4. This fact is what implies the aspect ratio of ISO standard paper (A3, A4, A5, etc).
If a piece of A4 has long and short sides sides of a and b respectively and a sheet of A3 has long and short sides c and d respectively, and the aspect ratio of A4 and A4 is the same, then:
a/b = c/d
and the long side of A4 is the same as the short side of A3:
a = d
and the short side of an A4 is half the long side of and A3:
b = c/2
d/(c/2) = c/d
(d^2)/(c/2) = c
(d^2)/(c^2) = 1/2
d/c = 1/√2
so the ratio of d/c (the short to long side) of A3 (and therefore any ISO paper size) is 1/√2 or approximately 0.707
I don’t know why I find this interesting, but I thought you might too.