Get this stuff out of my head.

Ever Wondered Why You Need to Set the Photocopier to 70%?

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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

so, substituting:

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.