Dimensions of A-series paper

We look at the dimensions of an A-series paper size. The crucial property is that if you fold it in half, the ratio of the long and short sides stays the same.

If $a$ is the length of the short side and $b$ is the length of the long side:

$\frac{a}{b} = \frac{\frac{1}{2}b}{a}$

Therefore

$b^2 = 2 a^2$

Here is an overview of A0 to A8 sizes, with Letter and Legal sizes thrown in for my North American friends.

We do not have to take square roots here to get the lengths since we are using rational trigonometry. Separations between points are represented as quadrances. So,

$A = a^2, B = b^2$

Therefore, for an A paper we have

$B = 2 A$

For the diagonal $C$ we use Pythagoras’ theorem, so

$C = A + B = A+ 2 A = 3 A$

For the exact dimensions you can use the fact that A0 is 1.0 $m^2$, A1 is A0 folded in half, etcetera.

I usually use A4 paper.

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