Interesting, I'd never thought about this before. In case you (or anyone else) are still wondering... If an A3 sheet is X units by Y units (with X the long sid

Interesting, I'd never thought about this before. In case you (or anyone else) are still wondering... If an A3 sheet is X units by Y units (with X the long side) and A4 is 2Y units by X units then their ratios are X/Y and 2Y/X, respectively. If these are equal we have 2Y/X = X/Y cross multiplying gives 2Y^2 = X^2 rearranging and taking a square root (X and Y are positive) gives X/Y = sqrt(2).