3

A4 (as the whole Ax series) sheets have an aspect ratio of 1.41:1

The plus side of this aspect ratio is scaling. You pick a sheet with an aspect ratio of √2, divide it into two equal halves parallel to its shortest sides, and you get a smaller sheet with an aspect ratio of √2.

Why do rectangles with this sides have this property? Do any rectangle with any other length have the similar property?

Quora Feans
  • 1,059
  • 7
    $1:x={1\over2}x:1$ has $x=\sqrt2$ as its only positive solution. – Intelligenti pauca Jul 20 '20 at 20:46
  • 6
    A similar notable phenomenon: when the ratio of the sides is the golden ratio (that is, $\frac{1 + \sqrt{5}}{2} \approx 1.618$), then removing the largest possible square leaves you with a rectangle of the same aspect ratio – Ben Grossmann Jul 20 '20 at 20:48

0 Answers0