How A4 Paper Got Its Size
We had to make a chart in school, which had to be printed on A3 paper, which we had run out of. That’s when someone said, “Let’s print them on two A4s and stick them together”. This got me thinking more deeply about how A4 was half of A3, and double of A5 – clearly this scaling symmetry was by design. Some quick research revealed that this scaling was used in Germany as early as in the early 1900s, when engineers wanted paper sizes that would scale neatly, whereby when they were folded or cut in half, the shape stayed the same. Most rectangles don’t necessarily behave this way. If you take a random sheet of paper and fold it in half along the longer side, the new rectangle will look wider, i.e. the aspect ratio (the ratio of the length of the rectangle to its breadth) changes. But someone had the genius idea to think about a ratio that doesn’t change when the sheet is folded or cut, and here’s the maths behind it. Suppose the paper has l and b as the...