Tuesday, November 18, 2008

the ISO paper size concept

I've been using ISO paper sizes (A4, A3, etc) since the dawn of (my) time. I have even worked for a company that makes optimisation software for paper industries around the world. But I have never ever questioned the rationale behind their sizes. Well it turns out that the sizes are such that if you take any paper sheet of size An and fold it across the long side you'll get two An+1 sheets. So, if An has (x, y) dimensions, then An+1 will have (y, x/2) dimensions. Keeping the ratio constant gives us x/y = y/(x/2) or x/y = 2y/x hence x/y=sqrt(2)! So the aspect ratio of the sides for every paper size is 1:sqrt(2). In other words the ratio of any square's side to its diagonal. Given that A0 has this ratio and an area of 1sqm, we get the (0.841, 1.189) dimensions, and applying the halving process we reach the all too familiar A4 paper size of (0.210, 0.297). Since the sqrt(2) is an irrational number (1,4142135623730950488016887242097...), actual dimensions are always rounded to the nearest millimetre; there's even a type for calculating that but I'll spare you the details. ISO 216 has all that and more. For a free summary of the standard you may also have a look at Wikipedia.