printer printer everywhere

When I got my tickets back from the printer at work, I thought the printer had eaten my paper in a strange way. But I had forgotten that in Europe the standard size of paper is A4 and not "Letter"! To my shock and surprise, the PDF output by the Renfe website for my train tickets this weekend fit perfectly on this oddly-shaped piece of paper that came out of the printer. The difference looks like this:

(graphic created by me)

American standard "Letter" paper is 8.5 in x 11 in (216 mm x 279mm). A4 standard paper is 8.27 in x 11.69 in (210mm x 297mm).


So I did a bit of research. As it turns out, the "A" sizes that are used in Europe are based on a standard aspect ratio of square root of 2. Additionally, each successive smaller size of paper has it's dimensions constructed as follows: if size A0 has dimensions C x D, where D is smaller, then size A1 will have dimensions D x C/2, A2 will have dimensions min(C/2, D) x max(C/2, D)/2, and so on. Note the pretty picture from Wikipedia:

(graphic taken from Wikipedia)

As always, I think the European system makes more sense, I was just momentarily surprised.