Paper sizes

I've tried in the past to explain how awesome the sqrt(2) ratio used as the basis of DIN/ISO page sizes is, but there are some very dumb people on HN: https://news.ycombinator.com/item?id=7821947

When someone claims uncritically that the ratio of any two integers is √2, I get a little edgy. I'm also having a hard time following this simplification:

    A / √A = A × A / A = A

Huh? This only holds if √A = A = 1. I haven't checked the rest, but this doesn't give me much confidence.

Of course, knowing those Europeans, these sizes do probably make tons of sense on paper (see what I did there?), even if this isn't the best explanation of it.

Is this the place to bring "inches vs cm" on the table ? :p

I really wish we'd switch to the ISO-216 sizes. A4 to A3 is so much more enjoyable and painless than Letter to Tabloid. This kind of thing came up often while making posters for campus because it was cheaper to NOT print out all of the posters on Tabloid. Rather, using a mix of Tabloid (for the important poster posting spots) and Letter (for unimportant spots and as flyers for handout). Always ended up having to spend more time to make two layouts because of it. And A4 to A5 for booklets without having to re-layout the document is a huge plus too! And for books, I like to use B4* to fold in half. (B5 pages are nicer than A5 pages for the kind of books I tend to read.) The proportions are all the same, so it just works! One layout, many paper size (of the same proportion) possibilities!

Edit: Additional note with regard to the book publication (depending on printing and binding method used)... Sometimes/often this is printed on something like A3 size for bleeding and with crop marks. The A3 paper is then folded and cut, so that the pages become B5 size. (Signatures essentially composed of folded B4 as a consequence of the cropping. There is of course difference between the outermost sheet and the innermost sheet in each paper signature, which is why it's all cropped at the end.)