They always do things better elsewhere. In his 2011 Gresham College Lecture John Barrow takes a swipe at us Americans because “There are only three countries in the world that do not use the paper size aspect ratios I have talking about so far, the so-called International Standard, the USA, Canada and Mexico. They use a curious collection of historically somewhat ad hoc paper sizes.”

Here’s a diagram showing the “logical”  International Standard folding down of an A0 sheet (which measures 1 square meter  — but only approximately, as you’ll find if you do the math. But when you stray from the theoretical world of mathematics clunky reality tends to get in the way, like the thickness of the blade making a cut, or the tick mark on a ruler, and the inability of people to hit exactly the same number every time they do a measurement). Superimposed in red in the diagram are American Legal and Letter sizes. But it is true that if you start with an A0 sheet and fold away, you should be able to end up with a tiny 52mm x 74mm A8 bit of paper — in theory you can go on till you reach A10. For those of you who remember being told paper could only be folded six or seven times, think rather of cuts than folds, and view this video of a 13th fold being successfully completed. (Video via Mental Floss.)

(If you don’t see a video here, click on the title of this post in order to view it in your browser,)

Now American cut paper sizes are of course not just an ad hoc choice. They are based upon ANSI (American National Standards Institute) standard ANSI/ASME Y14.1, which used Letter size, 8½” x 11″ as its basis. Contrary to what Professor Barrow implies in his lecture God did not include a paper aspect ratio of 1:√2 in his briefing to Moses on Mount Sinai. It may well be neat and nice that A3 and A4 etc. all enjoy a relationship between length and breadth which is based on √2 and can each be derived by cutting their predecessors in half maintaining the same proportional relationship between the long side and the width. But neat and nice is just neat and nice. As Barrow tells us about √2, “This number, famously, is an irrational number, and that fact was discovered by the Ancient Greeks. It was known, supposedly, to the Pythagoreans, and there are stories and legends that the first person to discover it was regarded as an enemy of the people and thrown into the sea because he had unveiled something that was indeed irrational and therefore dangerous to the world of thought.” Clearly we in America have taken care to protect ourselves against that irrationally (if only by adopting a completely different basis of irrationality), and while it may be annoying to the purist that the margins of a document printed on legal paper will change if reduced and printed out on a letter size sheet, it really doesn’t matter in any practical and meaningful sense, does it?

Paper sizes were only standardized in the last quarter of the 20th century. Prior to that they were maintained by custom and convention. Britain’s participation in the International Standard no doubt has something to do with its membership of the EU: maybe they’ll want to get back to good old foolscap again. The reason a sheet of paper is of a certain size originally resulted not from far-sighted papermakers conferring as to what they should do in accordance with some Platonic ideal. The aspect ration, which may or may not have had something to do with the Golden Ratio, was decided upon by each vatman who would make his mould as best suited him. He’d no doubt try to get the biggest sheet out at any one time, and the width would be governed by the extent of his reach with arms stretched wide. The breadth would then follow with considerations of weight and balance coming into the picture. Make it too big and you won’t be able to dip the mould and lift it: make it too small and you’ll get exhausted making handkerchief-sized paper. Who’s to say that the idea of what shape a page should be may not have been influenced by the size of a sheep or a calf, as early papermakers were of course competing with parchment and vellum?

Long before the late 20th century paper sizes for book work had been fixed by the sizes of printing presses. Of course printing press sizes would initially have been influenced by the sizes of paper available. Mutual reinforcement continued until it would became insane to produce paper measuring 26″ x 39″ or a multiple thereof for the American market, where a standard of 25″ x 38″ had evolved.