Paper seems to be the only metric unit that defies the main goal to be easy to calculate. Yes, you can calculate area of the paper somehow, but you can’t measure it easily.
It’s supposed to cut neatly in half, but how do you line up your papercutter when the edges aren’t an even number of centimeters?
I know it’s supposed to be in the ratio of cube root of 2 or something, to be the same shape when cut in half, but what on earth good is that?
It was supposed to help Kodak, I guess, since when they cut 8x10 glossy paper into half it becomes 2 5x7’s with an inch of scrap.
But metric photos aren’t scrap free either, because the “A” size shape is not very usable.
And there’s also the A, B, C size business. This isn’t metric’s theme, to use letters.
The Germans didn’t invent that proportion, though - it was the Greeks. They called it the “Golden Rectangle” and used it whenever they could. It’s easier to construct geometrically than arithmetically. You just take a square and draw a radius with its center at one corner from the opposite corner to where it intersects the side of the circle to the longer length.
If you nest a bunch of these together with those arcs intact, you get a geometric spiral, which those little guys inside the nautilus shells have been doing since way before Euclid.
The Greeks thought that the Golden proportion was the most pleasing to the eye, and it was postulated, though I’m not sure ever decided, that using lyre strings with similarly proportional lengths would make the most beautiful music.
Hold up a sheet of A4 and a sheet of US Letter size and see if you don’t think the A4 is a little handsomer.
Of course, Dystopos is describing the Golden Ratio, which is (1+ sqrt(5))/2. It has nothing to do with the ratio of A sizes paper’s length and width, which is sqrt(2).
The cool thing about sqrt(2) as a ratio is this. Say I have a sheet of paper X units wide and Xsqrt(2) units long. It has a ratio of length/width of sqrt(2). Now say we cut that paper in half the short way. Now we have two pieces X units long and Xsqrt(2)/2 units wide. (Assuming the paper is always longer than wide) These new sheets of paper have a ratio of length/width of 1/(sqrt(2)/2). Multiply the top and bottom of that fraction by sqrt(2) and you get…
drumroll…
sqrt(2)
The paper has the same proportions when cut in half. (I know someone already said that) Try that with 8.5 by 11.
In very practical terms: The advantage of A4 sized paper is that if you want to photocopy two sheets together, you put the machine on 50% and you put them both on the copier and PRESTO! the two pages exactly fit in the same proportion.
If you do that with 8.5 x 11, you don’t get the same proportion.
I have also talked to communications experts who claim that the A4 size is better for the human eye to scan and read than 8.5 x 11.
Very minor nitpick - to photocopy two sheets of A4 onto a single sheet of A4 you set the magnification to 1/sqrt(2) = 71%.
It also comes in handy when you want to include very large diagrams in a report - just print a diagram on A3 paper, fold it three times (once in half, and then fold the right half in half again) and it fits flush with the rest of the document (A4) in the binder.