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It blows our hivemind that the United States doesn't use the ISO 216 paper size standard (A4, A5 and the gang).
Like, we consider ourselves worldly people and are aware of America's little idiosyncrasies like mass incarceration, the widespread availability of assault weapons and not being able to transfer money via your banking app, but come on - look how absolutely great it is to be European:
The American mind cannot comprehend this diagram
[Diagram of paper sizes as listed below]
ISO 216 A series papers formats
AO
A1
A3
A5
A7
A6
Et.
A4
Instead, Americans prostrate themselves to bizarrely-named paper types of seemingly random size: Letter, Legal, Tabloid (Ledger) and all other types of sordid nonsense. We're not even going to include a picture because this is a family-friendly finance blog.
As a math nerd, I appreciate the fractaline nature of your paper.
But as an american, what is the practical advantage?? The sizes are so far apart, and you dont get papers with different ratios? Like for example Letter and Legal are both 8.5 inches wide, can be used in any standard cheap household printer, legal is just longer so you can fit more stuff on the page. Letter paper folds into thirds to fit snuggly in an envelope and legal folds into fourths. Other paper sizes are so niche and rarely used why does it matter if theyre a perfect mathematical ratio or not?
The advantage is folding.
When folded at the middle it becomes the next size.
So if you have an A4 paper but don't have the proper C4 envelope, you can fold the paper in half and put it in a C5 envelope. This is standard.
Let's then imagine that you don't have a C5 envelope either, but only have the remaining Christmas card envelopes, which are C6. So you just fold your paper one more time at the middle and it'll fit again.
Also, the area of A0 is 1 square meter. You probably don't nornally have an A0 paper around, but that doesn't matter, because you can take 8 pieces of A3 or 16 pieces of A4 papers, tape them together and it'll be A0.
Now it isn't actually a square meter. It's the same area, but it's not square. No, the length and width makes the golden fucking ratio. This might be irrelevant for a legal document, but it's pretty neat if you want to make a nice drawing.
Paper come in reams. Reams come in boxes. Boxes come on pallets. The paper boxes fit perfectly on a pallet in both length and width, so the layers of boxes can be placed either way in an interlocked pattern. This is mostly a box design thing though. American paper also fit on American pallets, but without the connection through the sizes, you cannot make a pallet with mixed sizes and expect it to fit.
Forgot to add: the real beauty isn't the paper size. It's simply having a standard. Cans and bottles and lots of stuff follow similar metric standards. It's possible to mix everything and still make it fit snuggly on a euro pallet.
Isn't the ratio of length and width of A-papers square root of 2 and not the golden ratio?
Correct. A piece of paper with the golden (aspect) ratio would have the property that if you remove the large square (with side length equal to the shortest side of the rectangle) then the remaining rectangle has the same (golden) aspect ratio.
The ISO216 ratio of 1:sqrt(2) has the property that if you cut the paper in half then both halves have the same aspect ratio as the original larger piece.
People tend to confuse these two properties as they both involve the remaining rectangle having the same aspect ratio as the original piece, but the process to bisect the sheet is different.