π rule
::: spoiler alt-text 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. :::
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.