this post was submitted on 28 Nov 2023
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Well yes, the rest of the world does have better paper. 21×29.7, the only ratio to conserve itself when halving the sheet
Wait, is that true? Is there something special about that ratio in particular that lets it conserve ratio when dividing?
And IIRC, A0 is 1m²
There also is B0, which is exactly 1 by the root of 2 meters.
Beautiful.
Yes it's true. It's the square root of 2, which is why it works.
Legend has it that Leonardo da Vinci came up with it
Here's a fun CGP Grey video on the matter: https://youtu.be/pUF5esTscZI?si=9czdx4u8jWruZoui
untrackered link: https://youtu.be/pUF5esTscZI
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Here you go, proof at ~2 min in.
Edit: for those who don't want to use YouTube anymore. If a is the long side and b is the short side of a rectangle. Halving the rectangle will make the long side b and the short side 1/2 a. If the ratio is preserved when halving, we get:
a/b=b/(1/2 a)
a^2=2b^2
a^2/b^2=2
a/b=sqrt(2)
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Here you go, proof at ~2 min in.
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Yes, this particular ratio allows the fact that you can fold a A3 paper in two and get two A4 sheet
Besides the Grey video heres an oldie but goodie Numberphile video about it
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It's called the Golden Ratio and has a lot of neat properties! Da Vinci and other nerds love(d) using it in art.
I didn't know there are part of the world which doesn't put A4 in their printers
Relation 1 to SQR 2, from A0 of 1m2 to A5 letter format (A4, A5 most used in the EU), every time the half of the next bigger format. Easy to remember.
https://www.papersizes.org/a-paper-sizes.htm