this post was submitted on 28 Nov 2023
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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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Numberphile video
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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.