Papersize, how often do you really think about that? Why does that ubiquitous A4 paper have that specific name and size anyway? 210×297 mm seems pretty random.
Well, it isn't. Far from it.
America uses its own collection of random paper sizes, but the rest of us use the very clever and elegant ISO 216 standard.
It starts with a bit of math.
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It starts with a bit of math, that says that a piece of paper with an aspect ratio of 1:√2, can be folded in half and keep that exact same aspect ratio, only 90° rotated.
Imagine what you get if you fold a square piece of paper in half: it has half the original height, but still the same width. Its aspect ratio has changed from 1:1 to 2:1, it has a very different shape now.
Fold it again and it will have an aspect ratio of either 1:1 again, or 4:1, depending on which way you fold it.
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Imagine how easy it is if you can fold a piece of paper in half, and get the exact same shape, exactly half the size, every time you fold it in half.
That's a magic shape you could as the basis for a standard for paper sizes! Let's call this standard "A".
So they started with a big piece of paper with an aspect ratio of 1:√2, and called that "0".
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How big exactly? Well, sensible people are metric, so they took a 1m² area as the basis, which meant an 841×1189 mm piece of paper: "A0".
Fold that in half, and you get "A1". Fold that in half and you get "A2", then "A3" and "A4", all the way up to "A10".
So an A4 is an A0 folded in half 4 times, which results in the aforementioned 210×297 mm.
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But wait, why a 1m² area as standard? Why not a 1m width: 1000×1414 mm?
Sounds nice: same 1:√2 shape as in "A", only slightly larger.
Let's call that standard "B" then, which makes a B4 250×353 mm, slightly larger than an A4.
https://en.wikipedia.org/wiki/ISO_216
#funfacts #papersize #iso216 #a4 #metric #math
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