If you continue the A4 paper scale the sheet of A34 would fit inside a human cell and A
negative 47 would be bigger than the earth.
The main size of the A4 paper scale is somewhat unsurprising the A4 piece of paper.
A4 is exactly 297 millimetres by 210 millimetres.
Even if that may sound a bit arbitrary it isn't.
it's a very deliberate measurement.
Someone hasn't just plucked that out of thin numbers.
What they did was start with a zero and work their way down.
We can reverse the process quite easily if you have two A4 sheets and you put them side
by side they make exactly the same shape of one A3.
Two A3s together and you an A2 and two A2s give you an A1 and two A1s side by side is
the same size as a A0.
That's where it all started.
An A0 is exactly one meter squared in area.
It's a very nice and very precise area and then you start halving it to work your way
down the scale.
So you cut it in half, A1s have half a square meter of area, A2s have a quarter square meter
of area, A3s have an eighth of a square meter of area, and A4s have a sixteenth of a square
meter of area.
It's one to the two to the power of whatever A is.
It's brilliant.
US paper sizes, their poster child is of course the letter sized pieced of paper.
And if you're wondering where they got the measurement of a letter size, which is exactly
eight and a half inches by eleven inches, well it comes from the fact that well it comes
from, if you take from there to there right, if you go from maybe there(ish.)
About that, if you get about a quarter that's about US letters that's the best we got.
Someone really has pulled that out of there assumption, we really have no idea where US
letter sizes come from.
The main argument I've heard is that you get a guy's arm, that is four times that length
because if you fold it in half and then fold it in half again, and that's the size of paper
as you get it printed, so US letter size is based on how you would fold a sheet.
I will admit that one valid criticism of my entirely unbiased history of paper sizes is
that both of the scales are based on arbitrary units ultimately.
So the A4 paper scale is based on a meter, that's just some unit humans made up, and
the US paper sizes with the letter sizes it's wonderfully precise eight and a half by eleven
inches is based on the inch.
An equally valid but arbitrary unit of measurement.
Unfortunately that's not the case.
Meters are vastly superior to inches.
A meter, is exactly one forty millionth of the circumference of the earth, well, at its
best we could measure at the time, but the point remains when you hold a piece of A4
paper in your hands the object you are holding, it's size is determined by the planet we live
on.
How brilliant is that?
You're holding part of the earth in your hands.
And with an inch, and inch is officially well about, well about that, I mean the official
original definition of an inch is that it is three barley corns.
What do you expect from a measurement that was developed as far as we're aware, the 600's.
Our earliest definition of the inch comes from the year 1324 when King Edward II specified
that one inch is exactly three grains of barley, dry and round, those are both very important
attributed, placed end to end length ways.
Of course something spherical laying length ways is an unnecessary thing to say but this
is the whole point right, you can either have a paper scale based on the planet we all know
and love using scientific measurements, or you can have a paper size based on a dead
king who enjoyed lining up seeds.
That said we don't actually care about the history of paper sizes, what we do care about
is are they still useful?
Are they good for the here and now?
And you don't just need one size of paper you need a whole range of different useful
sizes, and as I said before A4 paper does this nicely.
By halving or doubling you can get a whole range of sizes.
US paper, to their credit, also do this very well.
They have a whole range of different sizes to suit the various needs of the modern American.
As I said before they have letter size, that's what you use when you're writing a letter,
that's the eight and a half by eleven inches we talked about.
Then you have government letter size.
This is for if you're writing to the government, maybe to tell them what a great job they've
been doing recently.
And that's a different size, that's eight inches by ten and a half inches.
You then have ledger, should you be writing a ledger, that's seventeen inches by eleven
inches, you have tabloid, that eleven inches by seventeen inches, which you may notice
is remarkably similar to ledger.
Ledger and tabloid are exactly the same size one is just turned on it's side.
You don't get a different size piece of paper by rotating it slightly, but that's beside
the point.
You then work your way down to legal, that's what you do if you're suing someone.
That's eight and a half inches by fourteen inches, which is actually the same size as
normal letter except it's a little bit longer so you've got room for all the small print
at the bottom.
And then you've got junior legal that's what you use when you're suing a child.
That's eight inches by five inches, kindof the fun size legal piece of paper.
Now A4 paper has a much nicer predictable scale.
Not only can you calculate the next size up and down very easily just by doubling or halving,
whereas the US scale is completely arbitrary.
But there is no limit on the A4 paper scale.
US sizes you only get the ones that you've been handed down, doesn't sound like freedom
to me.
Whereas A4 paper you're as free to go as large or as small as you want.
In fact you can keep halving and keep getting smaller and smaller and smaller with pretty
much no limit.
There is one slight limit in that the size is always rounded to the nearest millimetre.
So once you hit A19 your so small your piece of paper when rounded is two millimetres by
one millimetre.
Anything below that is one millimetre by one millimetre or non-existent.
But theoretically if you don't bother rounding you can actually continue for as long as you
want.
Should you get all the way down to A34, that's actually 9.06 micro meters by 6.41 micro meters.
That's smaller than a human cell.
And in the other direction you can get bigger and bigger and bigger.
If you double A0 you get what I call A-1.
Technically that's not it's real name but go with me here.
If you keep doubling in the opposite direction by the time you get to A-47 that's now 14,094
kilometres along the long side and 9966 kilometres along the short side.
That piece of paper A-47 is bigger than the earth.
The last thing to bear in mind is aspect radio.
When you're enlarging or reducing something from one size piece of paper you don't want
to change the radio of the two sides.
Otherwise you'd get things that are either squashed down or stretched out.
Things are going to look weird.
And if the aspect changes from paper size to paper size you get either that weird distorted
effect or you end up with blank spots around your images.
And that's wasted paper, that's bad for the environment.
What you really want is for every different paper size to be in the same ratio.
Which is exactly what you get for A4 paper.
With US paper, every single size is a different ratio.
With the notable exception of ledger and tabloid.
They're both the same radio as they both exactly the same piece of paper.
All the other ones vary dramatically.
The smallest radio is letter that's where the long side is 1.2941 times the short size
and biggest radio is fun size junior legal where the long size is 1.6 times the short
size.
And every other piece of paper is a different radio somewhere in-between.
A4 paper is completely consistent it is always 1.414213562 and so on, it is always exactly
the square root of 2.
But why the square root of 2?
Why not some less awkward ratio?
And there is a very good point, you could choose any nice convenient ratio and then
use it across an entire range of paper size.
It didn't have to be the square root of 2.
The only reason it is the square root of 2 is because we wanted to keep the other property
the A4 paper scale has.
The fact that if you cut any A paper in half, you get two of the size below it.
And if you put any two together you get the next size up.
That very useful property only exists if you use exactly the square root of two for your
paper sizes.
And that's why we do that.
The square root of two, I mean the whole A4 paper per scale wasn't just plucked out of
the air, someone didn't just go you know what from there to there can I just get like a
quarter of that?
No!
it was very carefully calculated to be the optimal radio for paper sizes.
And that's why the A paper scale is the only rational choice when it comes to paper sizes.