The Logic Behind Metric Paper Sizes

Oily Pakora writes "Those of us in the United States are so used to our Letter and Legal paper sizes. We've seen the A4 paper size option in our printer trays and in printer preference menus. Metric sizes used almost everywhere in the world, save for the US and Canada. Here is an interesting article that discusses all of the aspects of metric paper. For those who enjoy a bit of math, did you know that in the Metric paper system, the height-to-width ratio of all pages is the square root of 2? This means that you can place two sheets of A4 side-by-side and they will equal an A3 sheet exactly, and two sheets of A3 will equal an A2."

Comments

Side-by-sideness

[TyrelHaveman]

You can also put two 8.5x11 (Letter) sheets of paper side by side and it equals an 11x17 (Tabloid) sheet of paper...

Re:Side-by-sideness

[N1RCV]

In the engineering world (in USA). Letter size is A size. Tabloid is B size. 2 B sizes (22x17) is C size. And 24x36 is D size.

Re:Side-by-sideness

[SSpade]

But 11x17 is not the same shape as 8 1/2x11.

That's the real beauty of A4/A3 etc. All the sizes in a given series (A00, A0, A1, A2, A3, A4, A5... or B1, B2, B3...) are the same shape.

So you can photocopy an A4 document onto A3 paper expanding it by the right proportion and it'll fit perfectly. And you can copy two A4 documents onto A3 paper and it'll fit perfectly. Or use psnup to put A4 formatted documents reduced to 2-up on A4 paper with no wasted space.

Try that with letter or legal size....

Re:Side-by-sideness

[barawn]

When you discuss the advantages of metric, it really is about convenience[1]. There's nothing that you can do with metric that you can't with the English system; it is just, generally, more difficult to do with the English system. If you don't care about convenience, and you live in the USA, then you probably don't have any reason to use metric.

That's not quite true - one of the reasons that the Imperial system is moderately convenient for building is that base 12 is divisible by 2,3,4 and 6, so you'll encounter less rounding error if you need to split things up into common numbers. Base 10 is only divisible by 2 and 5. (Incidentally, this is of course why one of the older civilizations used base 60 - it's divisible by 2, 3, 4, 5, and 6, and it's the reason we have 60 seconds in a minute, 60 minutes in an hour).

So, for instance, if you want to break a 1' object into thirds, you can do it exactly. Try doing it with meters - it's 33 and a third centimeters. Most people would say "screw it, it's 333 mm" - but if you now take those "1/3 m" sticks and put 300 of them end to end, you don't have 100 m - you have 99.9 m, and you're a full ten centimeters short. In imperial, 1/3 of a yard is 1 foot. No rounding errors.

There really *are* advantages to the Imperial system - most people, however, simply assume that Imperial sucks and leave it at that.

Metric paper, however, is better designed than US. Being able to print 2 A4 on 1 without much work really kicks.

Re:Drugs teach American kids the metric system.

[Anonymous Coward]

That joke is in the title. From the "forty-rods-to-the-hogshead department."

More usefully...

[MartinG]

you can place two sheets of A4 side-by-side and they will equal an A3 sheet exactly,

More usefully, you can fold an a4 piece of paper in half and it will fit nicely in an a5 envelope.

Re:More usefully...

[srleffler]

you can fold an a4 piece of paper in half and it will fit nicely in an a5 envelope.

Not quite. The envelope would be exactly the same size as the folded paper, which would be too tight a fit. The A4 paper folded in half fits beautifully into a C5 envelope, however, and if you fold it in half again it will fit in a C6. If you don't want to fold your document, you buy a C4 envelope. What a neat system.

Do the math, indeed

[lambent]

Square milimeters of paper:

Letter: 60322.46 mm^2 (215.9mm x 279.4mm)

A4: 62370 mm^2 (210mm × 297mm)

A4 - Letter = 2047.54, or about 3 and 3/16 square inches.

A4 is bigger.

Re:Aka the golden mean

[odsign]

No it's not. The golden mean is (1+sqrt(5))/2. That page you linked even says so.

Re:Drugs teach American kids the metric system.

[compro01]

if i remember corectly a "hogshead" is 63 gallons.

and a rod is 5.5 yards or 16.5 feets so....

damn your car is a gas guzzeler!

504 gallons to go 1 mile!

Re:Yet another reason for the US to switch to metr

[SkankhodBeeblebrox]

Your government did try to switch over, not once, not twice, but three times! (with limited success, according to the 2nd link)

Also according to that 2nd link,

"Federal agencies were required by this legislation, with certain exceptions, to use the metric system in their procurement, grants and other business-related activities by the end of 1992. "

Not sure what that means to a typical U.S. Citizen, but it appears the U.S. will be metric someday :)

Re:Oooo.... root 2!

[Rupert]

Those aren't the same shape.

17 / 11 = 1.55
11 / 8.5 = 1.29

A4 paper is twice the size and the same shape as A5. A3 is twice the size and the same shape as A4. It goes up to A0, which is (ooh) 16 times bigger than A4.

Re:2 x A4 = A3

[hpa]

A0 paper is one square meter.

A4 paper is 2^-4 = 1/16 square meter.

Re:Yet another reason for the US to switch to metr

[fireduck]

except that the US apparently sanctioned the metric system in 1886, and the American Bureau of Standards made the metric system it's standard in 1964. (nice timeline here ). There've been various attempts to further adopt in more recent history, but basically the US doesn't want to change. The metric system is nonexistant as far as general use is concerned. The only "off the top of my head" metric use I can think of are 2 L bottles of coke. nothing else gets metric treatment.

A complex way to point out simplity.

[MrChuck]

...factor of 2

Gee, I just learned that if you take a sheet of A3 and cut it in half, that's A4.
Need a couple sheets of A5? Fine, grab paper from the printer and cut come A4's in half. (or A3's into 4).

But geez, about making a really simple system sound complex...

Me? I've just personally given up Fahrenheit. The GirlF is coping with "wow, it must have dropped 5 degrees in the last half hour."

I'll be ready, cause I saw the movie in school, 'splaining that we'd be all metric by 1976.

Re:A complex way to point out simplity.

[Tony-A]

Gee, I just learned that if you take a sheet of A3 and cut it in half, that's A4.

If you take a D-size sheet of drafting paper,
cut into halves, you have two sheets of C-size drafting paper
cut into quarters, you have four sheets of B-size drafting paper, aka quarto
cut into eight pieces, you have eight sheet of A-size, aka letter, aka octavo.

The metric sizes preserve aspect ratio, the english sizes do not.

Re:A complex way to point out simplity.

[ZeLonewolf]

No, but since you ask:

The number is the measurement below the bust.

an A-cup is a 1-inch difference between the measurement below the bust versus around the bust.
B-cup is 2 inches, C-cup is 3 inches, etc.
DD is the same as E, DDD is the same as EE which is the same as F. This holds valid through an H cup. After that, the interval is 2 inches, with the doubled letter being the in-between value.
This, H-cup is 8", and I-cup is 10", and a 9" difference would be an HH-cup.

The largest bra size manufactured without a special order is a size 60N.

Re:A complex way to point out simplity.

[Anonymous Coward]

just to be picky, that's not quite right:

The number is the number over the bust. The cup letter determines the underbust.

if the overbust is 34" or up, add 5" to the cup size difference.
if the overbust is 32" or down, add only 3.

That means someone wearing a 36C has a 36" overbust and a 28" underbust. (36" -3" -5")

So a 32C (32-3-3=26") has the same underbust as a 34A (34-5-3=26", also)...

(and AA is 1/2" instead of 0.)

Re:2 x A4 = A3

[chris_mahan]

a square meter. a square meter is the base of a cube meter. The cube meter is the volume of one ton of fresh water at sea level at the equator at zero degrees Celcius. 1 ton is 1000 kilo gram. each kilo gram is thus 10cm*10cm*10cm, which happens to also be a liter. 1 gram is 1 millionth of a ton, of 1cm*1cm*1cm. so if a bottle of water is 1000 grams (1 kilo gram), it is also 1 liter. So now I know the volume, the weight, and the measurement of the container. Pretty nifty no?
Density is expressed in a ratio from fresh water at zero degrees at sea level at the equator. Let's say the density of velveta cheese is 1.001. With this, I could tell you the size of a kilo of velveeta, and how large a container to use, and thus how much paper to use to wrap it in. Then I could express this in how many per A0, A1, or A2, since they are derived from the meter. Get it?

Class dismissed.

Re:2 x A4 = A3

[Phisbut]

Cold salt water is -18 Celcius. Inside of your mouth is +36 Celcius. Make those marks on a piece of paper with whatever you're using (assuming you have the tools to make a thermometer), and fold in half (five times over if you can). You'll now have a thermometer with nice floating point numbers where the folds are two-ninths of a degree each.

Not a *whole* lot more complicated when you're good in math ;-)

Not English

[Gonoff]

The metric sizes preserve aspect ratio, the english sizes do not

The sizes of paper you use are not English. In England, and the rest of this country, we use the international standard that includes A4. I suspect that you can buy other standards but I have no idea whatI would have to do if I needed "letter" or "legal" size paper.

Re:Not English

[beanyk]

The sizes of paper you use are not English. In England, and the rest of this country, we use the international standard that includes A4.

This confused me for a while after moving to the U.S. from Ireland. When they say "English" here about units of measurement, they mean what we call "Imperial".

Re:Not English

[Spudley]

Not only do we not use 'English' paper sizes in England, but we never used them.

Before we adopted A4 as our standard printer paper, typing paper was generally sold here in the wonderfully named Foolscap page size.

It was only a few years ago that stationery shops in England stopped selling Foolscap paper... around about the same time that Inkjet printers finally killed the market for dot matrix.

It was standardised printer models that killed off the Foolscap standard.

Wrong

[ChrisMaple]

The density of water is defined as 1 at its maximum, 3.98 degrees C. Zero would be a poor choice, because water likes to freeze there and its density changes drastically. (Handbook of Chemistry and Physics, 58th edistion, page F11)

Re:The Metric System Sucks!!

[Night Goat]

Way to plagiarize, buddy.
http://www.metricsucks.com

At least cite your sources if you're going to pass off others' humor as your own.

Actually...

[cr0sh]

This number is otherwise known as the "golden ratio", it was discovered back in classical Greece and it was known to be the most aesthetically pleasing of all ratios. The Parthenon in Athens was built so that its length and width were dictated by this ratio, it was also used by many Renaissance artists to draw the human body so it seems "perfect".

These supposed "truisms" are actually mostly false - most are due to attempting to find the ratio where it didn't exist in the first place (ala Hoagland's "City of Mars" "mathematical layout", the Great Pyramid's "mathematical layout", etc)...

If you want a great book on the subject of the phi, check out the book "The Golden Ratio" by Mario Livio (ISBN 0-7679-0816-3) to learn more about it than you would ever care to know...

Look at the numbers...

[imsabbel]

and you will see as a true geek that process structure sizes use the same shrinking factors (0.35um, 0.25,0.18,0.13,0.09,....)

Actually

[geekoid]

the US was on course to be completly metric years ago, unfortunatly Reagon cut the funding. I remeber learning the metric system in grade schools in the 70's. Some road signs started appearing that had both speeds on it, as well as speedomoeters. Every public displayed thermometers showd Celsius and Farenheit. Factories had begun the process of changing over, then no more funding.
But, if the only way to get elected is to 'cut taxes', what do you think is going to happen?