The Logic Behind Metric Paper Sizes 1461
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."
Comment removed (Score:3, Funny)
Re:Drugs teach American kids the metric system. (Score:4, Informative)
A complex way to point out simplity. (Score:4, Informative)
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. (Score:5, Informative)
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.
Not English (Score:5, Informative)
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 (Score:4, Informative)
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 (Score:5, Informative)
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.
Re:Not English (Score:5, Funny)
"PC Load Letter? What the fuck does that mean?!?"
Re:A complex way to point out simplity. (Score:4, Funny)
Re:A complex way to point out simplity. (Score:5, Informative)
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. (Score:5, Funny)
Re:A complex way to point out simplity. (Score:4, Funny)
weird thing is, i saw that same movie in 1987
When I was in the army (Score:4, Funny)
My first day in the army was the 3rd of December, 2001. Ahem.
Re:A complex way to point out simplity. (Score:5, Funny)
It's called "The Rest Of The World". You'll find we do a lot of things differently here, if you ever bother to look.
Um. Sorry. Bad day.
Re:A complex way to point out simplity. (Score:5, Funny)
Not for long...
Re:Drugs teach American kids the metric system. (Score:5, Interesting)
Re:Drugs teach American kids the metric system. (Score:5, Interesting)
Some lovely linkage:here [idler.co.uk], here [phrases.org.uk] and here [looktours.com].
Re:Drugs teach American kids the metric system. (Score:4, Interesting)
I followed your link to "The Idler" and that site tells a different tale about the origin of "on the wagon," quoted below:
--
"Incidentally this also is the origin of 'on the wagon', after finishing his drink from the last tavern before the gallows, the prisoner would be put 'on the wagon' for the last time, destined never to drink again before his death."
Re:Drugs teach American kids the metric system. (Score:4, Funny)
Silly websites, with their alternative opinions.
Re:Drugs teach American kids the metric system. (Score:5, Informative)
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:Drugs teach American kids the metric system. (Score:5, Funny)
Yep, sounds like a True American car to me.
Re:Drugs teach American kids the metric system. (Score:4, Funny)
504 gallons to go 1 mile!
From here [oteromesa.org], the gas mileage of a modern aircraft carrier is seventeen feet per gallon...so he's getting 40% less distance per unit of fuel.
Consequently, I speculate that his vehicle must be an aircraft carrier...operating on land.
My only question is, where the hell does he park it?
Re:Drugs teach American kids the metric system. (Score:5, Funny)
If it's still fully equipped and armed, then the correct answer is:
Wherever he wants to.
Re:Drugs teach American kids the metric system. (Score:5, Funny)
Re:Just in case the server crashes and burns... (Score:4, Funny)
2 x A4 = A3 (Score:5, Insightful)
Re:2 x A4 = A3 (Score:5, Funny)
Re:2 x A4 = A3 (Score:5, Insightful)
It feels just like that hearing about "US Letter", Yards, Pounds, Stones, Miles et al. YOU HAVE SEEN THE METRIC SYSTEM
(btw, thanks France!)
Re:2 x A4 = A3 (Score:5, Funny)
I wonder why Westerners insist on using both a fork and spoon to eat after they've seen the Spork.
Re:2 x A4 = A3 (Score:4, Funny)
Re:2 x A4 = A3 (Score:4, Insightful)
Re:2 x A4 = A3 (Score:5, Insightful)
On the contrary - you've spent over 100 billion dollars in the last year showing just how much you hate other people doing things differently.
Mod parent up. (Score:4, Funny)
Re:2 x A4 = A3 (Score:5, Informative)
A4 paper is 2^-4 = 1/16 square meter.
Re:2 x A4 = A3 (Score:5, Informative)
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.
Wrong (Score:4, Informative)
It's articles like this (Score:5, Funny)
-B
Re:It's articles like this (Score:5, Funny)
oh, i dunno...can't say i'd mind something rolled with a sheet of A0... @_@
Side-by-sideness (Score:5, Informative)
Re:Side-by-sideness (Score:3, Informative)
Re:Side-by-sideness (Score:4, Interesting)
The DIN A formats all have the ratio of square root 2. That makes it very easy to scale stuff up or down, e.g. if you use a copy machine: copy 2 DIN A4 (= DIN A3) on one DIN A4 without messing up the margins. Cut the sheet in half and you have 2 DIN A5 pages that exactly look like the DIN A4 pages, only half the size.
Re:Side-by-sideness (Score:5, Informative)
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 (Score:5, Insightful)
Putting them side-by-side isn't as interesting as cutting them in half, though. I discovered this when I started printing photos from my inkjet. Photo paper is generally available in the stores in limited sizes. I can buy a bunch of A4, and cut it in half, and I have two A5s. Do it again, and I have A6s, which is nearly a 4x6. Best of all, these paper sizes are all standard, which is good, because my printer doesn't like me to define my own paper sizes. With the American system, I have to measure and cut, which is more difficult.
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.
[1] Of course, using metric in the US imposes a certain amount of inconvenience from compatability issues, but that's another argument.
Re:Side-by-sideness (Score:5, Informative)
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:Side-by-sideness (Score:5, Insightful)
I would have infinitely greater respect for the Imperial system if all of it did indeed work in twelves, like with feet and inches. But inches are not divided into twelfths but sixteenths. Then there are three feet in a yard, 5.5 yards in a rod, 40 rods in a furlong, 8 furlongs (or a nice round 1760 yards) in a mile. 16 ounces in a pound, 14 pounds in a stone, 2000 pounds in a ton. Don't get me started on liquid measure. And ultimately, you have to measure so closely that you *have* to use decimal places of the smallest unit (like 11.6 inches or whatever) - which means tens all round.
Remind me again what makes it easier to use?
Just go with tens. Tens are simple.
Re:Side-by-sideness (Score:5, Funny)
My buddy Heff taught me that trick.
Obligatory (Score:5, Funny)
Audi A4 (Score:5, Funny)
Re:Audi A4 (Score:5, Funny)
Two Audis == One BAM ("Big Assed Mercedes")
Two Mercedes == One average European house.
Wow, those Europeans can apply simple metric system math to everything!
Meanwhile, in America:
Two Mini Coopers side by side == One speed bump for a Hummer H2.
Two Audis in the driveway == A good house to break into.
Two Mercedes == Really, really tacky.
Two Hummers == The energy consumption of a typical third-world country
Two thrid world countries == A re-unified Germany. (I keed!)
Yet another reason for the US to switch to metric (Score:3, Insightful)
Re:Yet another reason for the US to switch to metr (Score:3, Insightful)
Re:Yet another reason for the US to switch to metr (Score:5, Informative)
Re:Yet another reason for the US to switch to metr (Score:5, Informative)
Also according to that 2nd link,
Not sure what that means to a typical U.S. Citizen, but it appears the U.S. will be metric someday
I love it. It helped me get more points on a Chem (Score:4, Funny)
This happened years ago. I had a Chem. test and the question had something to do with densities - I can't remember. But the point is, I remembered that the density of water is one, all the units where metric, and calculating the density, volume, and mass were a no brainer with the metric system.
I once got into a friendly argument with an engineer over the merits of the metric system. His argument "Foot-Lbs. I know what that is - that's obvious! Newton - what the fuck is a Newton."
Re:Yet another reason for the US to switch to metr (Score:5, Insightful)
Re:Yet another reason for the US to switch to metr (Score:5, Funny)
|------| = 10 inches, when in fact
|---------| = 10 inches.
This has caused them to become totally confused with regard to units of measure, and they are thus unable to convert imperial to metric units. Thus, if we were to switch to using the metric system, we would no longer be able to bake apple pies, a situation we are just not willing to accept.
Re:Yet another reason for the US to switch to metr (Score:5, Insightful)
Can you describe a few of these times? I'm being serious... as a novice work worker and DIY home improvement and maintenance guy, I find using mixed fractions very annoying. Yes, you get accustomed to them, but I hardly say that makes it acceptable (hey, people get accustomed to Windows crashing, and find it acceptable to have to reboot or reinstall - I'm not one of them).
Besides, it's not like you can't use fraction in metrics, either - so you say 1/2 cm instead of 5 mm, if it floats your boat.
Re:Huh? (Score:5, Interesting)
Compare that with, say, the foot. 12 inches - easily divisible by 3, 4, and 6. Makes building that shit a lot easier :)
Same goes with volumes - it's easy to convert gallons to quarts to pints. You have to memorize more units (which I agree sucks), but it makes making that recepie easier when you realize you have more guests coming.
Re:Yet another reason for the US to switch to metr (Score:5, Insightful)
It's easy to pick the numbers you like. There are always numbers a given multiplier won't divide nicely to.
The Metric System Sucks!! (Score:5, Funny)
* Government conspiracy
* Microsoft Windows
* Rap Music
* Hondas and their drivers
* Transistors
* Pokemon
* Jerry Springer
* Televangelism
* Toxic waste
* The Republicans
* The Democrats
* Defective and bogus hardware
* Wrenches that dont fit
* Starbucks coffee
* Communism
* Soccer
* The Euro
Re:The Metric System Sucks!! (Score:4, Informative)
http://www.metricsucks.com
At least cite your sources if you're going to pass off others' humor as your own.
It's official... (Score:5, Funny)
I just read an article on metric pages and found it incredibly intresting.
At one point I said "Wow, Cool"
I think I've gone beyond 'geek'.
I feel dirty.
Re:It's official... (Score:5, Funny)
Luckily you can clean yourself up while being compliant to the standard!
Pulp Numerology (Score:4, Interesting)
If you enjoy math.. (Score:5, Funny)
More usefully... (Score:5, Informative)
More usefully, you can fold an a4 piece of paper in half and it will fit nicely in an a5 envelope.
Re:More usefully... (Score:4, Informative)
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.
2 x (8.5 x 11) = (11 x 17) (Score:3, Funny)
I'm not sure about "legal" paper and the rest.
And don't worry everyone, Microsoft is aware [microsoft.com] of the problem! To quote: "The paper sizes in the United States and Canada (such as letter, legal, and so on) do not satisfy the needs of all users in the world market."
Fear not! They'll solve this problem by embracing and extending the ISO paper-size standard. The new sizes will be MS-A4, MS-A3, etc. Of couse, you will only be able to print to these pages from MS apps, but what else is there?
the metric system is fun (Score:5, Funny)
And of course, 5 sheets of almost any metric sized paper folded into origami lions will inevitably merge to form Voltron, a robot so powerful that it will usually let it's enemies kick it's butt around for a good 15 to 20 minutes before it forms the blazing sword and finishes the fight.
Yes... it's your damn fault! (Score:5, Insightful)
Do you have any idea how much trouble and stress you've caused by making Letter the default even with UK set as the country?
Re:Yes... it's your damn fault! (Score:4, Interesting)
So, I went out to get a metric tape measure. Couldn't find a single one in my tiny Texas town. Eventually, I went to the Internet (Amazon.com) to find it. I wanted to get a tape measure with just centimeters on it, but had to settle for one with both inches and centimeters.
Just so I'm never stuck without a metric tape measure again, I bought two of them. Cost me $25 apiece.
Signed, an American who loves the metric system, was scientifically trained with the metric system, and if made emperor of the universe would provide free metric system education to the population at government expense.
metric will win in the end (Score:5, Interesting)
I think the metric system is like Open Source:
It's going to win in the long run -
simply because it's the logical way to go!
If you look at the evolution of things, there have always been different ways of doing stuff, but in the end one of them won - simply because it was undeniably the best way to go - and the others lost out..
American Paper is ugly (Score:4, Interesting)
Obligatory homer paraphrasing (Score:5, Funny)
I only know how to divide by ten!
Ratio Not Only Factor (Score:4, Insightful)
On an unrelated note, one benefit of the English system is that measurements tend to be divisible in more ways. For example, 10 is evenly divisible by 1, 2 and 5. 12 (upon which much of the English system is based) is evenly divisible by 1, 2, 3, 4, and 6.
Not that I think that's a reason not to switch over
Re:Ratio Not Only Factor (Score:4, Insightful)
But there is always 12/9... 1 and 1/3
Metric when divided by the numbers below results in 3 whole numbers, 2 simple fractions (10/4 = 2.5), 3 nice repeating fractions, and 1 ugly fraction (10/7)
Imperial results in 5 whole numbers, 3 simple fractions, 1 nice repeating fraction, and 2 ugly fractions
While Imperial has a higher ratio of nice clean whole numbers when divided, can you tell me 12/7 or 12/11 without a calculator, 10/7? Isn't nice either but all you can really glean from this is that there will always be ugly numbers no matter what system you use.
Metric has a huge advantage with units and scientific notation, how many inches are in a light-year? With metric turning light-years into cm is a lot easier.
At the end of the day though, most of the advantages or disadvantages of using either are nullified by using technology. Creating a worldwide standard system is more important to remove issues in calculations between the two systems.
They are all relative systems as well, as long as unless one system has some "magic relationship" with nature I haven't heard of (metric is based off natural things yes, but water was a bad choice) its simply a choice and a system of standards.
Medevo
Just as Interesting (Score:5, Interesting)
Call me an incorrigible geek, but that little tidbit made me giddy.
Look at the numbers... (Score:4, Informative)
Not as English as you think.... (Score:5, Interesting)
Since I design things (not code), I have to ask what units they want their things in - I remember one conversation with a wholly US based company going like this:
"What units do you want the database delivered in?"
- [SARCASM BOLD] "We are a scientific company.[/SARCASM BOLD]>
"Oh, right."
They made me feel pretty stupid for asking. I'd say across the product industry it's something like 50/50 right now.
Another Cool Ratio (Score:5, Interesting)
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".
It is impossible of cause to prove mathematically that this ratio is the best looking of all irrational numbers any more than it is possible to prove mathematically who is the most attractive human, however it's endurance seems to suggest that it has some base to it. It has links with Fibonacci numbers, it also is encountered when drawing regular pentagrams and decagons.
Due to the aesthetically pleasing nature of this ratio I think it would be fairly cool to have a series of paper sizes based on this ratio for artistic uses, rather than the practical but bland "A" series or the fairly pointless American and Canadian series.
Actually... (Score:4, Informative)
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...
Metric & The US (Score:5, Insightful)
I was once talking with some of family and I happened to say something like: 'It was 2 meters from me...' Immediately, one of my uncles interjected a joking comment about how I was the 'product' of the 'new' Math. We then proceeded to go off on a tangent about the merits of the two systems and how expensive it would be to switch to metric.
At that point though, I was struck by how his comment was loaded with negative connotation, which obviously did not stem simply from an aversion to the cost of a hypothetical switch to metric. I realized that the source of his distaste for metric was really just the instinctive reaction social animals use to build communities. The 'Us Vs. Them' filter that we all use to clump ourselves into social groups.
From this perspective, a human perspective, it makes complete sense to have differing systems of measurement. There would be obvious advantages if we all spoke the same language, but no one is proposing that we make everyone learn Chinese (quit being ethnocentric!). Even if everyone DID speak Chinese, people would still use their native languages at home, en familia. Why? Because the stratification of languages helps us to identify our social groups. In this way, we're 'The people who use miles', and they're/you're 'The people who use kilometers'. Communities, when you come down to it, are just sets of these bifurcations.
Taking all that into consideration, I've thrown in with the english system curmudgeons. Why? For the same reason I'm in favor of driver's tests in 16 languages. Because being human ain't about being efficient, it's about communities.
Re:Metric & The US (Score:5, Funny)
Don't tell George Bush that he's using Arabic numerals...
The simplest reason A4 won't take off in the US (Score:4, Insightful)
As an American physicist, I use SI units for work, but happily use US units for everything else. I don't know why it just pisses off the rest of the world that we like Farenheit, inches, etc. WHO CARES! Why doesn't Europe get ONE FREAKING TYPE OF ELECTRICAL PLUG!
I found it funny that the article predicted the US switching, as I really don't see it happening.
Can anyone tell me why any A4 paper I get in Europe has a purple tinge to it? I find that very annoying.
Re:The simplest reason A4 won't take off in the US (Score:4, Funny)
Joke on USers: (Score:4, Funny)
Even thought the french helped you! That's the real loser part.
BTW: It was Napoleon who established the metric system big time in large parts of his area of influence.
Shame he couldn't follow the other guidelines:
Universal Rule Number One: Never start a land war in Asia.
Holy crap. (Score:4, Funny)
Slow News Day of the Year Award nominee here.
The biggest reason the U.S.A. doesn't use metric (Score:5, Interesting)
Recall that industrial mass production is essentially a 20th century invention, and that by the 1940's it still had not really spread beyond the U.S. and Europe. In World War II, most European industrial capacity was destroyed at one point or another, providing a clean slate to rethink standards for every industry, and to adopt logical standards with no switchover cost.
After WWII, Europe wisely went to the metric system. Developing countries wisely adopted it as well. But the U.S., with its factories intact (and now back to making cars and vacuum cleaners) was saddled (and remains cursed with) with tremendous switching costs. The expense in lost customers and supplier confusion is too great for a company in most industries to unilaterally change. And agreements to change all at once are very hard to achieve.
Empirical evidence:
Newer US major industries (e.g. semiconductors) usually work in metric
(As noted elsewhere) US science is in metric; because switchover costs are lower scientists could switch almost right away.
Well-meaning attempts to effect a switch have been ignored by industry (because of the cost)
US industries with a big international component are often metric (bicycle manufacture)
I suppose the conclusion to draw is that the US is unlikely to switch until either something destroys its industrial factories, or the "old" unswitched industries become so dwarfed by new metric ones that it is actually cheaper for them to change.
Actually (Score:4, Informative)
But, if the only way to get elected is to 'cut taxes', what do you think is going to happen?
Re:Psst. (Score:5, Insightful)
No, but it's very pleasant that an A3 page folded in half is exactly the same size as an A4 page. root-two is just the mathematical means to that end.
Re:Oooo.... root 2! (Score:5, Insightful)
You don't get it. It keeps going, recursively. Two A4's equal an A3, and two A3's equal an A2, and so on. The deal is that the paper is in such proportion that all A* papers are in the exact same proportion. That's not true if you double a 8 1/2 by 11. The proportion there is .77272, while the proportion for a doubled sheet, 11x17 is .647059.
I'm betting the Golden Ratio comes into A4 paper somehow; anyone want to comment?
Re:Oooo.... root 2! (Score:5, Insightful)
Re:Oooo.... root 2! (Score:5, Informative)
Re:Neat (Score:5, Funny)
Do the math, indeed (Score:4, Informative)
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.
oops (Score:4, Funny)
skinnier is still ugly though.
Re:oops (Score:4, Insightful)
Re:Yes, but... (Score:5, Funny)
Re:I will fight this metric paper with every OUNCE (Score:5, Funny)
Re:And this is superior why? (Score:5, Insightful)
If you are a *real* skinflint and have good eyes you can scale down to A6 and print double sided. It works quite well with a decent laser printer.
The reverse is true obviously if you want to scale up. You can tape (A4 usually because it's the most common) pages together to make A3, A2 and A1 sheets and it all fits together exactly.
Having said that, I kind of assumed that the same thing applied to US paper sizes. Surprised it doesn't.