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

Pulp Numerology

[Bingo Foo]

Hey, if pulp numerology is your thing, look here.

Re:Drugs teach American kids the metric system.

[Ubergrendle]

Origin of the phrase "one for the road". In London, while on the way to the gallows, the cart would stop at each pub along the way. The criminal would be allowed a drink at every pub, almost always 'on the house' so that the soul would not come back to make due on a debt. Also, i suspect pity played a large role.

metric will win in the end

[garglblaster]

This is my personal opinion, however:

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..

Re:Side-by-sideness

[salzbrot]

That is true, but the 8.5 x 11 has a width-length ratio of about 1.29, whereas the 11 x 17 has a ratio of 1.54. A sheet of 17 x 22 again has the ratio of 1.29 and so on.

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.

American Paper is ugly

[Potor]

I am a Canuck expat in Europe, and I grew up with 8.5x11 paper. Now, however, I shudder when I see it. A4 is so much more aesthetically pleasing to me, probably because it looks less clunky than its fatter and shorter American cousin. And, since the headline asks, I have found the scaling of the metric series to be very handy; it is easy to ask for precisely the size of paper you want.

Re:Huh?

[rnelsonee]

I can... metric is obviously heavily biased to factors of 10 - a pretty useless number as it only has a few divisors (2, which always a factor of the base/radix used, and 5). So when you want to divide your 1 meter board into 4, you're now stuck with 2.5 cm pieces. Okay, not too bad. What about dividing it by 3? A repeating decimal is now your new measurment. Bah, same with 6. If you get stuck in classes for most of your life, you probably won't care about this. But try to build a bar with a metric ruler and you'll see why these are desirable traits.

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.

Just as Interesting

[Momomoto]

It's frightening how well they've thought out things like this. From the article:

Technical drawing pens follow the same size-ratio principle. The standard sizes differ by a factor sqrt(2): 2.00 mm, 1.40 mm, 1.00 mm, 0.70 mm, 0.50 mm, 0.35 mm, 0.25 mm, 0.18 mm, 0.13 mm. So after drawing with a 0.35 mm pen on A3 paper and reducing it to A4, you can continue with the 0.25 mm pen. (ISO 9175-1)

Call me an incorrigible geek, but that little tidbit made me giddy.

Not as English as you think....

[rilister]

Honestly, US companies are genuinely converting to Metric, believe it or not. I work in a consultancy and work with a variety of clients, including a bunch in the worlds of science and medicine.

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.

Re:Yes... it's your damn fault!

[Uma Thurman]

I have some idea, yes. You see, I've laid tile in the past, and one of the things you do is center the pattern on the floor, with equal sized partial tiles at the edges. This requires division of the distances by 2. It's really cumbersome to divide 34 7/8 inches by two in your head, for example.

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.

Re:Drugs teach American kids the metric system.

[Sirch]

Not quite. The saying actually refers to the trip from the prison to the Tyburn Tree in London. The prisoner to be hanged would be given drink to calm him down for the hanging. The closest pub to the place of hanging that lay upon the route was a mile away. The prisoner would have a drink at this last pub, and then be given a drink to have on his way to the gallows. Interestingly, this is also the origin of "on the wagon" as one of the guards travelling with the prisoner was not allowed to enter the pubs with him. So couldn't drink, and had to stay on the wagon.

Some lovely linkage:here, here and here.

Also makes weight calculation easy

[hazee]

The metric system also makes it easy to calculate the weight of an amount of paper. Photocopy paper is typically 80 grams per square meter. A0 paper is exactly 1 square meter, hence 80 grams; keep halving this until you arrive at 5 grams for a sheet of A4 paper. Easy! Could be useful when trying to calculate postage, typically done by weight. Try doing that with weird-o imperial sizes...

Another Cool Ratio

[donscarletti]

Although having paper with a 2^0.5 aspect ratio is by far the most practical solution it is not the most aesthetic solution. Photos and slides use an aspect ratio that is not used by any other type of paper. That ratio is (1 + 5^0.5) / 2 or approximately 1.61803399 .

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.

IHBT. i bite.

[ViVeLaMe]

nope, it isn't the same shape.
Long side / short side = ?
17/11 = 1.54545(54...)
11/8.5 = 1.29411(..)
they haven't the same shape.
you were right to post anonimously..

Re:Drugs teach American kids the metric system.

[Delta-9]

" this is also the origin of "on the wagon" as one of the guards travelling with the prisoner was not allowed to enter the pubs with him. So couldn't drink, and had to stay on the wagon."

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:Side-by-sideness

[plam]

Wow. That will really come in handy when I want to expand my thesis to poster size.

Oh wait. That will never happen.

Expand? No. But perhaps someone wants to copy your thesis 2-up, and that's a lot easier with metric sizes.

The biggest reason the U.S.A. doesn't use metric

[GlobalEcho]

Though all the speculation about US backwardness and hostility toward foreign systems is certainly entertaining, there's a benign historical explanation that I find compelling. It goes something like this:

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.

Re:2 x A4 = A3

[sl70]

My wife, who is Japanese, pointed out a VERY good use of chopsticks: for picking dropped objects like screws from the inside of computer cases (when your hand won't fit inside).
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