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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."
You can also put two 8.5x11 (Letter) sheets of paper side by side and it equals an 11x17 (Tabloid) sheet of paper...
That joke is in the title. From the "forty-rods-to-the-hogshead department."
M.
--
http://incuso.altervista.org
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.
-- MartinG To mail me: echo kewyjlcxyzvjfxbqwh | tr bcefhjklqvwxyz
Wow...1.6180339887499 now is equal to root 2... Funny for as I can remeber root 2 was more like 1.4142135623730... Guess I need to alter ever calculator I own to correct their grevious error giving me the actual root of 2 so that they will give me your new fangled Golden mean instead...Or not...
Either that was tongue-in-cheek, which I respect, or you are under the age of 30.
... I was in elementary school at the time. I agree, metric makes a lot more sense in -all- manner of implementation. Unfortunately by the time I left elementary school (lets see ... 1982?) they had all but given up.
They did try
It definitely makes international travel interesting. It is bad enough when you have to explain your country's politics, but explaining your measurement system (especially in the areas where said system originated) is plain frustrating.
It is more productive to voice thoughtful opinions (reply) than to judge (moderate) others.
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.
Okay, this is entirely cosmetic, but I actually prefer the look of Letter sized paper to A4. A4 is so skinny and tall, whereas Letter seems more proportional and better for letters (no pun intended).
No it's not. The golden mean is (1+sqrt(5))/2. That page you linked even says so.
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!
upon the advice of my lawyer, i have no sig at this time
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
The equivalent to A3 paper is tabloid or ledger paper; at 11x17" (28x43cm) ( it is twice the size of a standard 8.5x11" (21.6x28cm) letter-size sheet. (you're on your own for the rest of the metric conversion in this post)
Typical printers do letter and legal (8.5x14"), large format office printers also does tabloid. Some large format photo places will do prints up to 24x36". Plotters typically work on a 36 or 48" wide roll.
Having lived a couple years in Australia, the elegance of metric papers is appreciated, though I'm not sure what the 'legal' paper equivalent would be - B something.
The Metric Act of 1975 and the Omnibus Trade and Competitiveness Act of 1988 actually mandate the usage of the metric system for business activities in the US. Which is why you sometimes see road signs with Km in them
PC = Paper Cassette, IIRC
--
E_NOSIG
Must be, for oldest article put up as news by Slashdot. I found this in '96 when I started doing prepress work in metric paper sizes in Germany.
But what the article doesn't mention is that for many of these, there's an oversize, like A3 oversize when you need to do full-bleed on an A3 page (printing goes to the edge of the paper).
A0 paper is one square meter.
A4 paper is 2^-4 = 1/16 square meter.
Or, you could have just gone to their website and entered "a4 paper" in the search box. :-)
Tada! You'd get this.
(Note that when clicking that link, you'll probably be asked to enter your zip code before seeing the page.)
This web-page: International Standard Paper Sizes contains all the information you would ever need about the history and advantages of A4 paper and its relationship with the US standards.
bring it on! --- JFK
PC stands for Paper Cassette. There's also MP (Multi-Purpose), LE (Lower Envelope), LC (Lower Cassette) and more.
A4 is 5.9mm narrower than letter and 17.6mm taller. The width difference is no big deal... it's tiny, and you can compensate for it feasably by just changing the left and right margins without causing any problems, but the height difference is large enough that if you try to adjust the top and bottom margins to make an a4 page fit on a letter page, your top and bottom margins can often be too small for a printer to manage at all (unless it's one of those photo printers that can print right to the edge of a page, and even then, there might be limitations on the circumstances in which that's permitted).
File under 'M' for 'Manic ranting'
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.
I've never seen the actual paper, but all software I've used has defaulted to using Letter, despite my living in a metric country. And I've had innumerable documents print badly or truncated because they were formatted Letter. Most irritating is that I have to make files to send to Americans and thus have to use Letter, which throws up an error that I have to bypass when I proof them on my laser.
Uuuh...dude, most scientist and engineers are using metric. Go have a look at the US NIST labs.
It's the rest of the American public that doesn't get it.
Those aren't the same shape.
17 / 11 = 1.55
11 / 8.5 = 1.29
There are two primary shapes that repeat.
11/8.5 = 1.29
17/11 = 1.55
22/17 = 1.29
34/22 = 1.55
and so on.. A-F sizes.
The old dot matrix printers with continuous paper with the holes down the side used to use Letter sized paper.
You get it on correspondence from America (complete with the date typed back to front) and sometimes Word / oo.ow will try to print to it if you forget to change the defaults.
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.
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.
"Piter, too, is dead."
The A4 format is a much better size for laying out type. 8.5" is just a bit too wide for easy reading, A4 lets you layout aesthetic pages, and at the proper width for faster reading.
US sizing also doubles/halves for other standard sheets, but the other sizes are akward to work with (think 17x22 or 5.5x8.5).
Most any printer, typesetter or graphic designer in the US will tell you that they'd rather work with metric.
A0 = folded no times, 0.84 x 1.189m. ,0.21 x 0.297m.
:-) "Going metric" is a euphemism in the drug dealing industry for expanding one's operations from small-time street dealing -- either buying hash by the kilo, or selling powders by the gramme.}
A1 = A0 folded once, 0.594 x 0.84m.
A2 = A1 folded once = A0 folded twice, 0.42 x 0.594m.
A3 = A2 folded once = A0 folded 3x, 0.297 x 0.42m.
A4 = A3 folded once = A0 folded 4x
and so on. The number counts how many times a one square metre sheet has been folded in half. Makes blinding sense really. I've been used to A4 size paper all my life and couldn't understand why anyone would want anything else.
BTW, since someone mentioned paper and drugs: if you fold an A4 sheet of 80g/m2 paper {the most common gauge} at 45 degrees from a corner so one short side lines up along the long side, then cut off the excess so you are left with a square, then that square will weigh - as near as damn it is to swearing - 3.5g, equivalent to 1/8oz -- the canonical street measure for hashish in the UK. {Class A's are usually metric though
ever tried folding?
"Piter, too, is dead."
Luckily you can clean yourself up while being compliant to the standard!
In some countries (e.g., Germany) even many brands of toilet paper have format A6.
And further down: readers fascinated by the idea of Central Europeans using A6 as a toilet paper size might also be interested to hear that the U.S. have for the same application field a standard square format of 4.5×4.5 in = 114×114 mm, which is for instance documented in New Jersey Specification No. 7572-01 (May 1997), section 2.3.
Talk about being (sorry) anal retentive.
All right, what's two A1's equal?
A0 is the biggest one.
Well, 1 kliogram is defined as the mass of the international kilogram protoyp stored somewhere in Paris.
The cube meter is the volume of a cube where each edge is 1m. 1m is defined as a the distance light travels in 1/299798252seconds.
Evolution of Language Through The Ages: 6000 BC : ungh, grrf, booga 2000 AD : grep, awk, sed
The origins of the meter is quite interesting. In essence, it's here: http://physics.nist.gov/cuu/Units/meter.html
o ri gin.htm
But of the 2 guys tasked to do it, one went mad trying to find the "truth" (or the "exactness") whilst the other realised it was a measure determined by committee -or the representatives of the people, if you will.
Most of the other measurements *before* were determined by medeival methods - the Yard is defined thus:
"A yard was originally the length of a man's belt or girdle, as it was called. In the 12th century, King Henry I of England fixed the yard as the distance from his nose to the thumb of his out-stretched arm. Today it is 36 inches, about the distance from nose to out-stretched arm of a man."
http://www.iofm.net/community/kidscorner/maths/
Rather than breathing life into the influence of royalty in my life - and I have enough reminders that the UK isn't a democratic state in the truest semse, thankyou very much - I'm going to stick to meters.
h.
Patriotism is a virtue of the vicious
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
After 3 days without programming, life becomes meaningless
- The Tao of Programming
Or, when you can't handle it you jump over the cliff.
Rather an apropriate name to go with the comment!
The advantage of the 'Metric' paper sizes is obvious, the mill only makes one size stock (A0) and (someone) can cut it to any requested size without loss.
An other advantage, when you get a, say A4 envelope, you know how to easily fold an A3 or A2 sheet to fit in it. No need for a large inventory of funny sized envelopes or odly folded documents.
"The likes of Facebook and WhatsApp are free to those whose privacy is of zero value."
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.
I'll see your Constitution and raise you a Queen.
And how is what you described... *not* intertia?
Funny how you can double non-metric paper sizes and get a standard paper size too:
A folded and trimmed 8 1/2" x 11" page = 5" x 8" (a standard page size).
Two 8 1/2" x 11" pages = 11" x 17" (a standard bond paper size).
Two 11" x 17" pages = 17" x 22" (the standard Bond paper size for determining basis weight).
There used to be a 8-1/2x10-1/2 paper size that competed with the 8-1/2x11 paper size, so be glad that was thrown out!
r sizes.pdf
I snared the following from the American Forest & Pulp Association website.
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Why is the standard paper size in the U.S. 8 ½" x 11"?
Back in the late 1600's, the Dutch invented the two-sheet mold. The average maximum stretch of an experienced vatman's arms was 44". Many molds at that time were around 17" front to back because the laid lines and watermarks had to run from left to right. Sounds big?...well to maximize the efficiency of paper making, a sheet this big was made, and then quartered, forming four 8.5" x 11" pieces.
This was well before paper machines dominated hand made paper labor. A couple centuries later when machines dominated the trade (although many hand made paper makers still existed), and the United States decided on a standard paper size, they stuck with the same size so as to keep the hand made paper makers in business.
Oddly enough, the United States used two different sizes - the 8" x 10.5" and the 8.5" x 11". Separate committees came up with separate standards, the 8" x 10.5" for the government and the 8.5" x 11" for the rest of us. Once these committees found out about each other a couple years later, they agreed to disagree until the early 1980's when Reagan finally proclaimed that the 8.5" x 11" was the official standard sized paper.
United States History
Not until World War I or shortly after was a standard paper size agreed to in the United States. Interestingly enough, within six months of each other, two different paper sizes were set as the standard; one for the government and one for the rest of us.
1. In 1921, the first director of the Bureau of the Budget established an interagency advisory group with the President's approval called the Permanent Conference on Printing which established the 8" x 10½" as the general U.S. government letterhead standard. This extended an earlier establishment made by the former President Hoover, the Secretary of Commerce at the time, who established the 8" x 10½" as the standard letterhead size for his department.
2. Now, during the same year, a Committee on the Simplification of Paper Sizes consisting of printing industry representatives was appointed to work with the Bureau of Standards as part of Hoover's program for the Elimination of Waste in Industry. This group came up with basic sizes for all types of printing and writing papers. The size for "letter" was a 17" x 22" sheet while the "legal" size was 17" x 28" sheet. The later known U.S. letter format was these sizes halved (8 ½" x 11" and 8 ½" by 14").
Even in the selection of the 8 ½" x 11", no special analysis was made to prove this was the optimum size for commercial letterhead. The Committee that developed the sizes did so using one objective - "to reduce inventory requirements for paper into sizes which would cut from a minimum trimming waste."
References:
1. Labarre Dictionary of Paper and Paper-Making Terms, 1937 Edition.
2. Kuhn, Markus . 1996. http://www.cl.cam.ac.uk/~mgk25/iso-paper.html
3. Dunn, A. D. 1972. Notes on the Standardization of Paper Sizes. http://www.cl.cam.ac.uk/~mgk25/volatile/dunn-pape
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)
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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.
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...
Reason is the Path to God - Anon
Here in Chile we use full-blown metric system: m, km/h... Yet the de facto standard paper is LETTER!! And for legal documents the paper size is 8.5 x 13 inches. Yes, inches. I don't know when in history a transition happened, if it happened (maybe after WWII --just speculating).
The fork is actually a rather recent invention, tableware-wise. The oldest is the knife, followed by the spoon. For centuries, those two (and more commonly, fingers) were the standard tools used by Europeans to eat with. To show off their wealth (and sometimes get ridiculed by commoners for their effeminacy) the upper classes might eat meat and such with a pair of knives. The fork was the clever invention of someone who figured that putting a pair of pokers on the same handle would give him more control. (This also allowed table knives to be made without pointed tips.) It wasn't until the 17th century that forks started becoming common on the tables of Europe, and later in North America.
http://alternatives.rzero.com/
"Same goes with volumes - it's easy to convert gallons to quarts to pints."
Of course, those aren't part of what the Americans refer to the English system. The English have 20 fl oz in a pint whereas the Americans have 16. Also, there is a slight difference between the size of a fl oz too. Then there's the American ton, but that's another story...
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,....)
HI O WISE PRINCE. WHT TOOK U SO DAM LONG?
Actually, according to this
most of the measurements in the Fahrenheit scale are completely arbitrary and just a bunch of fudge factors.
And you'll node that 0 is NOT freezing point of water in Fahrenheit.
But then again, most of the older Imperial measures are based on the length of someone nose, the distance from London to Paris, or a whole bunch of arcane stuff that seemed like good ideas at the time.
Lost at C:>. Found at C.
Of course, that RFC is based on, and explicitly refers to the more authoritative ISO 8601 standard, which makes so much sense that I sometimes feel like printing it out, rolling it up and beating some Americans over the head with it.
Mozilla
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?
The Kruger Dunning explains most post on
a bit of math for the non-metric paper people...
did you know that the height-to-width ratio for the non-metric paper sizing also works out:
8.5"x11", 11"x17", 17"x22", 22"x34" etc. is how size most commonly increments (and of course 8.5"x14" is an exception)..
also, paper weight is determined by a 'ream' of paper: a ream being defined as 500 sheets of 11"x17" paper: so 500 8.5"x11" sheets of 20lb paper weighs 5lbs.
... one of the reason 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
.... AND it doesn't stop you from use the exact same convenient divisor of base 12. In fact the above building material sizes show this exactly.
I'm an architest and I can tell you that the Imperial system sucks big time and is not convenient at all.
Adding up Imperial measurements is a freaking nightmare.
In the rest of the world we use standard sizes for construction materials like 150x150mm wall tiles, 300x300 floor tiles, 600x600 raised floor tiles, 900x900 carpet tiles, 1200x2400 (or higher) gypsum wall panels.... get it - it's all on a sensible module that you can use to line everything up on
And you can easily add them all up.
The other thing that no one has mentioned is scale and the A system.
The majority of drawings we make are A1 sizes - which nicely scales to A3. A 1:50 drawing at A1 becomes a 1:100 scale at A3 - not the freaking ridiculous Imperial scales.
Then you can get a ruler with a 1cm scale on it and every cm is a metre.
Note that if you scale a A3 to A4 then everything becomes an inconvenient scale. What happens is that you reduce A3 to A4 for a Fax transmission the receiver scales it back up to A3 to use.
Note that the same issue occurs with A1 to A2 or A2 to A3. You need to scale down two levels in the A system to maintain scale - which is fine for most uses.
So the Imperial system sucks in all ways for Architects and construction in general.
Actually, please don't use D/M/Y. I at least when seeing "/" used as a delimiter in dates assume the date is in the American M/D/Y order. The correct delimiter is "." as in D.M.Y (e.g. today is 16.5.2004).
My sig will be released in 2015 third quarter. Rating pending.