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The definition, or rationale, given for the B series, is bizarre: geometric means between the A series format with a particular number and the A series format with one lower number. Perhaps that's true, but is this really the reason the B series was invented, or useful? Isn't a more useful explanation is that while the A0 was defined to have an area of 1m^2, the B0 was defined to have a (short) side of 1m? 192.114.107.4 ( talk) 07:55, 7 April 2009 (UTC)
I made a change to the rationale for using 1:sqrt(2) rationale for A paper as well as the inclusion of a few equations for proof. If someone can take a look at the changes and see whether or not they agree, I'd appreciate. I found the previous explanation to be badly written and confusing. Kakomu ( talk) 21:15, 9 September 2008 (UTC)
I propose the merger for two reasons:
Okay, I'm done. Melchoir 03:30, 21 March 2006 (UTC)
I think this is a good idea rafael.cosman
Okay, I'll get on it. Melchoir 04:18, 24 March 2006 (UTC)
I propose that someone add inch equivalents to these measurements because Americans can't just see a measurement like 200mm and know how long that is. 71.227.254.181 23:57, 2 November 2006 (UTC)
Why single out Americans for special treatment? This is an international English encyclopedia.
Although I'm all for making Wikipedia as accessible as possible, I must admit that I can't seem to muster any compassion for someone who doesn't know what a mm is. Shinobu 09:46, 16 November 2006 (UTC)
Question: should the inch equivalents be based on the A4 rounded measurements or the formula? Using the formula there is a difference (due to a rounding error) for a few of the inch values. Jw6aa 03:47, 12 February 2007 (UTC)
Answer: From a practical point of view, the inch equivalent should be based on the final measurements, not the formula. The ISO 216 is not for theoretical use but for printing and the like, where the final page size is all that matters in the end. - Tommi Kovala (unregistered user) 10:38, 21 March 2007 (GMT)
There shouldn't be any conversion to the Imperial system. The rest of the world has gotten up to time in a practical system and american isn't special or anything. -30 is 0 celsius, which is easier? Was the guy who thought of that on opium (then again, he probably was)
I added inches but I guarantee this will be taken down by the wiki-overlords. There's a good reason to give inches as comparison at least in the line comparing US Paper Sizes to the international ones. That's especially true because when someone buys letter size paper it says quite plainly, 8.5" x 11", many times it does not say the metric equivalent. So inches maybe should not be all over the place, but it deserves an area in that line at least. —Preceding unsigned comment added by 74.72.44.116 ( talk) 18:00, 6 September 2010 (UTC)
The table on the left should be deleted. The lower table is really very nice, but the drawings should be scaled consistently. jcp 05:38, 5 April 2007 (UTC)
I'm pretty sure that the side parallel to the shorter side is another one of the shorter sides. I think probably perpendicular is what is meant.
Note that a Second Edition has been published as of 2007. I can't find information about what the revisions are, but someone should find out and update the article. —Preceding unsigned comment added by 69.46.127.11 ( talk) 17:20, 10 September 2007 (UTC)
For example, in the table with the various paper sizes "A4= 210 x 297". This is "x" by "y", or let's call it "length x height." Then we see "A3 = 297 x 420" or "y" by "x" or "height" by "length." This information is formatted the same way on almost any page on the Internet I could find, many of which had "pre-Wikipedia" feel to them, so I'm not questioning the accuracy at all. Is there a standard (ISO, ANSI, DIN, etc.) for the order for giving length and height measurements? (use "height" as a replaceable term for "width" if necessary). I notice that A3 has a horizontal orientation while A4 has a vertical orientation, and they give their "x" and "y" dimensions oppositely. Any significance to that? I know that putting an A4 sheet in front of a drafter in vertical orientation would earn you a weird look from him, so the orientation's aren't arbitrary.
On a side note, is there a standardization for whether "width" or "height" is the correct term for the "y" dimension?
Also, is there a standard order for quoting length and height/width in general? It seems like the natural order would be length (x) by width/height (y), being that human field of vision is significantly more horizontally oriented than vertically, so I was surprised to see A3 (and the other "fat" sizes) given with "y" dimension first. Being that drawing/drafting standards are as ambitious as they are, I can't imagine that no one has thought of this aspect B4. (my apologies for both of those awful, awful paper standardization puns). —Preceding unsigned comment added by 68.38.154.77 ( talk) 00:46, 15 September 2007 (UTC)
Considering there is no difference in mathematics or programming (different programs use either column or row major), English language as defined by Oxford, can set the rule for consistent measurements of column major. I.e.: column by row, height by width, 297 x 210 mm. Column major also happens to be logically alphabetical, allowing for an easy mnemonic. E.g., column by row is c x r. Height by width is h x w.
Now we need teachers to wave their hands to students:
for columns from top to bottom, then up slightly to the students' right, then straight down and repeat. Rather than waving their hand from left to right for columns.
for rows from students' left to right, then left and slightly down, then to the student's right and repeat. Rather than waving their hand from top to bottom for rows, which confuses the initial anchor understanding amongst students. — Preceding unsigned comment added by Eiger3970 ( talk • contribs) 03:53, 31 March 2015 (UTC)
there is a link to the main page on the sub-section on A4, but it's not a link.
can someone who isn't a code-noob (thats me) make this work properly!
thanks! —Preceding unsigned comment added by 128.243.253.111 ( talk) 18:24, 6 February 2008 (UTC)
I can't see the purpose of the " + 0.2 " in the formula which is described as yielding the "exact millimeter measurement" of the paper (the one with 1000/(...)) in it. Am I missing something? (I've never edited a wikipedia page before so am not about to try now :-). Neil Conway —Preceding unsigned comment added by 194.81.223.66 ( talk) 13:33, 7 February 2008 (UTC)
Short: =(1000 * SQRT(1/SQRT(2)) / (SQRT(2)^A1)) - 0.2
Long: =(1000 * SQRT(1/SQRT(2)) * SQRT(2) / (SQRT(2)^A1)) - 0.2
— Preceding unsigned comment added by 184.160.164.76 ( talk) 01:09, 28 July 2012 (UTC)
It is not clear precisely how ISO 216 defines smaller paper sizes.
A0 paper is defined as having 1 m^2 area, and an aspect ratio of the square root of 2.
y * x = 1000000 mm, y / x = root(2)
y * x = 1000000 mm, y = root(2) * x
root(2) * x * x = 1000000 mm
root(2) * x ^ 2 = 1000000 mm
x^2 = ( 1000000 mm / root(2) )
x = root( 1000000 mm / root(2) ) ==============> Precise definition of A0 width
x = 840.89641525371454303112547623321 mm
y * x = 1000000 mm, y / x = root(2)
y * x = 1000000 mm, x = y / root(2)
y * ( y / root(2) ) = 1000000 mm
y^2 / root(2) = 1000000 mm
y^2 = 1000000 mm * root(2)
y = root( 1000000 mm * root(2) ) ==============> Precise definition of A0 height
y = 1189.2071150027210667174999705605 mm
Other A sizes are divisions of these A0 definitions.
_____________________________________________________
SO: If we start with A0 at 1 square meter by definition (1,000,000 mm^2) with an aspect ratio of 1:SquareRoot(2).
Do we find successively smaller A(n) sizes by
dividing the base A0 area ( 1,000,000 m^2 ) by 2^n and rounding >=0.5 up & <0.5 down,
or
dividing the larger dimension of the A(n-1) paper size by 2 and always rounding down to the nearest mm.
It seems the first method is more precise and does not require any recursion, but what does the ISO Standard actually specify?
The table of sizes indicates the bad 2nd method. If the Base A0 Area method is the correct one, we need to alter the article's table. Ace Frahm ( talk) 16:30, 23 February 2013 (UTC)
Summing up regarding formulas and definitions:
NisJørgensen ( talk) 16:22, 19 December 2017 (UTC)
Why not mention of A00 paper? It is in common use in draughting offices.
Also, the C sizes are not covered by ISO 216 and should only be referenced from these page. No detailed description necessary. 79.77.113.193 ( talk) 20:22, 19 April 2008 (UTC)
How thick/thin is A4 paper - 1mm/1μm/1nm/1pm?
Are material properties the only contraints for paper thinness?
Is there any special pen/ink to write on thinner papers?
Is there any minimum limit on thinness of paper to be accepted as evidence in a court of law? Anwar ( talk) 09:15, 9 May 2008 (UTC)
This page and the Paper size page appear to have the same purpose / function and contain much of the same information. I suggest they be merged. —Preceding unsigned comment added by 88.106.221.168 ( talk) 11:45, 25 August 2008 (UTC)
Anyone actually ever seen one of these up close? Unless they're used for defining the size of raffle tickets and the like, I can't see much call for anything under A8... Particularly not the envelopes! (I think I bought a novelty A8-ish size set of christmas cards with envelopes once - they fit ok, but were a bit fiddly to write and I wouldn't dreamt of trying to post them; A10 is almost stamp sized! Also I have an A7 notebook I bought because I spotted it going cheap in a trinket shop when on a trip and it had a nice design ... it proved to be very difficult to actually use! A6 is a lot more common (file cards, shorthand notebooks etc).
Not complaining or asking for removal, I'm just interested to hear if anyone actually uses such things in daily life or industry. 193.63.174.10 ( talk) 11:23, 23 October 2008 (UTC)
...or is this explained on its own page somewhere (to which we should link)?
I know what it is - wide and high enough that a piece of A4 folded into 3 along its long edge will fit neatly inside, typically for short missives with a max of about five pages... e.g. restaurant menus or other landscape type promo material, or a portrait letter / invoice / etc, typically with part of the letterhead (containing the recipient's name, mailing address and any other immediately relevant info) then being visible through a clear plastic window on the front, and the main content safely folded away on the other 2/3rds and not able to be shaken into view. But there's not even a short expo like that, and I'm not sure immediately where to or whether to include it 193.63.174.10 ( talk) 11:30, 23 October 2008 (UTC)
Isn't the B-sizes generally used for envelopes? I vaguely remember using a B4-envelope to mail forms that shouldn't be folded, and B5-envelopes for "normal" folded letters written on A4-sheets. Should this be mentioned? —Preceding unsigned comment added by 92.251.150.23 ( talk) 23:02, 11 April 2009 (UTC)
If you put DL into the wikipedia search box, there is an entry for "Dimension Lengthwise" which directs you back to this page. Although there is no discussion on this page, DL is mentioned as the final entry into the C series table at the top of page. As the C series is for envelopes, this seems logical. —Preceding
unsigned comment added by
116.212.199.202 (
talk)
00:17, 4 March 2010 (UTC)
The article mentions the publication of DIN 216 in Germany in 1922, but can anyone address the history of the adoption of these standard sizes of papers in the various countries of Europe. It would be particularly interesting to discuss when the UK went over to this metric standard. -- SteveMcCluskey ( talk) 22:36, 7 May 2009 (UTC)
This is a pretty good article, but like a lot of articles it forgets to give the quintessential piece of info, in this case, WHY did everyone except the US move to this system? I did a kind of O & M course a few years back, and the tutor said that the wonderful thing about this system is that you can cut a single piece of paper 1 square metre into any combination of A sizes and not waste a single square centimetre! This is kind of evident in the diagrams shown but it is not explicitly referred to. The other - even more fantastic thing - is that you can magnify (say) an A5 sheet on a Xerox, and the resulting A4 printout has EXACTLY the same proportions as the original A5 sheet! And draftsmen can purchase special sets of pens to use on these pages. The thickness of the lines the pens draw are calibrated to the different sizes of these sheets. So you can draw lines on an A4 sheet using the pen intended for that sheet size, then put that sheet on a Xerox and print a smaller version of your draft work on an A5 sheet. The picture will have exactly the same proportions as the bigger one. Then you can take a different pen (the one having a finer line and designed to work on A5 sheets ) and continue with your work. And so on for all sizes, magnifying up or reducing down. Try that with magnifying or reducing between quarto and foolscap!
I was around when Austalia converted from foolscap to A4 as the standard office size. I remember that at the beginning we all thought that the A4 sheet was absurdly short. Now, when I find some old document amongst my trivia and nostalgia items, I think, this looks like some medieval scroll. Actually, the article really needs some reference to the old imperial standards to round it out.
Btw, I am not a mathematician, but I gather that these A4 etc ratios are NOT the same thing as the golden mean, but that they are somehow connected. Is that true? Myles325a ( talk) 07:28, 1 October 2009 (UTC)
Yes, if you put the sides on the same line and cut it by golden mean you get the propotion of the sides. So the propotions between the edges correspond to golden mean if im not mistaken. —Preceding unsigned comment added by 80.223.217.22 ( talk) 20:22, 2 December 2009 (UTC)
What rational was there ever for developing the C series? Surely there must have been a more pressing reason than that it is "the geometric ratio between the B series and the A series"? Woscafrench ( talk) 00:24, 21 February 2010 (UTC)
I think the C series is to give sizes for envelopes. —Preceding
unsigned comment added by
116.212.199.202 (
talk)
00:15, 4 March 2010 (UTC)
The page content should be substantially reduced. No reason to have size tables twice, the nice size char for all three series is also presented twice. The specific property of "magic" aspect ratio is explained four times including the formal verification of ∀a≠0,b≠0: a/b = 2b/a ⇒ a/b = √2. Although I like formal verifications of statements, although Encyclopedic content must be verifiable, in my humble opinion, it is inappropriate present formal mathematic verifications of statements on pages like this one. If it is appropriate here, then someone should add formal explanation why weight of 1/16m2 80g/m2 paper is 5g also ...
And page should be renamed to reflect the ISO 269 formats are discussed here as well. Especially when you can ask Wikipedia for page related to ISO 269 and you will got one (different from this one). It's confusing.
To be short - to many duplications, too many unrelated information, too long, too hard to read.
193.179.199.50 ( talk) 12:19, 27 July 2010 (UTC)
The article doesn't explain the idea behind A0+, A1+, A2+ and A3+.-- Oneiros ( talk) 12:51, 18 October 2010 (UTC)
This Lichtenberg ratio article's content is pretty much already represented here, but in case there's any more, let's merge it before deleting; OK? Dicklyon ( talk) 22:47, 15 January 2011 (UTC)
In the current Brother adverts on TV certainly in the UK but almost certainly airing in other markets. Brother claim that A3 is 143% bigger than A4 in a sales pitch for their A3 format copiers.
Surely as A3 is twice as big as A4 then the claim should be 100%, can anyone help with this query? —Preceding unsigned comment added by 81.97.128.97 ( talk) 14:38, 20 February 2011 (UTC)
I understand why the C series is useful, and indeed many of the envelopes available in stationery shops are labelled in C sizes, but I can't understand what B is for and I don't believe I've ever seen it in use. Can anyone enlighten me? Beorhtwulf ( talk) 22:16, 28 February 2011 (UTC)
Aspect ratio is commonly given by the longer side first, 5:3, 3:2, 4:3, 16:9 ... Anyone a reason why not doing so in this article? NuclearEnergy ( talk) 20:39, 2 April 2011 (UTC)
Im not sure √2:1 would look right and anyway, aren't 1:x ratios usually written as 1:x and not x:1? Benboy00 ( talk) 09:13, 30 April 2011 (UTC)
I'm not sure quite what the "Application" section means with the stuff about scaled photocopying, but the English doesn't sound quite right or coherent. I fixed this a little, but I think either a rewrite or just a deletion may be more appropriate. Benboy00 ( talk) 09:14, 30 April 2011 (UTC)
Why does almost everything in the article appear twice? Pdfpdf ( talk) 12:13, 11 September 2011 (UTC)
The opening says that "ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, with the United States and Canada the only two exceptions." but the history section says that "Although they have also officially adopted the ISO 216 paper format, Colombia, Mexico, The Philippines and Chile also use mostly U.S. paper sizes in ordinary usage."
In my experience, while it might be true that Chile has adopted the standard, in practice the most commonly used format is carta (letter). The Wikipedia article on Chile concurs: [ [1]]. So either the opening should say ISO 216 specifies the official paper size of most countries in the world today, or if it wishes to continue specifying the paper size used, it should also mention that Colombia, Mexico, The Philippines and Chile are exceptions.
-- Siker ( talk) 10:20, 23 June 2012 (UTC)
I agree with Siker, in Mexico you'd be hard pressed to find a store selling A4 paper, Letter and Legal being the norm (and what the government actually uses, despite official adoption of ISO 216). — Preceding unsigned comment added by 67.161.35.102 ( talk) 10:17, 19 July 2012 (UTC)
I think diagonal sizes of the standarts (A4, A5, etc.) should be given in the tables.-- 194.27.186.205 ( talk) 09:00, 21 December 2015 (UTC)
Crediting Portmann for developing the German standard in the 20th century ignores the statement that France already had the current and ISO A2, A3, B3, B4, and B5 in 1798. What did Portmann actually develop? Since this material is unsourced, I am deleting it until someone comes forward with well-sourced information about what Portmann or the DIN standard contributed.— Finell 01:53, 11 May 2016 (UTC)
The change that was undone: https://en.wikipedia.org/?title=ISO_216&diff=next&oldid=882463098
Discarding the naming convention for short/long sides, quoting the text:
...x/y = y/x/2, which reduces to x/y = √2...
Rearranging the formula leads to:
x2 = y2/2
which reduces to
x2/y2 = 1/2} => x/y = 1/√2 => y/x = √2
meaning that the numerator and denominator in the fraction on LHS should be swapped.
Yossik ov ( talk) 19:09, 9 February 2019 (UTC)
A good-faith editor reworded an apparent recitation of the specification (using "shall"); I tried to rewrite the paragraph using encyclopedic language ("The pen widths are specified to be..."), but hit a problem. There are three (3!) references, and all are defective. We have the absurdity of a commercial organisation charging 50 Swiss francs or so to read the wording of the specification, and are left relying on various manglings. The fact that using pen nib sizes in the root(2) sequence would match the corresponding drawing scaling is an obvious, ineluctable mathematical fact that (in a rational world at least) needs no "source". But perhaps the standard actually gives specific thicknesses for lines at different drawing sizes? If so, the wording should reflect this; but no reference tells us. The metrication.com site appears to give specified line widths for A0 and A1, then claims "just use the same for A2, A3, and A4, which is nonsense. The designingbuildings.co.uk site (can't spell "its") shows ISO pens mixed in with other pens, and just mumbles about the general principle. Markus Kuhn (can spell "its") again just gives the general principle. Does anyone have access to the standard itself? Or a statement of all the facts of the stardard written in prose that is not a copyright violation? Imaginatorium ( talk) 03:59, 3 April 2019 (UTC)
An editor has asked for a discussion to address the redirect C-size. Please participate in the redirect discussion if you wish to do so. signed, Rosguill talk 23:21, 5 February 2020 (UTC)
This is the
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ISO 216 article. This is not a forum for general discussion of the article's subject. |
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This article is rated B-class on Wikipedia's
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The definition, or rationale, given for the B series, is bizarre: geometric means between the A series format with a particular number and the A series format with one lower number. Perhaps that's true, but is this really the reason the B series was invented, or useful? Isn't a more useful explanation is that while the A0 was defined to have an area of 1m^2, the B0 was defined to have a (short) side of 1m? 192.114.107.4 ( talk) 07:55, 7 April 2009 (UTC)
I made a change to the rationale for using 1:sqrt(2) rationale for A paper as well as the inclusion of a few equations for proof. If someone can take a look at the changes and see whether or not they agree, I'd appreciate. I found the previous explanation to be badly written and confusing. Kakomu ( talk) 21:15, 9 September 2008 (UTC)
I propose the merger for two reasons:
Okay, I'm done. Melchoir 03:30, 21 March 2006 (UTC)
I think this is a good idea rafael.cosman
Okay, I'll get on it. Melchoir 04:18, 24 March 2006 (UTC)
I propose that someone add inch equivalents to these measurements because Americans can't just see a measurement like 200mm and know how long that is. 71.227.254.181 23:57, 2 November 2006 (UTC)
Why single out Americans for special treatment? This is an international English encyclopedia.
Although I'm all for making Wikipedia as accessible as possible, I must admit that I can't seem to muster any compassion for someone who doesn't know what a mm is. Shinobu 09:46, 16 November 2006 (UTC)
Question: should the inch equivalents be based on the A4 rounded measurements or the formula? Using the formula there is a difference (due to a rounding error) for a few of the inch values. Jw6aa 03:47, 12 February 2007 (UTC)
Answer: From a practical point of view, the inch equivalent should be based on the final measurements, not the formula. The ISO 216 is not for theoretical use but for printing and the like, where the final page size is all that matters in the end. - Tommi Kovala (unregistered user) 10:38, 21 March 2007 (GMT)
There shouldn't be any conversion to the Imperial system. The rest of the world has gotten up to time in a practical system and american isn't special or anything. -30 is 0 celsius, which is easier? Was the guy who thought of that on opium (then again, he probably was)
I added inches but I guarantee this will be taken down by the wiki-overlords. There's a good reason to give inches as comparison at least in the line comparing US Paper Sizes to the international ones. That's especially true because when someone buys letter size paper it says quite plainly, 8.5" x 11", many times it does not say the metric equivalent. So inches maybe should not be all over the place, but it deserves an area in that line at least. —Preceding unsigned comment added by 74.72.44.116 ( talk) 18:00, 6 September 2010 (UTC)
The table on the left should be deleted. The lower table is really very nice, but the drawings should be scaled consistently. jcp 05:38, 5 April 2007 (UTC)
I'm pretty sure that the side parallel to the shorter side is another one of the shorter sides. I think probably perpendicular is what is meant.
Note that a Second Edition has been published as of 2007. I can't find information about what the revisions are, but someone should find out and update the article. —Preceding unsigned comment added by 69.46.127.11 ( talk) 17:20, 10 September 2007 (UTC)
For example, in the table with the various paper sizes "A4= 210 x 297". This is "x" by "y", or let's call it "length x height." Then we see "A3 = 297 x 420" or "y" by "x" or "height" by "length." This information is formatted the same way on almost any page on the Internet I could find, many of which had "pre-Wikipedia" feel to them, so I'm not questioning the accuracy at all. Is there a standard (ISO, ANSI, DIN, etc.) for the order for giving length and height measurements? (use "height" as a replaceable term for "width" if necessary). I notice that A3 has a horizontal orientation while A4 has a vertical orientation, and they give their "x" and "y" dimensions oppositely. Any significance to that? I know that putting an A4 sheet in front of a drafter in vertical orientation would earn you a weird look from him, so the orientation's aren't arbitrary.
On a side note, is there a standardization for whether "width" or "height" is the correct term for the "y" dimension?
Also, is there a standard order for quoting length and height/width in general? It seems like the natural order would be length (x) by width/height (y), being that human field of vision is significantly more horizontally oriented than vertically, so I was surprised to see A3 (and the other "fat" sizes) given with "y" dimension first. Being that drawing/drafting standards are as ambitious as they are, I can't imagine that no one has thought of this aspect B4. (my apologies for both of those awful, awful paper standardization puns). —Preceding unsigned comment added by 68.38.154.77 ( talk) 00:46, 15 September 2007 (UTC)
Considering there is no difference in mathematics or programming (different programs use either column or row major), English language as defined by Oxford, can set the rule for consistent measurements of column major. I.e.: column by row, height by width, 297 x 210 mm. Column major also happens to be logically alphabetical, allowing for an easy mnemonic. E.g., column by row is c x r. Height by width is h x w.
Now we need teachers to wave their hands to students:
for columns from top to bottom, then up slightly to the students' right, then straight down and repeat. Rather than waving their hand from left to right for columns.
for rows from students' left to right, then left and slightly down, then to the student's right and repeat. Rather than waving their hand from top to bottom for rows, which confuses the initial anchor understanding amongst students. — Preceding unsigned comment added by Eiger3970 ( talk • contribs) 03:53, 31 March 2015 (UTC)
there is a link to the main page on the sub-section on A4, but it's not a link.
can someone who isn't a code-noob (thats me) make this work properly!
thanks! —Preceding unsigned comment added by 128.243.253.111 ( talk) 18:24, 6 February 2008 (UTC)
I can't see the purpose of the " + 0.2 " in the formula which is described as yielding the "exact millimeter measurement" of the paper (the one with 1000/(...)) in it. Am I missing something? (I've never edited a wikipedia page before so am not about to try now :-). Neil Conway —Preceding unsigned comment added by 194.81.223.66 ( talk) 13:33, 7 February 2008 (UTC)
Short: =(1000 * SQRT(1/SQRT(2)) / (SQRT(2)^A1)) - 0.2
Long: =(1000 * SQRT(1/SQRT(2)) * SQRT(2) / (SQRT(2)^A1)) - 0.2
— Preceding unsigned comment added by 184.160.164.76 ( talk) 01:09, 28 July 2012 (UTC)
It is not clear precisely how ISO 216 defines smaller paper sizes.
A0 paper is defined as having 1 m^2 area, and an aspect ratio of the square root of 2.
y * x = 1000000 mm, y / x = root(2)
y * x = 1000000 mm, y = root(2) * x
root(2) * x * x = 1000000 mm
root(2) * x ^ 2 = 1000000 mm
x^2 = ( 1000000 mm / root(2) )
x = root( 1000000 mm / root(2) ) ==============> Precise definition of A0 width
x = 840.89641525371454303112547623321 mm
y * x = 1000000 mm, y / x = root(2)
y * x = 1000000 mm, x = y / root(2)
y * ( y / root(2) ) = 1000000 mm
y^2 / root(2) = 1000000 mm
y^2 = 1000000 mm * root(2)
y = root( 1000000 mm * root(2) ) ==============> Precise definition of A0 height
y = 1189.2071150027210667174999705605 mm
Other A sizes are divisions of these A0 definitions.
_____________________________________________________
SO: If we start with A0 at 1 square meter by definition (1,000,000 mm^2) with an aspect ratio of 1:SquareRoot(2).
Do we find successively smaller A(n) sizes by
dividing the base A0 area ( 1,000,000 m^2 ) by 2^n and rounding >=0.5 up & <0.5 down,
or
dividing the larger dimension of the A(n-1) paper size by 2 and always rounding down to the nearest mm.
It seems the first method is more precise and does not require any recursion, but what does the ISO Standard actually specify?
The table of sizes indicates the bad 2nd method. If the Base A0 Area method is the correct one, we need to alter the article's table. Ace Frahm ( talk) 16:30, 23 February 2013 (UTC)
Summing up regarding formulas and definitions:
NisJørgensen ( talk) 16:22, 19 December 2017 (UTC)
Why not mention of A00 paper? It is in common use in draughting offices.
Also, the C sizes are not covered by ISO 216 and should only be referenced from these page. No detailed description necessary. 79.77.113.193 ( talk) 20:22, 19 April 2008 (UTC)
How thick/thin is A4 paper - 1mm/1μm/1nm/1pm?
Are material properties the only contraints for paper thinness?
Is there any special pen/ink to write on thinner papers?
Is there any minimum limit on thinness of paper to be accepted as evidence in a court of law? Anwar ( talk) 09:15, 9 May 2008 (UTC)
This page and the Paper size page appear to have the same purpose / function and contain much of the same information. I suggest they be merged. —Preceding unsigned comment added by 88.106.221.168 ( talk) 11:45, 25 August 2008 (UTC)
Anyone actually ever seen one of these up close? Unless they're used for defining the size of raffle tickets and the like, I can't see much call for anything under A8... Particularly not the envelopes! (I think I bought a novelty A8-ish size set of christmas cards with envelopes once - they fit ok, but were a bit fiddly to write and I wouldn't dreamt of trying to post them; A10 is almost stamp sized! Also I have an A7 notebook I bought because I spotted it going cheap in a trinket shop when on a trip and it had a nice design ... it proved to be very difficult to actually use! A6 is a lot more common (file cards, shorthand notebooks etc).
Not complaining or asking for removal, I'm just interested to hear if anyone actually uses such things in daily life or industry. 193.63.174.10 ( talk) 11:23, 23 October 2008 (UTC)
...or is this explained on its own page somewhere (to which we should link)?
I know what it is - wide and high enough that a piece of A4 folded into 3 along its long edge will fit neatly inside, typically for short missives with a max of about five pages... e.g. restaurant menus or other landscape type promo material, or a portrait letter / invoice / etc, typically with part of the letterhead (containing the recipient's name, mailing address and any other immediately relevant info) then being visible through a clear plastic window on the front, and the main content safely folded away on the other 2/3rds and not able to be shaken into view. But there's not even a short expo like that, and I'm not sure immediately where to or whether to include it 193.63.174.10 ( talk) 11:30, 23 October 2008 (UTC)
Isn't the B-sizes generally used for envelopes? I vaguely remember using a B4-envelope to mail forms that shouldn't be folded, and B5-envelopes for "normal" folded letters written on A4-sheets. Should this be mentioned? —Preceding unsigned comment added by 92.251.150.23 ( talk) 23:02, 11 April 2009 (UTC)
If you put DL into the wikipedia search box, there is an entry for "Dimension Lengthwise" which directs you back to this page. Although there is no discussion on this page, DL is mentioned as the final entry into the C series table at the top of page. As the C series is for envelopes, this seems logical. —Preceding
unsigned comment added by
116.212.199.202 (
talk)
00:17, 4 March 2010 (UTC)
The article mentions the publication of DIN 216 in Germany in 1922, but can anyone address the history of the adoption of these standard sizes of papers in the various countries of Europe. It would be particularly interesting to discuss when the UK went over to this metric standard. -- SteveMcCluskey ( talk) 22:36, 7 May 2009 (UTC)
This is a pretty good article, but like a lot of articles it forgets to give the quintessential piece of info, in this case, WHY did everyone except the US move to this system? I did a kind of O & M course a few years back, and the tutor said that the wonderful thing about this system is that you can cut a single piece of paper 1 square metre into any combination of A sizes and not waste a single square centimetre! This is kind of evident in the diagrams shown but it is not explicitly referred to. The other - even more fantastic thing - is that you can magnify (say) an A5 sheet on a Xerox, and the resulting A4 printout has EXACTLY the same proportions as the original A5 sheet! And draftsmen can purchase special sets of pens to use on these pages. The thickness of the lines the pens draw are calibrated to the different sizes of these sheets. So you can draw lines on an A4 sheet using the pen intended for that sheet size, then put that sheet on a Xerox and print a smaller version of your draft work on an A5 sheet. The picture will have exactly the same proportions as the bigger one. Then you can take a different pen (the one having a finer line and designed to work on A5 sheets ) and continue with your work. And so on for all sizes, magnifying up or reducing down. Try that with magnifying or reducing between quarto and foolscap!
I was around when Austalia converted from foolscap to A4 as the standard office size. I remember that at the beginning we all thought that the A4 sheet was absurdly short. Now, when I find some old document amongst my trivia and nostalgia items, I think, this looks like some medieval scroll. Actually, the article really needs some reference to the old imperial standards to round it out.
Btw, I am not a mathematician, but I gather that these A4 etc ratios are NOT the same thing as the golden mean, but that they are somehow connected. Is that true? Myles325a ( talk) 07:28, 1 October 2009 (UTC)
Yes, if you put the sides on the same line and cut it by golden mean you get the propotion of the sides. So the propotions between the edges correspond to golden mean if im not mistaken. —Preceding unsigned comment added by 80.223.217.22 ( talk) 20:22, 2 December 2009 (UTC)
What rational was there ever for developing the C series? Surely there must have been a more pressing reason than that it is "the geometric ratio between the B series and the A series"? Woscafrench ( talk) 00:24, 21 February 2010 (UTC)
I think the C series is to give sizes for envelopes. —Preceding
unsigned comment added by
116.212.199.202 (
talk)
00:15, 4 March 2010 (UTC)
The page content should be substantially reduced. No reason to have size tables twice, the nice size char for all three series is also presented twice. The specific property of "magic" aspect ratio is explained four times including the formal verification of ∀a≠0,b≠0: a/b = 2b/a ⇒ a/b = √2. Although I like formal verifications of statements, although Encyclopedic content must be verifiable, in my humble opinion, it is inappropriate present formal mathematic verifications of statements on pages like this one. If it is appropriate here, then someone should add formal explanation why weight of 1/16m2 80g/m2 paper is 5g also ...
And page should be renamed to reflect the ISO 269 formats are discussed here as well. Especially when you can ask Wikipedia for page related to ISO 269 and you will got one (different from this one). It's confusing.
To be short - to many duplications, too many unrelated information, too long, too hard to read.
193.179.199.50 ( talk) 12:19, 27 July 2010 (UTC)
The article doesn't explain the idea behind A0+, A1+, A2+ and A3+.-- Oneiros ( talk) 12:51, 18 October 2010 (UTC)
This Lichtenberg ratio article's content is pretty much already represented here, but in case there's any more, let's merge it before deleting; OK? Dicklyon ( talk) 22:47, 15 January 2011 (UTC)
In the current Brother adverts on TV certainly in the UK but almost certainly airing in other markets. Brother claim that A3 is 143% bigger than A4 in a sales pitch for their A3 format copiers.
Surely as A3 is twice as big as A4 then the claim should be 100%, can anyone help with this query? —Preceding unsigned comment added by 81.97.128.97 ( talk) 14:38, 20 February 2011 (UTC)
I understand why the C series is useful, and indeed many of the envelopes available in stationery shops are labelled in C sizes, but I can't understand what B is for and I don't believe I've ever seen it in use. Can anyone enlighten me? Beorhtwulf ( talk) 22:16, 28 February 2011 (UTC)
Aspect ratio is commonly given by the longer side first, 5:3, 3:2, 4:3, 16:9 ... Anyone a reason why not doing so in this article? NuclearEnergy ( talk) 20:39, 2 April 2011 (UTC)
Im not sure √2:1 would look right and anyway, aren't 1:x ratios usually written as 1:x and not x:1? Benboy00 ( talk) 09:13, 30 April 2011 (UTC)
I'm not sure quite what the "Application" section means with the stuff about scaled photocopying, but the English doesn't sound quite right or coherent. I fixed this a little, but I think either a rewrite or just a deletion may be more appropriate. Benboy00 ( talk) 09:14, 30 April 2011 (UTC)
Why does almost everything in the article appear twice? Pdfpdf ( talk) 12:13, 11 September 2011 (UTC)
The opening says that "ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, with the United States and Canada the only two exceptions." but the history section says that "Although they have also officially adopted the ISO 216 paper format, Colombia, Mexico, The Philippines and Chile also use mostly U.S. paper sizes in ordinary usage."
In my experience, while it might be true that Chile has adopted the standard, in practice the most commonly used format is carta (letter). The Wikipedia article on Chile concurs: [ [1]]. So either the opening should say ISO 216 specifies the official paper size of most countries in the world today, or if it wishes to continue specifying the paper size used, it should also mention that Colombia, Mexico, The Philippines and Chile are exceptions.
-- Siker ( talk) 10:20, 23 June 2012 (UTC)
I agree with Siker, in Mexico you'd be hard pressed to find a store selling A4 paper, Letter and Legal being the norm (and what the government actually uses, despite official adoption of ISO 216). — Preceding unsigned comment added by 67.161.35.102 ( talk) 10:17, 19 July 2012 (UTC)
I think diagonal sizes of the standarts (A4, A5, etc.) should be given in the tables.-- 194.27.186.205 ( talk) 09:00, 21 December 2015 (UTC)
Crediting Portmann for developing the German standard in the 20th century ignores the statement that France already had the current and ISO A2, A3, B3, B4, and B5 in 1798. What did Portmann actually develop? Since this material is unsourced, I am deleting it until someone comes forward with well-sourced information about what Portmann or the DIN standard contributed.— Finell 01:53, 11 May 2016 (UTC)
The change that was undone: https://en.wikipedia.org/?title=ISO_216&diff=next&oldid=882463098
Discarding the naming convention for short/long sides, quoting the text:
...x/y = y/x/2, which reduces to x/y = √2...
Rearranging the formula leads to:
x2 = y2/2
which reduces to
x2/y2 = 1/2} => x/y = 1/√2 => y/x = √2
meaning that the numerator and denominator in the fraction on LHS should be swapped.
Yossik ov ( talk) 19:09, 9 February 2019 (UTC)
A good-faith editor reworded an apparent recitation of the specification (using "shall"); I tried to rewrite the paragraph using encyclopedic language ("The pen widths are specified to be..."), but hit a problem. There are three (3!) references, and all are defective. We have the absurdity of a commercial organisation charging 50 Swiss francs or so to read the wording of the specification, and are left relying on various manglings. The fact that using pen nib sizes in the root(2) sequence would match the corresponding drawing scaling is an obvious, ineluctable mathematical fact that (in a rational world at least) needs no "source". But perhaps the standard actually gives specific thicknesses for lines at different drawing sizes? If so, the wording should reflect this; but no reference tells us. The metrication.com site appears to give specified line widths for A0 and A1, then claims "just use the same for A2, A3, and A4, which is nonsense. The designingbuildings.co.uk site (can't spell "its") shows ISO pens mixed in with other pens, and just mumbles about the general principle. Markus Kuhn (can spell "its") again just gives the general principle. Does anyone have access to the standard itself? Or a statement of all the facts of the stardard written in prose that is not a copyright violation? Imaginatorium ( talk) 03:59, 3 April 2019 (UTC)
An editor has asked for a discussion to address the redirect C-size. Please participate in the redirect discussion if you wish to do so. signed, Rosguill talk 23:21, 5 February 2020 (UTC)