Editing ISO 216 (section)

== History ==
{{Redirect|Lichtenberg ratio|<math display="inline">\sqrt{2}</math>|Square root of 2}}

The oldest known mention of the advantages of basing a paper size on an [[aspect ratio]] of <math display="inline">\sqrt{2}</math> is found in a letter written on 25 October 1786 by the German scientist [[Georg Christoph Lichtenberg]] to [[Johann Beckmann]], both at the [[University of Göttingen]].<ref name="Beck">{{cite web |first=Georg Christoph |last=Lichtenberg
|title=Lichtenberg's letter to Johann Beckmann |translator-first=Markus |translator-last=Kuhn |translator-link=Markus Kuhn (computer scientist) |language=de, en |orig-year=Written 25 October 1786 |date=7 February 2006 |publisher=[[University of Cambridge]] |url=http://www.cl.cam.ac.uk/~mgk25/lichtenberg-letter.html |access-date=10 May 2016}} Published in {{cite book 
|last = Lichtenberg |first = Georg Christoph |title = Briefwechsel |trans-title=Correspondence |editor1-first=Ulrich |editor1-last=Joost |editor2-first=Albrecht |editor2-last=Schöne |editor-link2=Albrecht Schöne
|publisher = Beck |location = Munich |date = 1990 |volume=III (1785–1792)
|language=de |pages= 274–75
|url={{Google books |iz8cwXux3B0C |page=274 |plainurl=yes}} |access-date=10 May 2016 |isbn = 3-406-30958-5}}</ref> Early variants of the formats that would become ISO paper sizes A2, A3, B3, B4, and B5 then evolved in France, where they were listed in a 1798 French law on taxation of publications ({{langx|fr|Loi sur le timbre (Nº 2136)}}) that was based in part on page sizes.<ref name="B237">{{cite journal |title=Loi sur le timbre (Nº 2136) |trans-title=Stamp Act (No. 2136) |date=3 November 1798 |journal=Bulletin des Lois de la République |issue=237 |pages=1–2 |language=fr |publisher=Republic of France |location=Paris |url=http://www.cl.cam.ac.uk/~mgk25/loi-timbre.html |url-status=live |access-date=2024-01-20 |archive-url=https://web.archive.org/web/20090426170239/http://www.cl.cam.ac.uk/~mgk25/loi-timbre.html |archive-date=26 April 2009 |via=Markus Kuhn }}</ref>
[[Image:Comparison_paper_sizes.svg|thumb|Comparison of A4 (shaded grey) and C4 sizes with some similar paper and photographic paper sizes]]

Searching for a standard system of paper formats on a scientific basis at [[Die Brücke (institute)|the Bridge]] association ({{langx|de|Die Brücke}}), as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient, in 1911 [[Wilhelm Ostwald]] proposed, over a hundred years after the 1798 French law,<ref name="B237" /> a global standard{{snd}}a [[Die Brücke (institute)#Weltformat - World Standard|world format]] ({{lang|de|Weltformat}}){{snd}}for paper sizes based on the ratio <math display="inline">\sqrt{2}</math>, referring to the argument advanced by Lichtenberg's 1786 letter, but linking this to the [[metric system]] using {{convert|1|cm|lk=in}} as the width of the base format. {{ill |Walter Porstmann |de}} argued in a long article published in 1918, that a firm basis for the system of paper formats, which deal with surfaces, ought not be the length but the area; that is, linking the system of paper formats to the metric system using the square metre rather than the centimetre, constrained by <math display="inline">\tfrac{x}{y}=\sqrt{2}</math> and area <math display="inline">a = x \times y = 1</math> square metre, where <math display="inline">x</math> is the length of the shorter side and <math display="inline">y</math> is the length of the longer side, for the second equation both in metres. Porstmann also argued that formats for ''containers'' of paper, such as envelopes, should be 10% larger than the paper format itself.

In 1921, after a long discussion and another intervention by Porstmann, the Standardisation Committee of German Industry ({{lang|de|Normenausschuß der deutschen Industrie}}, or NADI in short), which is the [[Deutsches Institut für Normung|German Institute for Standardisation]] ({{lang|de|Deutsches Institut für Normung}}, or DIN in short) today, published German standard ''DI Norm 476'' the specification of four series of paper formats with ratio <math display="inline">\sqrt{2}</math>, with series A as the always preferred formats and basis for the other series. All measures are rounded to the nearest millimetre. A0 has a surface area of {{convert|1|m2}} up to a [[rounding error]], with a width of {{convert|841|mm}} and height of {{convert|1189|mm}}, so an actual area of {{convert|0.999949|m2}}; A4 is recommended as standard paper size for business, administrative and government correspondence; and A6 for postcards. Series B is based on B0 with width of {{convert|1|m}}, C0 is {{convert|917|×|1297|mm}}, and D0 {{convert|771|×|1090|mm}}. Series C is the basis for envelope formats.

The DIN paper-format concept was soon introduced as a national standard in many other countries, for example, Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Finland (1942), Uruguay (1942), Argentina (1943), Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), Israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965), South Africa (1966), France (1967), Peru (1967), Turkey (1967), Chile (1968), Greece (1970), Zimbabwe (1970), Singapore (1970), Bangladesh (1972), Thailand (1973), Barbados (1973), Australia (1974), Ecuador (1974), Colombia (1975) and Kuwait (1975).

It finally became both an international standard ([[ISO]] 216) as well as the official [[United Nations]] document format in 1975, and it is today used in almost all countries in the world, with the exception of several countries in the Americas.

In 1977, a large German car manufacturer performed a study of the paper formats found in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats.<ref name=":0" />