The Lister List

More On A4 (Silver) Rectangles

More about the Silver Rectangle and the international standards for paper sizes

I was interested in the query of Juan Pedro Rubio of Madrid which he posted to BOSmail on 9th February, 2005 asking about the availability in different countries of the international sizes of paper. This has now been adequately answered by others in the Group and all I want to add is that coloured A4 paper is sometimes handed out at BOS conventions for use in folding. White A4 paper is available in Britain in super abundance and cheaply, but coloured paper is obviously not so common. I have never investigated a source myself, but I presume that it can be obtained readily enough from stationery dealers, such as Staples. Can anyone say any more about this? I think, however it will turn out that there is not be nearly as much variety in A4 papers (or even A5 papers) as there is in the myriads of kinds of square origami paper available both from Western counties and Japan.

I was, however, more interested in J P Rubio's link to this website: This is a site devoted to International Standard paper sizes and is compiled by Markus Kuhn. In the past I have ransacked the Web for sites of this kind, and among other sites I found some earlier pages by Markus Kuhn. However, he has now extended his site and moved it to a new address at Cambridge, England. (I think his changes must be fairly recent.) It is excellent on the topic of international paper sizes, and I recommend people to visit it.

What interests me is that it has a section on the History of the ISO Paper Formats. (ISO means the International Standards Organisation). These standards are based on what we know as the ratio of the Silver Rectangle (1 X square root 2). It is usually held that the idea of using paper with a ratio of 1 X square root 2 originated in Germany in the 19th Century and was adopted as a DIN in 1922. (DIN means German Industrial Standard.)

However, I have previously come across suggestions that the French proposed to introduce paper sizes in this ratio during the Revolution in the 1790s. I have never, however, found anything definite about this.

Now Markus Kuhn writes that this ratio for paper sizes was probably first noted by Georg Christoph Lichtenberg of the University of Grottingen, Germany, in a letter that he wrote on 25th October, 1786 to Johann Beckmann. Following this, and after introducing the metre for measurements of length, the revolutionary French government published the "loi sur le timbre" (no. 2136) on 3rd November, 1794. This was a law for the taxation of paper which defined several formats that corresponded with what later became ISO paper sizes: "grand registre" = ISO A2, "grand papier" = ISO B3, "moyen papier" = ISO A3, "petit papier" = ISO B4, "demi feille" = ISO B5 and "effets de commerce" = ISO 1/2 B5.( Presumably this is B6.) Curiously there doesn't seem to have been a size equal to now ubiquitous A4.

The French format series never became widely known and was quickly forgotten. The future ISO formats, which were based on exactly the same design principles were reinvented over a hundred years later in Germany by Dr. Walter Porstmann and were adopted as the German DIN standard no. 476 in 1922. From Germany the "new" paper sizes spread to many other countries and were adopted as an ISO standard in 1977. The new standards were rapidly adopted in Britain in the 1970s, but they have not yet been adopted in the United States, where they continue to use "letter-size paper" instead of A4.

A4 can be obtained in the United States, but only with some difficulty. At the same time, American letter-size paper is not easy to obtain in Britain. I obtained a packet by doing a swap with an American friend. Photocopiers usually adopt to both sizes but some firms operating in both North America and other parts of the world have to keep stocks of both sizes of paper

One interesting fact mentioned by Markus Kuhn is that the 1 X Square Root 2 ratio is known, from Georg Christoph Lichtenberg as the “Lichtenberg Ratio” and he points out that it is occasionally confused with the Golden Ratio. However, Markus makes no mention of the term which we use in origami circles, namely, "The Silver Ratio". This is explained by John Cunliffe in his column in British Origami no. 75, April, 1979, page 12, where he writes that the British newspaper, the Sunday Telegraph had mentioned the need of the British Origami Society for a name for the 1 X square root 2 rectangle. A number of interesting suggestions were made by readers, but John wrote that his own preference was for the name put forward by no less than the dictionaries department of the Oxford University Press, publishers of the Oxford English Dictionary and many other dictionaries of differing kinds and sizes. They suggested "Silver Rectangle" So lexicographers at Oxford advanced from being mere recorders of words to creators of words. John Cunliffe concluded that he proposed that he would use the term "silver rectangle" for the time being. He went on to write the BOS Booklet no. 21 (April, 1983) with the name "The Silver Rectangle" and within the BOS this name has stuck. it would be interesting to know how far the term "Silver Rectangle" has spread in the wider world.

By another coincidence, BO 75 was the issue that contained my own entirely unrelated article about the Golden Rectangle; "Golden and Divine".

Martin Kuhn who compiled the web site from which this history was taken was born in Germany. After studying at the University of Erlangen in Germany, he took a master's degree at Purdue University in the Unite States. This was the university at which Professor Arnold Tubis was the head of the Physics Department. Arnold has now retired and lives in California, where he is still active in paperfolding. Martin Kuhn then went on to take his PhD at Cambridge where he is a lecturer at the Computer Laboratory. There is no indication that he is interested in Origami, but he is obviously interested in the mathematics of paper sizes. Could he be persuaded to take up the study of the mathematics of Origami and join the likes of Tom Hull, Eric Demaine and Galen Pickett?

However this may be, Martin does not mention the curious suggestion that the length of A4 (and therefore all the other ISO paper sizes) was derived from the ancient Roman Foot. It is a fact that A4 is exactly the length of a Roman Foot, using the best possible means of calculating it Thoki Yenn was convinced of this, although I myself cannot think that it is any other than one of those weird coincidences that seem to be written into the laws of nature. (The area of A0 size paper is one square metre and the other sizes follow from this.) See Thoki Yenn's Web site (which may be found by a link within the BOS Web site) and see also my own article "As Long as the Emperor's Foot" in Lister's List, also on the BOS Web site).

Martin Kuhn offers a link to another notion of the origin of the ISO standards which is also based on coincidence. This is put forward by Vernon Jenkins, who, in the manner of the exponents of the notorious "Bible Code" finds correspondences with numbers mentioned in the Bible and not least, the infamous number 666 (the number of the Beast) which occurs in the Book of Revelations.

But for our purpose, the fascinating revelation is that the French revolutionaries not only introduced the metre (and with it the gramme and litre), but also the concept of sheets of paper with the proportions of what we now call the Silver Rectangle. Incidentally, the scientists of the day based the metre on one ten millionth of the distance from the equator to the pole which they determined after exhaustive investigations using the limited technology of the time. Sadly, despite the most careful efforts to measure this distance, they got it wrong, but we are stuck with the metre as they decided it. What room for the print of the Roman Emperor’s foot?

David Lister

Grimsby, England.

Posted to the BOSmail Internet Group
11th February, 2005

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