The acronym ISO is used to denote the international convention in which the A4 paper size is included. The International Standards Organization has set the definitions for three series known as A, B and C. The proportion used in these series is a mathematical ratio long known to have special qualities for publishing purposes. The ISO standard also has advantages for working out the weight of multiple sheets for mailing.

Books, posters, writing paper, cards and other documents were printed in many nonstandard formats before this system was implemented. Theories about optimum page composition have been considered and debated at least as long as the printing press has existed. This standard, first proposed in France, but then forgotten, was again suggested by the German Georg Lichtenberg in the eighteenth century, and finally organized in that country early in the twentieth century.

This convention has come into use in the majority of countries in the world. By the year 1975, it had become so common that the International Standards Organization established this as the internationally accepted format. The exceptions are the United States, Canada, Mexico, and the Philippines, where the letter format (8.5 x 11) is used.

This metric system based standard is designated ISO 216, and it is built upon a proportion that is an expression of the square root of 2. Stated as a ratio, it is 1 to 1.4142. The basic sheet that the A4 is derived from is called A0. An A0 sheet measures 841 by 1,189 millimeters and equals one square meter.

The ISO 216 standard includes a second series called B, and the related series known as ISO 269 is comprised of the C series, usually used as envelopes. The relationship between the different series is a geometric progression. This progression is a consistent increase of the side lengths by a factor of 2 1/8. This produces sheets whose areas are geometric means of one another. So the area of a C0 is between an A0 and a B0, and a B1 format is between an A0 and an A1.

Shapes based upon the square root of 2 are a special ratio which produces the exact shape on a smaller scale when folded in half on the longer dimension. When a letter formatted sheet is folded, this is not the case. The advantage to this shape becomes clear when one wants to reproduce two facing pages scaled to A4 on an A3 sheet, which will result in a perfect fit.

Fans of paper folding, such as the Japanese origami, find this to be the most appropriate shape for this art form. When used in this manner, the format may be called silver rectangles, for the silver ratio, or even A4 rectangles. The silver ratio is in reference to the 1 to 1.1412 format.

Finally, the A0 format, and its smaller derivatives, including A4 paper size, are especially convenient for measurement of quantities of sheets. The weight of the square meter of A0 paper can be determined, so the smaller sizes weight is easily calculated as a fraction of that figure. As multiples of ten, the math is rather simple, and mass can also be determined this way.

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