A standard format for sheets used in commerce and desktop publishing is the ISO A4 paper size. The ISO, or International Standard Organization format, is comprised of three basic series entitled A, B, and C. For its versatile uses and maintaining a professional international business image, the scales and shape defined by this system are beneficial. This is also a convenient format for use in determining postal rates.
In the past, no standard sizes existed for sheets used for printing such things as letters, catalogs, magazines or posters. Different ideas about the size, and especially proportion of sheets go back to at least as far as Gutenberg. An eighteenth century German scientist named Lichtenberg first proposed the size that the A4 standard is based upon, and it came into use there in the early twentieth century.
Once begun in Germany, the standard spread quickly to other countries over the next fifty years. The ISO conferred international status on this system in the mid 1970s. In North America, the US and Canada still use the letter size, based on inches. Mexico, the Philippines and some South American countries have adopted the ISO system, yet the letter format is still in common use.
ISO 216 is the nomenclature used for the series including that which A4 is part of. The unique proportion of the sheets in this design is known as the square root of two, which written as a ratio is 1:1.4142. The basic sheet area is the equivalent of one square meter, and is designated A0. Full sheet dimensions are 841 x 1,189 millimeters, and subdivided sections are rounded to the nearest millimeter.
The B series is included in the ISO 216 division along with A, and the related type C is placed under the heading ISO 269.These series, all the same proportion, are further related as a geometric progression, meaning their dimensions increase by a factor of 2 1/8 according to the length of their sides. The A, B, and C variants are related as geometric means, so a B3 would be between the area of A2 and A3, and C1 ranges between A1 and B1. Thus, appropriate envelope dimensions exist for both A and B in the C range.
The beauty of the ratio for these series, 1:1.1412, is as a unique proportion because when sheets of this shape are folded in half, parallel to the shortest side, the resulting sheet is the same shape. This is not true of the letter format sheet. This is useful for the purposes of scaling and copying. When copying two facing pages from a book or of business documents printed in this aspect ratio, they fit perfectly on a sheet when scaled down.
Besides being convenient for scaling purposes, sheets of this proportion are used for paper folding, like origami, where they may be referred to as A4 rectangles. They are also called silver rectangles, because this shape that remains the same however many times it is folded or trimmed in half is called the silver ratio.
A useful property of the A0 sheet, and of the A4 paper size, is that, because the base size equals one square meter, it is an easy matter to compute weights and masses of bulk quantities. Since the standard weight of a square meter of paper is a known constant, and the smaller sizes derived from it are fractions of the whole, weights and masses are arrived at by simple arithmetic, much easier than letter format.
In the past, no standard sizes existed for sheets used for printing such things as letters, catalogs, magazines or posters. Different ideas about the size, and especially proportion of sheets go back to at least as far as Gutenberg. An eighteenth century German scientist named Lichtenberg first proposed the size that the A4 standard is based upon, and it came into use there in the early twentieth century.
Once begun in Germany, the standard spread quickly to other countries over the next fifty years. The ISO conferred international status on this system in the mid 1970s. In North America, the US and Canada still use the letter size, based on inches. Mexico, the Philippines and some South American countries have adopted the ISO system, yet the letter format is still in common use.
ISO 216 is the nomenclature used for the series including that which A4 is part of. The unique proportion of the sheets in this design is known as the square root of two, which written as a ratio is 1:1.4142. The basic sheet area is the equivalent of one square meter, and is designated A0. Full sheet dimensions are 841 x 1,189 millimeters, and subdivided sections are rounded to the nearest millimeter.
The B series is included in the ISO 216 division along with A, and the related type C is placed under the heading ISO 269.These series, all the same proportion, are further related as a geometric progression, meaning their dimensions increase by a factor of 2 1/8 according to the length of their sides. The A, B, and C variants are related as geometric means, so a B3 would be between the area of A2 and A3, and C1 ranges between A1 and B1. Thus, appropriate envelope dimensions exist for both A and B in the C range.
The beauty of the ratio for these series, 1:1.1412, is as a unique proportion because when sheets of this shape are folded in half, parallel to the shortest side, the resulting sheet is the same shape. This is not true of the letter format sheet. This is useful for the purposes of scaling and copying. When copying two facing pages from a book or of business documents printed in this aspect ratio, they fit perfectly on a sheet when scaled down.
Besides being convenient for scaling purposes, sheets of this proportion are used for paper folding, like origami, where they may be referred to as A4 rectangles. They are also called silver rectangles, because this shape that remains the same however many times it is folded or trimmed in half is called the silver ratio.
A useful property of the A0 sheet, and of the A4 paper size, is that, because the base size equals one square meter, it is an easy matter to compute weights and masses of bulk quantities. Since the standard weight of a square meter of paper is a known constant, and the smaller sizes derived from it are fractions of the whole, weights and masses are arrived at by simple arithmetic, much easier than letter format.
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