Even now, in the digital age, there is hardly a person who has not seen a sheet of paper. All of us have dealt with the most common format - A4. Those who drew wall newspapers at school or studied drawing at the institute got acquainted with A3, A2 and A1. And owners of sets of recording paper can sometimes find information on the package that the size of one sheet is presented in A6 or A7 format. Some have heard that paper sizes can be presented in B and C.
Let's try using a ruler to determine the size of sheets of A4 paper. We will find that it is 297 mm long and 210 mm wide. What makes these numbers interesting? If you cut any standard sheet of paper in half, the aspect ratio of the new sheets will remain the same as the previous large sheet. That is, smaller paper is obtained from larger paper by simple division. Sheet A4 is half of sheet A3, and sheet A5 is half of A4.
Maintaining proportions while reducing the size is very convenient for scaling images and many other operations wherever paper is used. For example, it is easy to calculate the weight of mail, knowing that the area of the largest sheet in series A is 1 square meter. Paper for printers has a density of 80 g / m2. So, sheet A4 (as 1/16 of the sheet A0) will weigh 5 grams. You can also calculate the weight of envelopes, guided by the above reasoning, because the sizes of paper sizes B and C (used for envelopes) obey the same ratios as for A.
Each of the formats is used in printing for a specific purpose. A8 are business cards, A7 are labels, A6 is the international size for postcards, A5 is flyers and flyers, A4 is documentation. The sizes of paper in size B are such that one of the sides of the sheet has an integer number of centimeters. This is convenient for creating products with images, as it is easier for the designer and layout designer to create a layout. In format B, passports and other official papers and letterheads, as well as thick envelopes, are produced. C-size paper, in addition to making soft envelopes, is used to print photographs.
There are other formats. In English-speaking countries, where the inch metric system is still preserved, they use the letter format, as well as legal and tabloid. The ratios between the sides of the paper are made according to the principle described above, but the length of the sides is a multiple of an integer number of inches. In A + format (aka RA), the paper size is slightly larger than that of A. So much so that, for example, A4 + folders could be made out of A4 + paper. There is an SRA format, which is a little larger than RA.
You can also notice that the standard paper sizes look quite aesthetically pleasing. The ratio of the short and long sides of the sheet is convenient not only technically. It obeys the proportion of the "silver section", not as famous as the "golden section", but also built on irrational numbers. The golden ratio (which, incidentally, is found in book sizes) is based on the square root of five. Silver is built on the basis of a root of two. And continuing to divide the sheet of paper in half to infinity, we could create a fractal sequence.