Entertaining mathematics: paper sizes

Even now, in the era of digital technology, it is unlikelythere is 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 in the school or studied drawing at the institute, got acquainted with A3, A2 and A1. And the owners of sets of paper for recording can sometimes find on the packaging information that the size of one sheet is presented in A6 or A7 format. Still others have heard that paper sizes can be represented in B and C format.

Try using the ruler to determine the dimensionssheets of A4 paper. We find that in length it is 297 mm, and in width - 210 mm. What are the interesting figures? If you cut any standard sheet of paper in half, the ratio of the length of the sides of the new sheets will remain the same as that of the old large sheet. That is, a smaller paper is obtained from a larger paper by simply dividing it. Sheet A4 is half the sheet A3, and sheet A5 is half A4.

Preservation of proportions when the size is reduced is veryIt is convenient for scaling images and many other operations wherever paper is used. For example, it is easy to calculate the weight of the mail, knowing that the area of ​​the largest sheet in the A series is 1 square meter. Paper for printers has a density of 80 g / m2. Hence, the A4 sheet (as 1/16 of the sheet A0) will weigh 5 grams. To calculate the weight of envelopes also it is possible, being guided by the resulted reasonings, after all the sizes of formats of paper B and C (used for envelopes) obey the same parities, as for A.

Each of the formats is used ina specific goal. A8 - business cards, A7 - labels, A6 - international size for postcards, A5 - flyers and flyers, A4 - documentation. The size of paper in B format is such that one side of the sheet has an integer number of centimeters. This is convenient for creating products with images, since it is easier for a designer and layout designer to create a layout. In format B, passports and other official papers and letterheads are produced, as well as tight envelopes. Paper format C, in addition to making soft envelopes, is used for printing photos.

There are other formats. In English-speaking countries, where the inch metric system is still preserved, the format is "Letter", as well as "Legal" and "Tabloid". The relationship between the sides of the paper is made according to the principle described above, but the length of the sides is a multiple of an integer number of inches. In the A + format (otherwise RA), the paper sizes are slightly larger than those of A. So much so that it is possible to make A4 folders from A4 + paper. There is an SRA format, which is slightly more than RA.

You can also notice that the standard sizesthe papers look quite aesthetically pleasing. The ratio of the short and long side of the sheet is convenient not only in technical terms. It obeys the proportion of the "silver section", not so known as the "golden section", but also built on irrational numbers. At the heart of the golden section (which, by the way, is found in the sizes of books) is the square root of five. Silver is built on the basis of the root of the two. And continuing to divide a piece of paper in half to infinity, we could create a fractal sequence.