Fun Math: Paper Sizes

Fun Math: Paper Sizes
Fun Math: Paper Sizes

Video: Fun Math: Paper Sizes

Video: Fun Math: Paper Sizes
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Even now, in the digital age, there is hardly a person who has not seen a piece of paper. All of us have de alt 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 note paper sets can sometimes find information on the packaging that the size of one sheet is presented in A6 or A7 format. Some others have heard that paper sizes can be represented in B and C format.

paper sizes
paper sizes

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. Why are 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 that of the old 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.

Retaining aspect ratio while downsizing is very handy for image scaling and many other operations wherever paper is used. For example, it is easy to calculatemail weight, knowing that the area of the largest sheet in series A is 1 square meter. Paper for printers has a density of 80 g / sq.m. This means that an A4 sheet (as 1/16 of an A0 sheet) 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.

paper sizes
paper sizes

Each of the formats is used in the printing industry for a specific purpose. A8 - business cards, A7 - labels, A6 - international size for postcards, A5 - leaflets and flyers, A4 - documentation. Size B paper is 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 a designer and layout designer to create a layout. Even in format B, passports and other official papers and forms, as well as thick envelopes, are made. C-size paper, in addition to making soft envelopes, is used for printing photographs.

There are other formats. In English-speaking countries, where the inch metric system is still preserved, the "Letter" format is used, 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 the A + format (otherwise RA), the paper sizes are slightly larger than those of A. So much so that, for example, folders for A4 could be made from A4 + paper. There is an SRA format that is still slightly larger than RA.

paper sheet sizes
paper sheet sizes

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

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