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# What do mathematics and embroidery have in common?

At first glance, nothing. But let’s look deeper. Ukrainian embroidery strikes with a variety of patterns – circles, rhombuses, dots, squares, triangles, spirals …

There are also figures in it, though their form is slightly different from the traditional one. Therefore, it is not surprising that when you look at the Ukrainian embroidery, you get the impression that you are in front of “Mathematics” for first-timers.

But not only is the connection of embroidery with the “queen of all sciences.” It turns out that most ornaments are created by the laws of symmetry, most often – mirror.

## Mathematical foundations of Ukrainian embroidery

Embroidery is a true science. Each technique provides its own order of drawing ornaments and sequence of arrangement of patterns. It is hard to imagine how much time the craftsmen spent to keep all their elements clear and even, at the same distance.

In the center of scientific research embroideries are not only types of ornamentation, color design of drawing, symbolism. Researchers are trying to understand how these compositions are formed and placed on the plane. They were able to determine that borders (ornamentation strips) are constructed using the following geometric phenomena:

• parallel transfer;
• mirror symmetry with vertical or horizontal axis;
• rotating symmetry.

This proves that embroidery is a difficult job. Each technique is based on certain calculations, so the craftsmen were very careful during their work. Now you understand why every embroidery is a work of art!

## How embroidery mathematics helps to create it

Due to the symmetry of embroidery, scientists have been able to create its mathematical model. What is it for? To create programs that allow embroidery machines to make patterns similar to traditional ones. Programmed the embroidery algorithm, the machine worked for a while – and all, you have the desired pattern. Isn’t it a miracle?

One program is called Inkscape. It is governed by seven types of symmetry curbs. It is used in the mass production of embroidered clothing. The use of mathematical modeling allows not only to reproduce traditional ornaments, but also to create new ones. Thus, machine embroidery allows you to make patterns of any shape without stitches of transition. So embroidery is not only a product of creativity. The symmetry of the ornaments and some calculations are important here.