Mirror symmetry and a sense of beauty

As we know from the school course of geometry, symmetry can be one of three types: central, axial and symmetry with respect to a plane. Central is the symmetry of an object with respect to a point (the simplest example is any circle), the axial symmetry is relative to a straight line, and the last kind of proportionality (relative to the plane) is known to us also as mirror symmetry.

Geometry with mathematics gives us clear criteria by which we can uniquely determine which object can be considered symmetrical and which is not. However, in addition to boring formulations, there is one more parameter that a person identifies almost unmistakably is beauty.

Even the ancient Greeks drew attention to the fact that symmetrical objects are inherent in harmony and beauty. The German mathematician G. Weil once wrote the work "Studies on symmetry", in which he argues that symmetry and beauty are closely interrelated. According to him, what is considered to be symmetrical has a good proportion of proportions, and symmetry itself is a special type of consistency of parts of the whole.

Mirror symmetry in geometry is often associated with regular polygons, but if you look closely, these figures are quite common in nature. Some of them can be seen in the form of crystals, others - in the form of simple microorganisms or viruses.

Mirror symmetry is very common in architecture. It is present in all the buildings of Ancient Egypt and temples of ancient Greece, amphitheatres, basilicas and triumphal arches of the Romans, churches and palaces of the Renaissance, as well as in many works of modern architecture.

In nature, mirror symmetry is characteristic of animals and plants that move or grow parallel to the earth's surface, and is also often found in the form of a reflection of the terrain in the water surface of a river, lake, etc. A vivid example of this are the colorful butterfly wings, the pattern on which is surprisingly exactly the same.

And now turn your attention to the person. Why do some people like to be written as handsome, while others are completely devoid of human attractiveness? British scientists, led by the evolutionary biologist William Brown, set out to obtain an accurate answer to this question and conducted a study in which 37 girls and 40 young people took part (a detailed report was published in the PNAS edition). First, scientists using a scanner created a three-dimensional body volume model of each of the participants in this test. Then researchers on 24 parameters determined how accurate the mirror symmetry of each model is. After that each volunteer was asked to evaluate the attractiveness of the participants of the opposite sex.

The result dispelled all doubts. The experiment confirmed that the mirror symmetry of the body has a direct effect on the beauty of man. And this is true for both men and women.

Which of this can be inferred? Ideals of beauty vary, but at the same time remain the same - the reason for attractiveness lies in symmetry. And this is true for everything that surrounds us in this wonderful world.