Since ancient times, man has developed ideas about beauty. All creations of nature are beautiful. People are beautiful in their own way, animals and plants are delightful. The spectacle of a precious stone or a s alt crystal pleases the eye, it is difficult not to admire a snowflake or a butterfly. But why is this happening? It seems to us that the appearance of objects is correct and complete, the right and left halves of which look the same, as in a mirror image.
Apparently, people of art were the first to think about the essence of beauty. Ancient sculptors who studied the structure of the human body, back in the 5th century BC. began to use the concept of "symmetry". This word is of Greek origin and means harmony, proportionality and similarity in the arrangement of the constituent parts. The ancient Greek philosopher Plato argued that only that which is symmetrical and proportionate can be beautiful.
In geometry and mathematics, three types of symmetry are considered: axial symmetry (with respect to a straight line), central (with respect to a point) and mirror (with respect to a plane).
If each of the points of the object has its own exact mapping within itrelative to its center - there is a central symmetry. Its examples are such geometric bodies as a cylinder, a ball, a regular prism, etc.
Axial symmetry of points relative to a straight line provides that this straight line intersects the middle of the segment connecting the points and is perpendicular to it. Examples of an axis of symmetry: the bisector of a non-expanded angle of an isosceles triangle, any straight line drawn through the center of a circle, etc. If a geometric figure is characterized by axial symmetry, the definition of mirror points can be visualized by simply bending it along the axis and folding equal halves “face to face”. The desired points will touch each other.
With mirror symmetry, the points of an object are located the same relative to the plane that passes through its center.
Nature is wise and rational, so almost all her creations have a harmonious structure. This applies to both living beings and inanimate objects. The structure of most life forms is characterized by one of three types of symmetry: bilateral, radial or spherical.
Most often, axial symmetry in nature can be observed in plants that develop perpendicular to the soil surface. In this case, symmetry is the result of rotating identical elements around a common axis located in the center. The angle and frequency of their location may be different. Trees are an example: spruce, maple and others. In some animals, axial symmetry also occurs, but it happensless often. Of course, nature rarely has mathematical precision, but the similarity of the elements of the body is still striking.
Biologists often consider not axial symmetry, but bilateral (bilateral). Its examples are the wings of a butterfly or dragonfly, plant leaves, flower petals, etc. In each case, the right and left parts of the living object are equal and are mirror images of each other.
Spherical symmetry is typical for the fruits of many plants, for some fish, shellfish and viruses. And examples of ray symmetry are starfish, some types of worms, echinoderms.
In the eyes of a person, asymmetry is most often associated with irregularity or inferiority. Therefore, in most of the creations of human hands, symmetry and harmony can be traced.
