Since ancient times, man has developed ideas about beauty. All the creations of nature are beautiful. People are beautiful in their own way, animals and plants are delightful. The sight of a gem or a crystal of salt pleases the eye, it is difficult not to admire the snowflake or butterfly. But why is this happening? It seems to us that the appearance of objects, the right and left half of which looks the same as in mirror reflection, is correct and complete.
Apparently, the first people to think about the essence of beauty were art. Ancient sculptors who studied the structure of the human body, back in the 5th century BC. began to apply the concept of "symmetry". This word is of Greek origin and means harmony, proportionality and similarity of the arrangement of the constituent parts. The philosopher of Ancient Greece 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 (relative to a straight line), central (relative to a point) and mirror (relative to a plane).
If each of the points of the object within it has its own exact mapping relative to its center, then there is central symmetry. Her examples are geometric bodies such as a cylinder, a ball, a regular prism, etc.
The axial symmetry of the points relative to the line provides that this line intersects the middle of the segment connecting the points and is perpendicular to it. Examples of the axis of symmetry: the bisector of the undeveloped angle of an isosceles triangle, any line drawn through the center of the circle, etc. If axial symmetry is characteristic of a geometric figure, the definition of mirror points can be visualized simply by bending it along the axis and folding equal halves face-to-face. The desired points will touch in this case.
With mirror symmetry, the points of the object are located identically relative to the plane, which passes through its center.
Nature is wise and rational, so almost all of her creations have a harmonious structure. This applies to living beings, and to 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 developing perpendicular to the soil surface. In this case, the symmetry is the result of the rotation of identical elements around a common axis located in the center. The angle and frequency of their location can be different. An example is trees: spruce, maple and others. In some animals, axial symmetry also occurs, but this is less common. Of course, mathematical accuracy is rarely inherent in nature, but the similarity of the elements of the body is still amazing.
Biologists more often consider not axial symmetry, but bilateral (bilateral). Its example is butterfly or dragonfly wings, plant leaves, flower petals, etc. In each case, the right and left parts of a living object are equal and represent a mirror image of each other.
Spherical symmetry is characteristic of the fruits of many plants, for some fish, mollusks and viruses. And examples of ray symmetry are starfish, some types of worms, and echinoderms.
In human eyes, asymmetry is most often associated with irregularity or inferiority. Therefore, in most creations of human hands, symmetry and harmony are traced.
