Perfection of lines - axial symmetry in life

Since ancient times man has worked out representationsabout beauty. All the creatures of nature are beautiful. In their own way, people are beautiful, animals and plants are amazing. Pleases the sight of a precious stone or salt crystal, it's hard not to enjoy a snowflake or a butterfly. But why does this happen? We seem to be correct and complete the kind of objects, the right and left half of which looks the same, as in the mirror image.

Apparently, the first people to think about the essence of beautyart. Ancient sculptors who studied the structure of the human body, back in the V century BC. began to apply the concept of "symmetry". This word is of Greek origin and means the harmony, proportionality and similarity of the arrangement of the constituent parts. The philosopher of Ancient Greece Plato argued that only what can be beautiful is symmetrical and proportional.

Three types of symmetry are considered in geometry and mathematics: 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 withinit has its own exact map with respect to its center - there is a central symmetry. Its example is such geometric bodies as a cylinder, a ball, a regular prism, etc.

Axial symmetry of points with respect to the straight lineprovides that this straight line crosses the middle of the segment connecting points, and is perpendicular to it. Examples of the axis of symmetry: the bisector of the non-expanded angle of an isosceles triangle, any straight line drawn through the center of a circle, etc. If the geometrical figure is characterized by axial symmetry, the definition of mirror points can be visualized simply by bending it along the axis and folding the equal halves face to face. The required points will come into contact at the same time.

With mirror symmetry, the points of the object are the same with respect to the plane that passes through its center.

Nature is wise and rational, so almost all of itcreations have a harmonious structure. This applies to living beings, and to inanimate objects. For the structure of most forms of life, one of three types of symmetry is characteristic: two-sided, ray or globular.

Most often axial symmetry in nature canobserved in plants developing perpendicular to the soil surface. In this case, symmetry is the result of rotation of identical elements around a common axis located in the center. The angle and frequency of their location may be different. Examples are trees: spruce, maple and others. In some animals, axial symmetry also occurs, but this happens less often. Of course, nature is rarely characterized by mathematical accuracy, but the similarity of the elements of the body is still astounding.

Biologists often consider non-axialsymmetry, and bilateral (bilateral). Her example is the wings of a butterfly or dragonfly, leaves of plants, petals of flowers, etc. In each case, the right and left parts of the 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. Examples of ray symmetry are starfish, some species of worms, echinoderms.

In the eyes of a person, asymmetry is most often associated with improper or defective behavior. Therefore, in most creations of human hands, symmetry and harmony are traced.