The concept of "central symmetry" of a figure implies the existence of a certain point - the center of symmetry. On both sides of it are points belonging to this figure. Each of them is symmetrical to itself.
It should be said that the concept of a center is absent in Euclidean geometry. Moreover, in the eleventh book, in the thirty-eighth sentence, there is a definition of a spatial symmetrical axis. The concept of the center first appeared in the 16th century.
Central symmetry is present in such well-known figures as a parallelogram and a circle. Both the first and second figures have one center. The center of symmetry of the parallelogram is located at the intersection of straight lines that emerge from opposite points; in a circle it is the center of itself. The straight line is characterized by the presence of an infinite number of such sections. Each of its points can be a center of symmetry. A straight box has nine planes. Of all symmetrical planes, three are perpendicular to the edges. The other six pass through the diagonals of the faces. However, there is a figure that does not have it. It is an arbitrary triangle.
In some sources, the concept of "central symmetry" is defined as follows: a geometric body (figure) is considered symmetrical with respect to the center C if each point A of the body has a point E lying within the same figure, so that the segment AE passing through center C, is cut in half in it. For the corresponding pairs of points there are equal segments.
The corresponding angles of the two halves of the figure in which central symmetry is present are also equal. Two figures lying on both sides of the central point, in this case, can be superimposed on each other. However, I must say that the overlay is carried out in a special way. Unlike mirror, central symmetry involves the rotation of one part of the figure one hundred and eighty degrees near the center. Thus, one part will stand in a mirror position relative to the second. The two parts of the figure can thus be superimposed on each other, without removing from the common plane.
In algebra, the study of odd and even functions is carried out using graphs. For an even function, the graph is built symmetrically with respect to the coordinate axis. For odd - with respect to the origin, that is, O. So, for an odd function, central symmetry is inherent, and for even - axial symmetry.
Central symmetry implies the presence of a second-order axis of symmetry in a plane figure. In this case, the axis will lie perpendicular to the plane.
Central symmetry in nature is fairly common. Among the variety of forms in abundance, you can find the most advanced designs. Such eye-catching specimens include various species of plants, mollusks, insects, and many animals. A person admires the charm of individual flowers, petals, he is surprised by the perfect construction of bee honeycombs, the location on the hat of sunflower seeds, leaves on the stem of plants. Central symmetry in life is ubiquitous.
