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 the points belonging to this figure. Each one is symmetrical to itself.
It should be said that the concept of the 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 the second figures have the same center. The center of symmetry of the parallelogram is located at the point of intersection of the lines coming out of opposite points; in a circle is the center of itself. A straight line is characterized by the presence of an infinite number of such segments. Each of its points can be a center of symmetry. A right parallelepiped has nine planes. Of all the symmetrical planes, three are perpendicular to the edges. The other six go 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“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, in such a way that the segment AE, passing through the center C, is divided half in it. There are equal segments for corresponding pairs of points.
The corresponding angles of the two halves of the figure, in which there is a central symmetry, are also equal. Two figures lying on both sides of the central point, in this case, can be superimposed on each other. However, it must be said that the imposition is carried out in a special way. Unlike mirror symmetry, central symmetry involves turning one part of the figure one hundred and eighty degrees around 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 taking them out of the common plane.
In algebra, odd and even functions are studied using graphs. For an even function, the graph is built symmetrically with respect to the coordinate axis. For an odd function, it is relative to the point of origin, that is, O. So, for an odd function, central symmetry is inherent, and for an even function, it is axial.
Central symmetry implies that a plane figure has a second-order symmetry axis. In this case, the axis will lie perpendicular to the plane.
Central symmetry is fairly common in nature. Among the variety of forms in abundance, you can find the most perfectsamples. These eye-catching specimens include various types of plants, mollusks, insects, and many animals. A person admires the charm of individual flowers, petals, he is surprised by the ideal construction of honeycombs, the arrangement of seeds on a sunflower hat, leaves on a plant stem. Central symmetry is ubiquitous in life.
