What is the central symmetry?

The concept of "central symmetry" of the figure assumes the existence of a certain point - the center of symmetry. On both sides of it are the points belonging to this figure. Each of them has a symmetrical self.

It should be said that the concept of center is absent in Euclidean geometry. In the eleventh book, in the thirty-eighth sentence, there is a definition of a spatial symmetric axis. The concept of the center first appeared in the 16th century.

Central symmetry is present in such figures known to all as the parallelogram and the circle. Both the first and the second figure have one center. The center of symmetry of the parallelogram is located at the point of intersection of straight lines emerging from opposite points; In the circle - this is the center of her own. For a straight line, there is an infinite number of such sections. Each of its points can be a center of symmetry. The straight parallelepiped has nine planes. Of all the 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 symmetric with respect to the center C if each point A of the body has a point E lying within the same figure, such that the segment AE, passing through Center C, is divided in it in half. For corresponding pairs of points there are equal segments.

The corresponding angles of the two halves of the figure, in which the 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, it must be said that the imposition is carried out in a special way. Unlike the mirror one, the central symmetry involves turning 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. Thus, two parts of the figure can be superimposed on each other without removing them from the common plane.

In the algebra of the study of odd and even functions is carried out using graphs. For an even function, the graph is symmetrically constructed with respect to the coordinate axis. For odd - with respect to the point of origin, that is, O. Thus, for an odd function, there is a central symmetry, and for an even function, there is an axial symmetry.

Central symmetry presupposes the presence of a symmetry axis of the second order in a plane figure. In this case, the axis will lie perpendicular to the plane.

Central symmetry in nature is quite common . Among the variety of forms in abundance you can meet the most perfect samples. To such samples, attracting the eye, include various species of plants, mollusks, insects, many animals. Man admires the charm of individual flowers, petals, he is surprised by the ideal construction of bee honeycombs, the arrangement on the hat of sunflower seeds, leaves on the stem of plants. Central symmetry in life is everywhere.