notion "central symmetry" figure assumes the existence of a certain point - the center of symmetry.On both sides of it are located the points belonging to this figure.Each of them has a symmetrical itself.
should be noted that the concept of the center is not in the Euclidean geometry.In the eleventh book in thirty-eight proposals is the definition of the spatial symmetry axis.The concept of the center was first introduced in the 16th century.
Central symmetry is present in all known figures such as a circle and a parallelogram.And the first and the second figure the center of one.The center of symmetry of a parallelogram is located at the intersection of lines emerging from opposite points;in a circle - it is the center of her.For direct characterized by an infinite number of such sites.Each point can be the center of symmetry.In the box there is a direct nine planes.Of all three symmetrical planes perpendicular to the ribs.Other six pass through the diagonal faces.However, there is a figure that does not have one.She is an arbitrary triangle.
In some sources the term "central symmetry" is defined as follows: a geometric body (figure) is considered symmetrical about the center C, when each point of the body has a point E lying within the same figure, so that the segment AEpassing through the center C, to cut it in half.For the corresponding pairs of points, there are equal lengths.
corresponding corners two half pieces in which there is a central symmetry are also equal.Two pieces lying on both sides of the central point in this case can be overlaid.However, it must be said that the application is carried out in a special way.Unlike a mirror, central symmetry involves the rotation of one of the figures of one hundred eighty degrees around the center.Thus, one part of the rise in the mirror relative to the second position.Two parts of the figures can thus be overlaid without prompting from a common plane.
In algebra izuchenin odd and even functions by using graphs.For even function graph is constructed symmetrically with respect to the coordinate axes.For odd - in relation to the point of origin, that is O. Thus, for the odd function is inherent in central symmetry, and for the even - axis.
central symmetry suggests the presence of a plane figure axis of symmetry of the second order.In this case, the axis is perpendicular to the plane of lie.
fairly common central symmetry in nature.Among the variety of forms in abundance can be found the most perfect specimens.These patterns, eye-view, include a variety of species of plants, mollusks, insects, many of the animals.Man admiring the beauty of the individual flowers, petals, it is surprising to build the perfect honeycomb arrangement on the cap of sunflower seeds, the leaves on the stem of the plant.Central symmetry is found everywhere in life.
