Human life is filled with symmetry. This is convenient, beautiful, no need to invent new standards. But what is it really and is it really beautiful in nature, as is commonly believed?
Symmetry
С древних времен люди стремятся упорядочить мир around yourself. Therefore, something is considered beautiful, but something is not very. From an aesthetic point of view, the golden and silver sections, as well as, of course, symmetry are considered attractive. This term is of Greek origin and literally means "proportionality." Of course, this is not only a coincidence on this basis, but also on some others. In the general sense, symmetry is such a property of an object, when, as a result of certain formations, the result is equal to the initial data. It is found both in living and inanimate nature, as well as in objects made by man.
First of all, the term "symmetry" is used ingeometry, but is used in many scientific fields, and its value remains generally unchanged. This phenomenon is quite common and is considered interesting, since several types of it, as well as elements, are distinguished. The use of symmetry is also interesting, because it is found not only in nature, but also in ornaments on fabric, borders of buildings, and many other man-made objects. It is worth considering this phenomenon in more detail, because it is extremely fascinating.
Use of the term in other scientific fields
In the future, symmetry will be considered withIn terms of geometry, however, it is worth mentioning that this word is used not only here. Biology, virology, chemistry, physics, crystallography - all this is an incomplete list of areas in which this phenomenon is studied from different angles and in different conditions. From what science this term refers to, for example, classification. Thus, the division into types varies greatly, although some basic ones, perhaps, remain the same everywhere.
Classification
There are several main types of symmetry, of which three are most often encountered:
- Mirror - observed with respect to one or several planes. The term is also used to denote the type of symmetry when a transformation such as reflection is used.
- Radial, radial or axial - there are several options in different
- Central - there is symmetry about a certain point.
In addition, the following types are also distinguished in geometry; they are much less common, but no less curious:
- sliding
- rotational;
- dotted;
- progressive;
- screw;
- fractal;
- etc.
In biology, all species are called somewhat differently.although in fact can be the same. Subdivision into certain groups occurs on the basis of the presence or absence, as well as the number of certain elements, such as centers, planes and axes of symmetry. They should be considered separately and in more detail.
Basic Elements
В явлении выделяют некоторые черты, одна из which is necessarily present. The so-called basic elements include planes, centers and axes of symmetry. It is in accordance with their presence, absence and quantity that the type is determined.
The center of symmetry is the point inside the figure.or a crystal in which the lines converge, connecting in pairs all sides parallel to each other. Of course, it does not always exist. If there are sides to which there is no parallel pair, then such a point cannot be found, since there is none. In accordance with the definition, it is obvious that the center of symmetry is that through which the figure can be reflected on itself. An example would be, for example, a circle and a point in its middle. This element is usually referred to as C.
The plane of symmetry is, of course, imaginary, butit is she who divides the figure into two equal parts. It can pass through one or several sides, be parallel to it, and can divide them. For the same figure there can be several planes at once. These elements are usually referred to as P.
But perhaps the most common is what is called the "axis of symmetry." This is not uncommon phenomenon can be seen both in geometry and in nature. And it is worthy of separate consideration.
Axles
Often an element with respect to which the figure can be called symmetrical,
stands a straight line or segment.In any case, this is not a point or a plane. Then the axes of symmetry of the figures are considered. There may be a lot of them, and they can be arranged as you like: to divide the sides or to be parallel to them, as well as cross corners or not. Axes of symmetry are usually denoted as L.
Examples are isosceles andequilateral triangles. In the first case, there will be a vertical axis of symmetry, on both sides of which there are equal faces, and in the second line they will cross each angle and coincide with all bisectors, medians and heights. Ordinary triangles do not possess it.
By the way, the set of all the above elements in crystallography and stereometry is called the degree of symmetry. This indicator depends on the number of axes, planes and centers.
Examples in geometry
It is conditionally possible to divide the entire set of objects.studying mathematicians on figures that have an axis of symmetry, and those that do not have one. All regular polygons, circles, ovals, as well as some special cases automatically fall into the first category, while the rest fall into the second group.
As in the case when it was said about the axissymmetry of a triangle, this element for a quadrilateral does not always exist. For a square, rectangle, rhombus or parallelogram, it is, but for an irregular shape, respectively, no. For a circle, the axis of symmetry is the set of lines that pass through its center.
In addition, it is interesting to consider and volumetricfigures from this point of view. At least one axis of symmetry in addition to all regular polygons and the ball will have some cones, as well as pyramids, parallelograms and some others. Each case must be considered separately.
Examples in nature
Mirror symmetry in life is called bilateral, it is found most
often.Anyone and many animals are examples of this. The axial axis is called radial and is much less common, as a rule, in the plant kingdom. And yet they are. For example, it is worth considering how many axes of symmetry does a star have, and does it have them at all? Of course, we are talking about sea inhabitants, and not about the subject of study of astronomers. And the correct answer is this: it depends on the number of rays of a star, for example, five, if it is five-pointed.
In addition, radial symmetry is observed in many flowers: chamomile, cornflowers, sunflowers, etc. There are a huge number of examples, they are literally everywhere around.
Arrhythmia
This term is primarily reminiscent of mostabout medicine and cardiology, but it initially has a slightly different meaning. In this case, the synonym is "asymmetry", that is, the absence or violation of regularity in one form or another. It can be seen as an accident, and sometimes it can be a wonderful technique, for example, in clothing or architecture. After all, there are a lot of symmetrical buildings, but the famous Leaning Tower of Pisa is slightly tilted, and although it is not the only one, this is the most famous example. It is known that this happened by chance, but this has its own charm.
Кроме того, очевидно, что лица и тела людей и animals are also not completely symmetrical. Even studies were conducted, according to the results of which the "correct" faces were regarded as inanimate or simply unattractive. Still, the perception of symmetry and this phenomenon itself is amazing and has not yet been fully studied, and therefore extremely interesting.
