People's lives are filled with symmetry. It is convenient, beautiful, no need to invent new standards. But what is she really and is she as beautiful in nature as is commonly believed?
Symmetry
Since ancient times, people have sought to streamline the world around them. Therefore, something is considered beautiful, and something not so. From an aesthetic point of view, the golden and silver sections are considered attractive, as well as, of course, symmetry. This term is of Greek origin and literally means "proportion". Of course, we are talking not only about coincidence on this basis, but also on some others. In a general sense, symmetry is such a property of an object when, as a result of certain formations, the result is equal to the original data. It is found in both animate and inanimate nature, as well as in objects made by man.
First of all, the term "symmetry" is used in geometry, but finds application in many scientific fields, and its meaning remains by and large unchanged. This phenomenon is quite commonoccurs and is considered interesting, since several of its types, as well as elements, differ. The use of symmetry is also interesting, because it is found not only in nature, but also in ornaments on fabric, building borders and many other man-made objects. It is worth considering this phenomenon in more detail, as it is extremely fascinating.
Use of the term in other scientific fields
In what follows, symmetry will be considered in terms of geometry, but 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 under different conditions. The classification, for example, depends on which science this term refers to. Thus, the division into types varies greatly, although some basic ones seem to remain the same everywhere.
Classification
There are several basic types of symmetry, of which three are the most common:
- Mirror - observed relative to one or more planes. It is also used to refer to a type of symmetry when a transformation such as reflection is used.
- Radial, radial or axial - there are several options in different
- Central - there is symmetryrelative to some point.
sources, in the general sense - symmetry with respect to a straight line. Can be considered as a special case of rotational variation.
In addition, the following types are also distinguished in geometry, they are much rarer, but no less interesting:
- sliding;
- rotational;
- spot;
- progressive;
- screw;
- fractal;
- etc.
In biology, all species are called somewhat differently, although in fact they can be the same. The division 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
Some features are distinguished in the phenomenon, one of 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 a point inside a figure or a crystal, where the lines converge, connecting in pairs all sides parallel to each other. Of course, it doesn't always exist. If there are sides to which there is no parallel pair, then such a point cannot be found, since there is none. According to the definition, it is obvious that the center of symmetry is that through which the figure can be reflected to itself. An example is, 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, but it is she who divides the figure into two equal to each otherparts. It can pass through one or more sides, be parallel to it, or it can divide them. For the same figure, several planes can exist at once. These elements are usually referred to as P.
But perhaps the most common is what is called "axis of symmetry". This frequent phenomenon can be seen both in geometry and in nature. And it deserves separate consideration.
Axes
Often the element with respect to which the figure can be called symmetrical is
a straight line or a segment protrudes. In any case, we are not talking about a point or a plane. Then the axes of symmetry of the figures are considered. There can be a lot of them, and they can be located in any way: divide sides or be parallel to them, as well as cross corners or not. Axes of symmetry are usually denoted as L.
Examples are isosceles and equilateral 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, the lines will intersect each corner and coincide with all bisectors, medians, and heights. Ordinary triangles do not have it.
By the way, the totality 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 whole set of objects of study of mathematicians into figures havingaxis of symmetry, and those that do not have it. 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 axis of symmetry of a triangle, this element does not always exist for a quadrilateral. For a square, rectangle, rhombus or parallelogram, it is, but for an irregular figure, accordingly, it is not. For a circle, the axis of symmetry is the set of straight lines that pass through its center.
Besides, it is interesting to consider three-dimensional figures 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 occurs mostoften. Any person and very many animals are an example of this. The axial one is called radial and is much less common, as a rule, in the plant world. And yet they are. For example, it is worth considering how many axes of symmetry a star has, and does it have them at all? Of course, we are talking about marine life, and not about the subject of study of astronomers. And the correct answer would be this: it depends on the number of rays of the star, for example, five, if it is five-pointed.
In addition, many flowers have radial symmetry: daisies, cornflowers, sunflowers, etc. There are a huge number of examples, they are literally everywhere around.
Arrhythmia
This term, first of all, reminds the majority of medicine and cardiology, but it initially has a slightly different meaning. In this case, the synonym will be "asymmetry", that is, the absence or violation of regularity in one form or another. It can be found as an accident, and sometimes it can be a beautiful device, 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 accident, but this has its own charm.
Furthermore, it is obvious that the faces and bodies of humans and animals are also not completely symmetrical. There have even been studies, according to the results of which the "correct" faces were regarded as inanimate or simply unattractive. Still, the perception of symmetry and this phenomenon in itself are amazing and have not yet been fully studied, and therefore extremely interesting.
