People’s life is filled with symmetry. It is convenient, beautiful, no need to invent new standards. But what is it really and is it so 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, 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, 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 initial data. This is found both in living 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 generally unchanged. This phenomenon is quite common and is considered interesting, since several of its types, 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 fabrics, building borders and many other man-made objects. It is worth considering this phenomenon in more detail, since it is extremely exciting.
Use of the term in other scientific fields
In the future, symmetry will be considered from the point of view 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 in different conditions. For example, the classification depends on what science this term refers to. So, the division into types varies greatly, although some of the main ones, perhaps, remain unchanged everywhere.
Classification
There are several main types of symmetry, of which three are most often found:
- Mirror - observed relative to one or more planes. Also, the term is used to indicate the type of symmetry when a transformation such as reflection is used.
- Beam, radial or axial - there are several options in varioussources, in a general sense - symmetry is relatively straight. It can be considered as a special case of the rotational variety.
- Central - symmetry is observed with respect to a certain point.
In addition, the following types are also distinguished in geometry, they are much less common, but no less curious:
- moving;
- rotational;
- point;
- 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 takes place on the basis of the presence or absence, as well as the number of some 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.
A center of symmetry is a point inside a figure or crystal at which 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 through which the figure can be reflected on itself. An example is, for example, a circle and a point in its middle. This item is usually referred to as C.
The plane of symmetry, of course, is imaginary, but it is it that 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, several planes can exist at once. These elements are commonly referred to as P.
But perhaps the most common is what is called the "axis of symmetry." This is a common phenomenon that can be seen both in geometry and in nature. And it is worthy of a separate consideration.
Axes
Often an element relative to which the figure can be called symmetrical,
a straight line or a segment protrudes. In any case, this is not about a point and not about a plane. Then the
axis of symmetry of the figures are considered. There can be a lot of them, and they can be arranged as you like: divide the sides or be parallel to them, as well as cross corners or not. The axis of symmetry is usually referred to 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 line they will intersect each angle and coincide with all bisectors, medians and heights. Ordinary triangles do not possess 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.
Geometry Examples
It is conditionally possible to divide the entire set of objects of study of mathematicians into figures having an axis of symmetry, and those that do not have it. All regular polygons, circles, ovals, and also some special cases automatically fall into the first category, while the rest fall into the second group.
As in the case when we spoke about the axis of symmetry of the triangle, this element for the quadrangle does not always exist. For a square, rectangle, rhombus or parallelogram, it is, but for an irregular figure, 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 volumetric figures from this point of view. In addition to all regular polygons and a ball, some cones, as well as pyramids, parallelograms and some others, will possess at least one axis of symmetry. Each case must be considered separately.
Examples in nature
Mirror symmetry in life is called bilateral, it is found most
often. Any person and so many animals are an example of this. Axial is called radial and is much less common, usually in the plant world. And still 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 is this: it depends on the number of rays of the 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, first of all, reminds the majority of medicine and cardiology, however, 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 met as an accident, and sometimes it can be a wonderful welcome, 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, it is the most famous example. It is known that this happened by chance, but this has its own charm.
In addition, it is obvious that the faces and bodies of people and animals are also not completely symmetrical. Even studies were conducted, according to the results of which the “right” persons were regarded as inanimate or simply unattractive. Nevertheless, the perception of symmetry and this phenomenon in itself are amazing and not yet fully understood, and therefore extremely interesting.