Symmetry is associated with harmony and order. And not in vain. Because the question, what is symmetry, is the answer in the form of a literal translation from Ancient Greek. And it turns out that it means proportionality and immutability. And what can be more orderly than a strict definition of location? And what can be called more harmonious than what strictly corresponds to the size?
What does symmetry mean in different sciences?
Biology. In it an important component of symmetry is that animals and plants have naturally located parts. And in this science there is no strict symmetry. There is always some asymmetry. It admits that the parts of the whole do not coincide with absolute precision.
Chemistry. Molecules of matter have a certain pattern in location. It is their symmetry that explains many properties of materials in crystallography and other sections of chemistry.
Physics. The system of bodies and the changes in it are described by means of equations. In them there are symmetrical components that allows to simplify all decision. This is done by searching for conserved quantities.
Mathematics. It is in it, basically, that explanation is given, what is symmetry. And more importance is given to it in geometry. Here, symmetry is the ability to be displayed in figures and bodies. In the narrow sense, it reduces simply to a mirror image.
How to define the symmetry of different dictionaries?
Whichever of them we look, the word "proportionality" will meet everywhere. Dal can also see such an interpretation as uniformity and equality. In other words, symmetric means the same. Here it is said that it is boring, it looks more interesting in what it is not.
On the question of what is symmetry, the Ozhegov dictionary already speaks of the similarity in the position of parts relative to a point, a straight line or a plane.
The Ushakov dictionary also mentions proportionality, as well as the complete correspondence of the two parts of the whole to each other.
When do they talk about asymmetry?
Prefix "a" denies the meaning of the main noun. Therefore, asymmetry means that the arrangement of elements does not lend itself to a certain regularity. There is no fixedness in it.
This term is used in situations where the two halves of the subject are not completely identical. Most often they are completely different.
In animate nature, asymmetry plays an important role. And it can be both useful and harmful. For example, the heart is placed in the left half of the chest. Due to this, the left lung is much smaller. But it is necessary.
About central and axial symmetry
In mathematics, its types are distinguished:
- central, that is, performed with respect to one point;
- axial, which is observed near a straight line;
- mirror, it is based on reflections;
- transfer symmetry.
What is the axis and center of symmetry? This is a point or line, with respect to which there is another point of the body. And such that the distance from the original to the resulting was divided in half by an axis or center of symmetry. During the motion of these points, they describe the same trajectories.
To understand what symmetry is about the axis, the easiest way is for an example. The notebook must be folded in half. The fold line will be the axis of symmetry. If we draw a perpendicular line to it, then all the points on it will have points lying at the same distance along the other side of the axis.
In situations where it is necessary to find the center of symmetry, it is necessary to proceed as follows. If the figures are two, then find the same points from them and connect them with a piece. Then split in half. When the figure is one, the knowledge of its properties can help. Often this center coincides with the point of intersection of diagonals or heights.
Which figures are symmetrical?
Geometric figures can have axial or central symmetry. But this is not an obligatory condition, there are many objects that do not possess it at all. For example, the parallelogram has a centralogram, but it does not have an axial one. And the non-isosceles trapezies and triangles have no symmetry at all.
If central symmetry is considered, the figures possessing it are quite numerous. This is a segment and a circle, a parallelogram and all regular polygons with a number of sides that is divided into two.
The center of symmetry of a segment (also of a circle) is its center, and for a parallelogram it coincides with the intersection of diagonals. While for regular polygons this point also coincides with the center of the figure.
If you can draw a line in the figure along which it can be folded, and the two halves coincide, then it (the line) will be the axis of symmetry. It is interesting how many axes of symmetry have different figures.
For example, an acute or obtuse angle has only one axis, which is its bisector.
If you want to find the axis in an isosceles triangle, then you need to hold the height to its base. The line and will be the axis of symmetry. And only one. And in the equilateral they will be three at once. In addition, the triangle also has a central symmetry about the point of intersection of heights.
A circle can have an infinite number of symmetry axes. Any straight line that passes through its center can fulfill this role.
Rectangle and diamond have two axes of symmetry. At the first they pass through the middle of the sides, and in the second they coincide with the diagonals.
The square unites the previous two figures and has 4 axes of symmetry at once. They at it same, as at a rhombus and a rectangle.