Symmetry is associated with harmony and order. And for good reason. Because when asked what symmetry is, there is an answer in the form of a literal translation from ancient Greek. And it turns out that it means proportionality and immutability. And what could be more orderly than a strict determination of the 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 assumes that the parts of the whole do not coincide with absolute precision.
Chemistry. Molecules of a substance have a certain regularity in their location. It is their symmetry that explains many properties of materials in crystallography and other sections of chemistry.
Physics. The system of bodies and changes in it are described using equations. They have symmetrical components, which allows to simplify the entire solution. This is done by searching for conserved values.
Maths. It is precisely in it that the explanation is given what symmetry is. Moreover, greater importance is given to it in geometry. Here symmetry is the ability to display in figures and bodies. In a narrow sense, it comes down simply to the mirror image.
How do different dictionaries define symmetry?
Whichever one we look into, the word “proportionality” will be found everywhere. In Dahl, one can also see such an interpretation as equilibrium and equality. In other words, symmetrical means the same. It also says that it is boring, it looks more interesting than what it is not.
When asked what symmetry is, Ozhegov's dictionary already speaks about the sameness in the position of the parts relative to a point, straight line or plane.
In Ushakov’s dictionary, proportionality is also mentioned, as well as the full correspondence of the two parts of the whole to each other.
When talking about asymmetry?
The prefix "a" denies the meaning of the main noun. Therefore, asymmetry means that the arrangement of the elements defies a certain pattern. There is no immutability in it.
This term is used in situations where the two halves of the subject are not completely coincident. Most often they are completely different.
In 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 significantly smaller. But it is necessary.
About central and axial symmetry
In mathematics there are such types of it:
- central, that is, performed with respect to one point;
- axial, which is observed near the straight line;
- mirror, it is based on reflections;
- transfer symmetry.
What is the axis and center of symmetry? This is a point or a line, relative to which any point of the body can find another one. Moreover, such that the distance from the original to the resulting is divided in half by the axis or center of symmetry. During the movement of these points, they describe the same trajectory.
Understanding what symmetry is about the axis is easiest with an example. The notebook sheet should be folded in half. The fold line will be the axis of symmetry. If you draw a perpendicular line to it, then all points on it will have points lying at the same distance on the other side of the axis.
In situations where it is necessary to find a center of symmetry, you need to proceed as follows. If there are two figures, then find the same points among them and connect them with a segment. Then split in half. When a figure is one, knowledge of its properties can help. Often this center coincides with the intersection point of the diagonals or heights.
What shapes are symmetrical?
Geometric shapes may have axial or central symmetry. But this is not a prerequisite, there are many objects that do not possess it at all. For example, the parallelogram has a central one, but it does not have an axial one. And non-equisplaced trapeziums and triangles have no symmetry at all.
If central symmetry is considered, there are quite a lot of figures possessing it. This is a segment and a circle, a parallelogram and all regular polygons with a number of sides, which is divided into two.
The center of symmetry of a segment (also a circle) is its center, and in a parallelogram it coincides with the intersection of the diagonals. While in regular polygons this point also coincides with the center of the figure.
If it is possible to draw a straight line in the figure, along which it can be folded, and the two halves coincide, then it (straight line) will be the axis of symmetry. It is interesting how many axes of symmetry have different shapes.
For example, a sharp or obtuse angle has only one axis, which is its bisector.
If you need to find an axis in an isosceles triangle, then you need to hold the height to its base. The line will be the axis of symmetry. And just one. And in the equilateral there will be three at once. In addition, the triangle also has a central symmetry about the intersection point of heights.
A circle can have an infinite number of axes of symmetry. Any line that passes through its center can fulfill this role.
Rectangle and rhombus have two axes of symmetry. At the first they pass through the middle of the sides, and at the second they coincide with the diagonals.
The square unites the previous two figures and has 4 axes of symmetry at once. They are like the diamond and the rectangle.