What is the axis of symmetry? This is a set of points that form a straight line, which is the basis of symmetry, that is, if a certain distance is laid off from a straight line on one side, then it will be reflected to the other side in the same size. The axis can be anything; a point, a line, a plane, and so on. But it is better to talk about this with illustrative examples.
Symmetry
In order to understand what the axis of symmetry is, you need to delve into the very definition of symmetry. This is the correspondence of a certain fragment of the body relative to any axis when its structure is unchanged, and the properties and shape of such an object remain the same with respect to its transformations. We can say that symmetry is a property of bodies to display. When a fragment cannot have such a correspondence, this is called asymmetry or arrhythmia.
Some figures do not have symmetry, which is why they are called irregular or asymmetric. These include various trapezoids (except for isosceles), triangles (except for isosceles and equilateral) and others.
Types of symmetry
We also discuss some types of symmetry in order to fully study this concept. They are divided as follows:
- Axial. The axis of symmetry is a line passing through the center of the body. Like this? If you superimpose the parts around the axis of symmetry, they will be equal. This can be seen in the example of a sphere.
- Mirror. The axis of symmetry here is the straight line, relative to which the body can be reflected and get the inverse mapping. For example, butterfly wings are mirror symmetrical.
- Central. The axis of symmetry is the point in the center of the body, with respect to which during all transformations the parts of the body are equal when superimposed.
History of symmetry
The very concept of symmetry is often the starting point in the theories and hypotheses of scientists of ancient times who were confident in the mathematical harmony of the universe, as well as in the manifestation of the divine principle. The ancient Greeks sacredly believed that the Universe is symmetrical, because the symmetry is magnificent. Man has long used the idea of symmetry in his knowledge of the picture of the universe.
In the V century BC, Pythagoras considered the sphere to be the most perfect form and thought that the Earth has the shape of a sphere and moves in the same way. He also believed that the Earth was moving in the form of some kind of "central fire", around which 6 planets (known at that time), the Moon, the Sun and all other stars were to rotate.
And the philosopher Plato considered the polyhedra as the personification of four natural elements:
- tetrahedron - fire, since its top is directed upwards;
- cube - earth, as it is the most stable body;
- octahedron - air, there is no explanation;
- icosahedron - water, since the body does not have rough geometric shapes, angles, and so on;
- the image of the entire universe was the dodecahedron.
Because of all these theories, regular polyhedra are called Plato bodies.
The architects of ancient Greece used symmetry. All their buildings were symmetrical, this is evidenced by the image of the ancient temple of Zeus in Olympia.
The Dutch artist M.K. Escher also resorted to symmetry in his paintings. In particular, a mosaic of two birds flying towards, became the basis of the painting "Day and Night."
Also, our art historians did not neglect the rules of symmetry, as can be seen in the example of Vasnetsov V. M.'s painting "The Heroes".
What can I say, symmetry is a key concept for all artists over the course of many centuries, but in the 20th century, all the scientists of the exact sciences also appreciated its meaning. The exact evidence is physical and cosmological theories, for example, the theory of relativity, string theory, absolutely all quantum mechanics. From the time of Ancient Babylon and ending with the advanced discoveries of modern science, the paths of studying symmetry and the discovery of its basic laws are traced.
Symmetry of geometric shapes and bodies.
Let’s take a closer look at geometric bodies. For example, the axis of symmetry of a parabola is a straight line passing through its apex and dissecting this body in half. This figure has one single axis.
And with geometric figures, the situation is different. The axis of symmetry of the rectangle is also a straight line, but there are several of them. You can draw the axis parallel to the length segments, or you can draw the length. But not so simple. Here the line does not have axes of symmetry, since its end is not defined. Only central symmetry could exist, but, accordingly, there will not be one.
You should also know that some bodies have many axes of symmetry. This is easy to guess. You don’t even need to talk about how many axes of symmetry a circle has. Any line passing through the center of the circle is such and these lines are an infinite number.
Some quadrangles may have two axes of symmetry. But the second should be perpendicular. This happens in the case of a rhombus and a rectangle. In the first axis of symmetry - diagonals, and in the second - the middle lines. Many of these axes are only in the square.
Symmetry in nature
Nature strikes with many examples of symmetry. Even our human body is symmetrical. Two eyes, two ears, a nose and a mouth are located symmetrically with respect to the central axis of the face. The arms, legs and the whole body are generally arranged symmetrically to the axis passing through the middle of our body.
And how many examples constantly surround us! These are flowers, leaves, petals, vegetables and fruits, animals and even honeycombs of bees have a pronounced geometric shape and symmetry. All nature is arranged in an orderly way, everything has its place, which once again confirms the perfection of the laws of nature, in which symmetry is the main condition.
Output
We are constantly surrounded by any phenomena and objects, for example, a rainbow, a drop, flowers, petals and so on. Their symmetry is obvious, to some extent it is due to gravity. Often in nature, the term "symmetry" is understood to mean a regular change of day and night, seasons, and so on.
Similar properties are observed wherever there is order and equality. Also, the laws of nature themselves - astronomical, chemical, biological and even genetic, are subject to certain principles of symmetry, as they have perfect systemicity, which means that balance has an all-encompassing scale. Consequently, axial symmetry is one of the fundamental laws of the universe as a whole.