Symmetry in space and its application. Presentation on the topic "movement in space central symmetry axial symmetry mirror symmetry parallel translation"

. Regular polyhedra.

Definition. A convex polyhedron is called correct , if all its faces are equal regular polygons and the same number of edges converge at each of its vertices.

It is quite easy to prove that there are only 5 regular polyhedra: regular tetrahedron, regular hexahedron, regular octahedron, regular icosahedron, regular dodecahedron. This amazing fact gave rise to ancient thinkers to correlate regular polyhedra with the primary elements of being.

There are many interesting applications of polyhedra theory. One of the outstanding results in this area is Euler's theorem , which is valid not only for regular, but also for all convex polyhedra.

Theorem: for convex polyhedra the relation is valid: G + V – P = 2, where B is the number of vertices, G is the number of faces, P is the number of edges.

Regular polyhedra have many interesting properties. One of the most striking properties is their duality: if you connect the centers of the faces of a regular hexahedron (cube) with segments, you get a regular octahedron; and, conversely, if you connect the centers of the faces of a regular octahedron with segments, you get a cube. Similarly, the regular icosahedron and dodecahedron are dual. A regular tetrahedron is dual to itself, i.e. If you connect the centers of the faces of a regular tetrahedron with segments, you will again get a regular tetrahedron.

. Symmetry in space.

Definition. Points A And IN are called symmetrical about the point ABOUT(center of symmetry), if ABOUT– the middle of the segment AB. Point O is considered symmetrical to itself.

Definition. Points A And IN are called symmetrical about a straight line A(axis of symmetry), if straight A AB and perpendicular to this segment. Every point is straight A

Definition. Points A And IN are called symmetrical relative to the plane β (plane of symmetry), if the plane β passes through the middle of the segment AB and perpendicular to this segment. Each point of the plane β is considered symmetrical to itself.

Definition. A point (straight line, plane) is called a center (axis, plane) of symmetry of a figure if each point of the figure is symmetrical with respect to it to some point of the same figure.

If a figure has a center (axis, plane) of symmetry, then it is said to have central (axial, mirror) symmetry. The center, axis and planes of symmetry of a polyhedron are called elements of symmetry this polyhedron.

Example. Correct tetrahedron:

– has no center of symmetry;

– has three axes of symmetry – straight lines passing through the middles of two opposite edges;

It has six planes of symmetry - planes passing through the edge perpendicular to the opposite (intersecting with the first) edge of the tetrahedron.

How many centers of symmetry does:

a) parallelepiped;

b) regular triangular prism;

c) dihedral angle;

d) segment;

How many axes of symmetry does:

a) segment;

b) regular triangle;

How many planes of symmetry does:

a) a regular quadrangular prism, different from a cube;

b) regular quadrangular pyramid;

c) regular triangular pyramid;

How many and what symmetry elements do regular polyhedra have:

a) regular tetrahedron;

b) regular hexahedron;

c) regular octahedron;

d) regular icosahedron;

e) regular dodecahedron?

MKOU "Anninskaya Secondary School with UIOP"

Symmetry in space

Symmetry

Symmetry in the broad sense is correspondence, immutability, manifested during any changes or transformations.

Central symmetry

Parallel transfer

Axial symmetry

Symmetry

Mirror image or mirror symmetry- the movement of Euclidean space, the set of fixed points of which is a hyperplane (in the case of three-dimensional space - just a plane).

Axial symmetry

With axial symmetry, each point of the figure goes to a point symmetrical to it relative to the plane

Axial symmetry

Central symmetry

Central symmetry with respect to a point A is a transformation of space that takes a point X to a point X′ such that A is the midpoint of the segment XX′.

Central symmetry

Central symmetry

It can be represented as a composition of reflection relative to a plane passing through the center of symmetry, with a rotation of 180° relative to a straight line passing through the center of symmetry and perpendicular to the above-mentioned plane of reflection.

Parallel transfer

Parallel transfer - special case movement in which all points in space move in the same direction over the same distance.

Parallel transfer

Symmetry in physics

In theoretical physics, the behavior of a physical system is described by certain equations. If these equations have any symmetries, then it is often possible to simplify their solution by finding conserved quantities (integrals of motion).

Symmetry in biology

Symmetry in biology is the regular arrangement of similar parts of the body or forms of a living organism, a collection of living organisms relative to the center or axis of symmetry.

Symmetry in chemistry

Symmetry is important to chemistry because it explains observations in spectroscopy, quantum chemistry, and crystallography.

Symmetry in religious symbols

It is suggested that the tendency of people to see purpose in symmetry is one of the reasons why symmetry is often an integral part of the symbols of the world's religions. Here are just a few of the many examples shown in the figure.

Symmetry in social interactions

People observe the symmetrical nature (also including asymmetrical balance) of social interaction in different contexts. They include assessments of reciprocity, empathy, apology, dialogue, respect, fairness, and revenge. Symmetrical interactions send the message “we are the same,” while asymmetrical interactions convey the message “I’m special, better than you.”

In this lesson we will describe the types of symmetry in space and get acquainted with the concept of a regular polyhedron.

As in planimetry, in space we will consider symmetry with respect to a point and with respect to a line, but in addition symmetry with respect to a plane will appear.

Definition.

Points A are called symmetrical with respect to point O (center of symmetry), if O is the middle of the segment. Point O is symmetrical to itself.

In order to obtain a point symmetrical to it relative to point O for a given point A, you need to draw a straight line through points A and O, draw a segment equal to OA from point O, and obtain the desired point (Figure 1).

Rice. 1. Symmetry about a point

Similarly, points B are symmetrical with respect to point O, since O is the middle of the segment.

Thus, a law is given according to which each point of the plane goes to another point of the plane, and we said that in this case any distances are preserved, that is.

Let's consider symmetry about a straight line in space.

To obtain a symmetrical point for a given point A with respect to some straight line a, you need to lower a perpendicular from point A to the straight line and plot an equal segment on it (Figure 2).

Rice. 2. Symmetry about a straight line in space

Definition.

Points A and are called symmetrical with respect to straight line a (axis of symmetry) if straight line a passes through the middle of the segment and is perpendicular to it. Each point on a straight line is symmetrical to itself.

Definition.

Points A are called symmetrical relative to the plane (plane of symmetry) if the plane passes through the middle of the segment and is perpendicular to it. Each point of the plane is symmetrical to itself (Figure 3).

Rice. 3. Symmetry relative to the plane

Some geometric figures may have a center of symmetry, an axis of symmetry, or a plane of symmetry.

Definition.

Point O is called the center of symmetry of a figure if each point of the figure is symmetrical relative to it to some point of the same figure.

For example, in a parallelogram and parallelepiped, the point of intersection of all diagonals is the center of symmetry. Let's illustrate for a parallelepiped.

Rice. 4. Center of symmetry of the parallelepiped

So, with symmetry about point O in a parallelepiped point A goes into point, point B into point, etc., thus the parallelepiped goes into itself.

Definition.

A straight line is called the axis of symmetry of a figure if each point of the figure is symmetrical relative to it to some point of the same figure.

For example, each diagonal of a rhombus is an axis of symmetry for it; the rhombus turns into itself when it is symmetric about any of the diagonals.

Let's consider an example in space - cuboid(the side edges are perpendicular to the bases, the bases have equal rectangles). Such a parallelepiped has axes of symmetry. One of them passes through the center of symmetry of the parallelepiped (the point of intersection of the diagonals) and the centers of the upper and lower bases.

Definition.

A plane is called a plane of symmetry of a figure if each point of the figure is symmetrical with respect to it to some point of the same figure.

For example, a rectangular parallelepiped has planes of symmetry. One of them passes through the middles of the opposite ribs of the upper and lower bases (Figure 5).

Rice. 5. Plane of symmetry of a rectangular parallelepiped

Elements of symmetry are inherent in regular polyhedra.

Definition.

A convex polyhedron is called regular if all its faces are equal regular polygons and converges at each vertex same number ribs

Theorem.

There is no regular polyhedron whose faces are regular n-gons for .

Proof:

Let's consider the case when is a regular hexagon. All of him internal corners are equal:

Then at internal angles will be larger.

At each vertex of the polyhedron at least three edges converge, which means that each vertex contains at least three flat angles. Their total sum (provided that each is greater than or equal to ) is greater than or equal to . This contradicts the statement: in a convex polyhedron, the sum of all plane angles at each vertex is less.

The theorem has been proven.

Cube (Figure 6):

Rice. 6. Cube

The cube is made up of six squares; a square is a regular polygon;

Each vertex is the vertex of three squares, for example, vertex A is common to the square faces ABCD, ;

The sum of all plane angles at each vertex is , since it consists of three right angles. This is less than what satisfies the concept of a regular polyhedron;

The cube has a center of symmetry - the point of intersection of the diagonals;

The cube has axes of symmetry, for example lines a and b (Figure 6), where line a passes through the midpoints of opposite faces, and b through the midpoints of opposite edges;

The cube has planes of symmetry, for example a plane that passes through lines a and b.

2. Regular tetrahedron (regular triangular pyramid, all edges of which are equal to each other):

Rice. 7. Regular tetrahedron

A regular tetrahedron is made up of four equilateral triangles;

The sum of all plane angles at each vertex is , since a regular tetrahedron consists of three plane angles along . This is less than what satisfies the concept of a regular polyhedron;

A regular tetrahedron has symmetry axes; they pass through the midpoints of opposite edges, for example the straight line MN. In addition, MN is the distance between the crossing straight lines AB and CD, MN is perpendicular to the edges AB and CD;

A regular tetrahedron has planes of symmetry, each passing through an edge and the middle of the opposite edge (Figure 7);

A regular tetrahedron has no center of symmetry.

3. Regular octahedron:

Consists of eight equilateral triangles;

Four edges converge at each vertex;

The sum of all plane angles at each vertex is , since a regular octahedron consists of four plane angles along . This is less than , which satisfies the concept of a regular polyhedron.

4. Regular icosahedron:

Consists of twenty equilateral triangles;

Five edges converge at each vertex;

The sum of all plane angles at each vertex is , since a regular icosahedron consists of five plane angles along . This is less than , which satisfies the concept of a regular polyhedron.

5. Regular dodecahedron:

Consists of twelve regular pentagons;

Three edges converge at each vertex;

The sum of all plane angles at each vertex is . This is less than , which satisfies the concept of a regular polyhedron.

So, we examined the types of symmetry in space and gave strict definitions. We also defined the concept of a regular polyhedron, looked at examples of such polyhedra and their properties.

Bibliography

1. I. M. Smirnova, V. A. Smirnov. Geometry. Grades 10-11: textbook for students educational institutions(basic and profile levels) / I. M. Smirnova, V. A. Smirnov. - 5th ed., rev. and additional - M.: Mnemosyne, 2008. - 288 p.: ill.
2. Sharygin I. F. Geometry. 10-11 grade: Textbook for general education educational institutions/ Sharygin I.F. - M.: Bustard, 1999. - 208 p.: ill.
3. E. V. Potoskuev, L. I. Zvalich. Geometry. Grade 10: Textbook for general education institutions with in-depth and specialized study of mathematics /E. V. Potoskuev, L. I. Zvalich. - 6th ed., stereotype. - M.: Bustard, 2008. - 233 p.: ill.

1. Matemonline.com ().
2. Fmclass.ru ().
3. 5klass.net ().

Homework

1. Indicate the number of symmetry axes of the rectangular parallelepiped;
2. indicate the number of symmetry axes of a regular pentagonal prism;
3. indicate the number of planes of symmetry of the octahedron;
4. build a pyramid that has all the elements of symmetry.

We live in a very beautiful and harmonious world. We are surrounded by objects that please the eye. For example, a butterfly Maple Leaf, snowflake. Look how beautiful they are. Have you paid attention to them? Today we will touch on this wonderful mathematical phenomenon - symmetry. Let's get acquainted with the concept of axial, central and mirror symmetries. We will learn to build and identify figures that are symmetrical relative to the axis, center and plane.

The word symmetry translated from Greek sounds like harmony, meaning beauty, proportionality, proportionality, uniformity in the arrangement of parts. Man has long used symmetry in architecture. Ancient temples, towers of medieval castles, modern buildings it gives harmony and completeness.

Central symmetry. Symmetry about a point or central symmetry- this is such a property geometric figure, when any point located on one side of the center of symmetry corresponds to another point located on the other side of the center. In this case, the points are located on a straight line segment passing through the center, dividing the segment in half. A O B

Axial symmetry. Symmetry about a straight line (or axial symmetry) is a property of a geometric figure when any point located on one side of a line will always correspond to a point located on the other side of the line, and the segments connecting these points will be perpendicular to the axis of symmetry and bisected by it. a AB

Mirror symmetry Points A and B are called symmetrical relative to the plane α (plane of symmetry) if the plane α passes through the middle of the segment AB and is perpendicular to this segment. Each point of the α plane is considered symmetrical to itself. AB α

2. Two axes of symmetry have... a) an isosceles triangle; b) isosceles trapezoid; c) rhombus. 2. Which statement is false? a) If a triangle has an axis of symmetry, then it is isosceles. b) If a triangle has two axes of symmetry, then it is equilateral. c) An equilateral triangle has two axes of symmetry.

3. Which statement is true? a) In a parallelogram, the point of intersection of the diagonals is the center of symmetry. b) B isosceles trapezoid the point of intersection of the diagonals is its center of symmetry. c) In an equilateral triangle, the point of intersection of the medians is the center of its symmetry. 3. Has four axes of symmetry... a) rectangle; b) rhombus; c) square.

4. From the fact that points O and A are symmetrical relative to point B, it does not follow that... a) AO = 2OB; b) OB = 2AO; c) OB = AB. 4. Points A and B are symmetrical about line a if they... a) lie on a perpendicular to line a; b) equidistant from line a; c) lie on a perpendicular to line a and are equidistant from it.

5. Diagonal AC of quadrilateral ABCO is its axis of symmetry. This quadrilateral cannot be... a) a parallelogram; b) rhombus; c) square. 5. From the fact that points M and N are symmetrical relative to point K, it follows that... a) MK = 0.5 KN; b) MN=2MK; c) NK = 2MN.

6.ВD - height in isosceles triangle ABC. Which statement is incorrect? a) ВD is the axis of symmetry of triangle ABC. b) Points A and C are symmetrical relative to point D. c) Point D is the center of symmetry of triangle ABC. 6. The diagonal MP of a convex quadrilateral MNPK is its axis of symmetry. This quadrilateral cannot be... a) a rectangle; b) rhombus; c) square.

7. Line a divides segment AB in half. Which statement is correct? a) Points A and B are symmetrical about straight line a. b) Points A and B are symmetrical with respect to the point of intersection of line a and segment AB. c) In this case there is neither axial nor central symmetry. 7. The straight line passing through the middle of one of the sides of the parallelogram is its axis of symmetry. Then this parallelogram cannot be... a) a rectangle; b) rhombus; c) square.

8. Among points A (3; - 4), B (- 3; - 4), C (- 3; 4), indicate a pair that is symmetrical about the origin of coordinates: a) A and B; b) B and C; c) A and C. 8. Among the points D (4; - 7), K (- 4; 7), P (- 4; - 7), indicate a pair that is symmetrical about the x-axis: a) K and D; b) K and R; c) P and D.

9. For the straight line y = x + 2, indicate a straight line that is symmetrical about the OY axis. a) y = -x + 2; b) y = x - 2; c) y = -x For a straight line y = x + 2, indicate a straight line that is symmetrical about the origin: a) y = -x + 2; b) y = x - 2; c) y = -x - 2.

Answers: вccabacbca 2вbcccbabbb

Symmetry of space

Tell me what is symmetry of space?

You need to start with definitions to get to the bottom of things. Many of yours physical laws far from reality, but simply an attempt to describe multidimensional processes using three-dimensional thinking. Symmetry is the design of a certain order of movement and focusing of energy. The universe is large and diverse, the types of forms of creation are infinitely diverse. Therefore, symmetry in your understanding and symmetry within the entire universe are different things. This is the same as comparing the decimal number system that you have adopted with, say, the binary or septal number system. Understand? This different approaches in organizing structuring. You have countless dice. You can stack them however you want: in many piles of two or five or seven cubes. In two big piles. In five big piles and so on. Next, in each pile you also define a certain system for distributing the cubes. This is the process of structuring space. Since the Divine Light is infinite, the number of structuring cubes is also infinite, therefore the variations in the addition of these divine cubes are infinite, and therefore the variations in the symmetry of space are infinite.

Your concept of symmetry comes from its binary nature, from systems of single reflection, these are the symmetry properties of the dual world in which you reside. In your world, any form has a symmetrical mirror reflection, any concept and direction of movement has a reflected double.

A reflected double? What do you mean.

It's like the other side of the coin. The same medal, but viewed from the opposite side. A look from the outside and a look from the inside. The reflected double is a view from the inside. Any phenomenon and any action can be viewed differently from different points of perception.

Wait, let's go in order. In nature, symmetry is widespread precisely binary symmetry. Snowflakes, plant leaves, crystal lattices, flowers, fruits and much more. Even in the structure of atoms there is symmetry. Why?

Let's go back to the perception filter again. You are the source of Divine light, enclosed in a lamp form. The border shape of your lamp is subtle but strong. And it can be organized in different ways. Now there are two holes in it, relatively speaking. Therefore, if your light comes out outside of you, it always comes out in binary form. When your light comes out of your holes-sensors of space, then outside of you it also encounters binary rays emanating from other forms reflecting you, is reflected from these rays, refracted and returns to you again through your two holes. This is a very simplified model, it is a model of binary perception. Dual reflection model. As your awareness expands, new openings-perceptions open in you and everything seems to become more complicated, the multivariance increases, and the symmetry of space becomes more complex.

When you talk about the symmetry of, say, a leaf of a tree, you see this symmetry in a planar version. But imagine the symmetry of a plant leaf in a three-dimensional version, when the reflection mirrors are placed in such a way that three identical parts are created. It’s difficult for you, because in your world everything has a pair. Then try to imagine a quaternary system of symmetry, when two leaves intersect in a longitudinal trunk. Or four sheets of paper, like in a book, are united by a common binding. Now imagine that the book has an infinite number of pages and the intertwining of these pages is also infinite.

I feel like your three-dimensional thinking and imagination are confused, this is normal. It’s difficult to change your mind right away, but you must believe that your system of perception, which is actually hidden very deeply in you and others, allows you to create and perceive any multidimensionality. Therefore, I will give you examples of spatial models and complicate them, so that you gradually get used to multidimensional perception not only mentally, but also in your imagination, although in fact they are the same thing.

So we take a point in space and an infinite number of rays emanating from it. As you understand, this is a description of you in the universe. For if the number of rays emanating from a point is infinite, then it describes all possible rays of space around you. But there are also countless such points. The points from which the rays emanate are the forms of God. As you can see, the symmetry of space was inherent initially in you and in the space around you. For every ray emanating from a point of reflection will find a reflected pair. But there will be not two such rays, but many pairs. Next, these rays encounter, say, a mirror and are reflected from it. If you imagine a ray as a straight line, then its reflection gives refraction, a bend in the other direction of this straight line. And accordingly, the dual pair of this beam will also be reflected from this mirror and give a symmetrical bend, as if in the other direction. This is how fractality is born, that is, the symmetry of reflections or reflected symmetry. Now let’s imagine that there is only one point from which the rays emanate, and there are an infinite number of mirrors, then there will be an infinite number of fractal reflections. Now imagine that what they reflect is not mirrors placed by someone. But simply the rays emanating from you as points of perception are reflected from myriads of rays of countless other forms of perception, from which countless rays also emanate. This is the multidimensional symmetry of space.

But in your concept, symmetry is the identical equality of halves. But if you look at a plant leaf or a fruit, then the symmetry there still undergoes distortions. That is, the reflections do not completely coincide down to the micron and beyond. So in your perception, the symmetry of space is also partially broken. When both rays that touch and reflect from each other have the same strength and directionality, then the reflection symmetry created is more accurate, when this is not the case, then the reflection of one ray is different from the reflection of the other ray. But this is if we talk about space as a whole. But your reflected ray then returns to you, and therefore for you, as for everyone, the power of direction and the power of reflection are equal, since this is your power.

Then tell me, in nature we observe certain symmetrical figures: spheres, triangles, rectangles. These figures are present in everything. Why? Moreover, there are experiments with sound. When sand poured onto the surface of a speaker takes on certain geometric shapes under the influence of sound vibrations.

There are a lot of questions here. But again you're trying to think linearly. Let's take a snowflake whose symmetry you can see. She is beautiful and never repeats herself. Why? Because microscopic snow particles are structured in a certain order, each time representing a different reflection of energy on the parameters of the cold, on the parameters of the environment in which they are reflected. But if you imagine a snowball, then it contains a huge number of snowflakes, a huge number of non-repeating symmetries. And if you could examine this new pattern, you would find a certain symmetry in it. That is, everything is structured in interaction with each other.

Vibrations of sound are precisely reflected energy. Its fluctuations in the reflective spectrum. In principle, everything is reflected energy and its fluctuations in the reflective spectrum. It’s just that you can perceive some of these vibrations with your eyes, some with your ears, some with your sense of smell, and so on. And some of them are not yet able to perceive.

Now let's move on. You observe the world around you and see in it the symmetry of reflections in the form of certain figures and symbols. But if you look deep into you, then there is also an infinity of symmetry and reflections. You just haven’t learned to look deep into yourself yet. You have created instruments in the form of microscopes and magnifying structures, but with the power of your thoughts you yourself can penetrate into all your components down to the primordial particles, and if you do this, you will discover amazing fractality and symmetry deep inside yourself. You have been looking outside of yourself all the time. But inside you there is the same infinite world, what you call microcosm, it is not known to you at all.

So now in our example, countless rays emanate from a point not only outside the point but also inside the point, in the opposite direction. And these rays of perception are also reflected, structured, fractalized.

There are many experiments with water, when the sounds of certain vibrations, say good words or classical music structures snowflakes in very beautiful patterns. There are many examples of the harmonizing effect on a person of music, certain colors and smells, paintings in the form of symmetrical mandalas, and so on. What it is? What happens?

Reflection. For example, a mandala is an energetic image of certain interconnections of rays of perception, arranged symmetrically. For you it's just a picture. But imagine it as an energy picture. When you meditate on it, your directed energy is reflected from the energy of the mandala and, as it were, copies it, makes a cast of it, and is reflected symmetrically to it. Understand? And it returns to you, structures your energy in a certain way and is again reflected outside. If you sit in mandala meditation for a long time, you seem to tune in. If you turn off all other sources of perception and completely focus on the mandala, then gradually your internal structuring becomes similar to the structure of the mandala, it is symmetrically reflected from it and a mandala is also born inside you, somewhat similar to the reflected one, but still possessing your characteristics and characteristics. The same thing happens with music, and with smells, and with flowers, and so on. You simply perceive more deeply the symmetry of another form and structure your form accordingly.

Why do the sounds of nature or certain music or certain signs harmonize a person? If everything is just a type of reflection and its diversity, why do we equally not tolerate, say, a cacaphony of sounds or, for example, the smells of decomposition? If there are no bad and good perceptions, why are we fairly equally attuned to certain perceptions?

Sustainability. Why is so much symmetrical around you? Because symmetrical configurations are stable. It's like a chair with one leg, three or four. What you call harmony is the most stable viable configurations of space. Unstable configurations disintegrate. If you bend the paper sequentially and symmetrically and fold it many times, then you can roll it up to a point, to a small ball, while there will be symmetry inside it, and many edges of the sheet of paper will have a huge number of contacts and adhesion to each other. And if a sheet of paper is simply crumpled, then there will be much less contact between the points of the paper and, accordingly, less adhesion, and the volume of the crumpled sheet will be greater. This design is less stable. If you, say, sit on a folded sheet of paper, then it is almost not deformed and, more importantly, the connections are not deformed. But if you sit on a crumpled sheet of paper, then it is deformed and many connections-contacts are broken. Therefore, symmetry is a consistent compaction.

So there is some kind of primordial unmanifest chaos, which under a certain creative influence takes on symmetrical forms?

Everything is mixed up for you. Non-manifestation is the absence of movement. Movement itself is either chaos or symmetry, that is, when particles move chaotically, this is already manifestation. When the rays are reflected asymmetrically, this is also manifestation. It's just there different types manifestations, and chaotic movement is no worse than symmetrical movement, it is just different. Present in the universe different kinds the construction of space, including what you call chaos.

But you say that symmetrical configurations are more stable. Then why chaotic configurations?

This various shapes creation of space, its organization and structuring. Sometimes chaotic movements provide new directions for structuring. Just as you cannot reject the energy of destruction, since it is also used in creation, so you should not reject chaotic structuring, which is also used in creation. The symmetrical structuring of space is more stable, but also more rigid and less mobile. It's like a pre-created zone for choosing the movement of energy, you know? If you take your freedom of choice, this is precisely chaos. If we take any hierarchy, it is rigid symmetry and fractality.

It turns out that chaotic structuring was introduced into the symmetry of space?

Or vice versa, symmetry was introduced into the chaotic structure.

If everything I see around me is just an agreement between people on how to see it, then why do I see space symmetrically and not chaotically? If everything is energy, then why do all people see the symmetry of a flower in a certain way? Why not chaos?

Because the reflected rays of a flower as a form of God are symmetrical. And you perceive precisely the direction of these rays. Look with light vision. When you look at a luminous object, then when you close your eyes, light configurations appear on the inner screen, this is light vision. If you imagine the world around you in the form of energy, you will see vibrations and movement of light lines and points of other figures. When you look at objects that seem formless to you and give them shape in your imagination, as in the case of clouds, this means that either there are no strict structurization connections in the object, that is, elements of chaos predominate, or you are simply not able to perceive such structuring. It's like a snowball, inside of which there are billions of snow with amazing symmetry, but the ball of snow itself is not very symmetrical.

I'm asking about the bystander effect. If we say movement elementary particles depends on the observer, does this mean that the observed symmetry of the space of nature also depends on us, on the observers of this symmetry, and not on the space itself?

Certainly. Remember the example with your reflected rays. The reflection of your beam depends on you. That is, from the properties of the beam itself. By passing Divine light through your prism of perception, you give it certain characteristics of perception, a certain degree of reflection. Therefore, the observer effect consists precisely in the fact that you and only you are reflected in your own way from other rays of perception. But at some point or in some space of a certain extent, your rays combine, this is reflection outside world, then this is your general picture of the world, this is the symmetry of space you see.

So, if we start to reflect chaotically, the picture of the world will change?

You place your accents a little wrong. You are always reflecting. It’s just that some of you and God’s forms reflect more symmetrically, and some more chaotically. Therefore, those who reflect more chaotically come into contact, intersect their perceptions with those who also reflect more chaotically. This is the law of similarity; like does not just attract like. Like only intersects with like. You cannot intersect with someone who is directed, relatively speaking, in the other direction. Like non-intersecting roads in your world, they exist and lead in certain directions. But your road is in a different area and goes in a different direction. But if your road girds everything Earth, then sooner or later it will intersect with all other roads.

Therefore, if you see symmetry in the surrounding space, it is simply the intersection of your perception with those who are also reflected more symmetrically.

Does this mean that somewhere there are worlds and spaces where everything is asymmetrical?

Certainly. Again, in your world, the concept of chaos has a negative connotation. Imagine if you lived in a universe that was primarily built on the chaotic movement of energy. Then any symmetry would seem to you something alien and negative and dark in your assessment of duality.

That is, the fact that we are directed towards light and goodness is only a consequence of the fact that our universe is more built on the symmetry of space?

Yes. You got it right. However, your concept of light is the opposite of the concept of darkness. But everything, both light in your understanding and darkness in your understanding, is the reflected light of God, the reflected energy of God. Therefore, light in your understanding is a symmetrical reflection of the energy of God. And darkness is a chaotic reflection of the energy of God. And in fact, your universe is an attempt to balance both. Give symmetry to chaos, and add chaotic components to symmetry. To get something in between. Because the symmetrical configuration is more stable, and the chaotic configuration is more variable.

It seems to me that harmony, that is, symmetry, still wins. If you look at nature, this is clearly visible.

The development of any form and any system has stages of direction. Symmetry replaces chaos. Chaos gives way to symmetry. Now you are at the stage of a symmetrical infusion of configurations, like the process of crystallization of, say, salt, your space is crystallizing into certain harmonious structures and new forms of connection, new configurations, new crystals are created. But then, in order to test the stability of these forms, a period of chaotic movement will begin, like the effect of wind and rain on geological rocks and mountains. And then the mountains undergo changes. Is a mountain symmetry or not? It is a combination of both. When a symmetrical form, under the influence of chaotic processes, changes its configuration, and this configuration is neither bad nor good. It's just a new combination of symmetry and chaos.

How can a person use the symmetry of space other than to harmonize himself?

Oh this is very interest Ask and you still have a lot to understand on this topic. He can use this symmetry in everything. For example, he can configure himself symmetrically to an external object and thus repeat, copy it. That is, to become similar to this object.

Did I understand correctly: if a person copies, say, the configuration of a plant, then he will become that plant?

It almost will, since it will sooner be somewhat different from the original. It will only be a copy. But you got it right. Those magicians who could transform into plants and animals did just that, copied the energy configuration of another object.

But that is not all. Knowing the configuration and symmetry of space, you can get from one point in space to any other. Now you are doing this chaotically by chance in your dreams and over very short distances. But it’s like a network of roads, a coordinate grid of the space of the universe. Knowing the coordinates, you seem to know a picture of the configuration, a picture of the symmetry of space, and by reproducing it with your consciousness, thus rearranging your configuration, you find yourself aligned with this space, as if you find yourself in a puzzle. If, by your configuration, you cannot fit into the picture like a puzzle, then you cannot perceive the boundaries of contact with other puzzles in the picture, understand? And there is much more you have to master in the symmetry of space. But it’s too early to talk about this.