For centuries, symmetry has remained a subject that has fascinated philosophers, astronomers, mathematicians, artists, architects and physicists. The ancient Greeks were completely obsessed with it - and even today we tend to encounter symmetry in everything from furniture arrangement to haircuts.

Just keep in mind that once you realize this, you'll probably feel an overwhelming urge to look for symmetry in everything you see.

(Total 10 photos)

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1. Broccoli Romanesco

Perhaps you saw Romanesco broccoli in the store and thought it was another example of a genetically modified product. But in fact, this is another example of the fractal symmetry of nature. Each broccoli floret has a logarithmic spiral pattern. Romanesco is similar in appearance to broccoli, and in taste and consistency - to cauliflower. It is rich in carotenoids, as well as vitamins C and K, which makes it not only beautiful, but also healthy food.

For thousands of years, people have marveled at the perfect hexagonal shape of honeycombs and asked themselves how bees could instinctively create a shape that humans could only reproduce with a compass and ruler. How and why do bees have a passion for creating hexagons? Mathematicians believe this is an ideal shape that allows them to store the maximum amount of honey possible using the minimum amount of wax. Either way, it's all a product of nature, and it's damn impressive.

3. Sunflowers

Sunflowers boast radial symmetry and an interesting type of symmetry known as the Fibonacci sequence. Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (each number is determined by the sum of the two previous numbers). If we took our time and counted the number of seeds in a sunflower, we would find that the number of spirals grows according to the principles of the Fibonacci sequence. There are many plants in nature (including Romanesco broccoli) whose petals, seeds and leaves correspond to this sequence, which is why it is so difficult to find a clover with four leaves.

But why do sunflowers and other plants follow mathematical rules? Like the hexagons in a hive, it's all a matter of efficiency.

4. Nautilus Shell

In addition to plants, some animals, such as the Nautilus, follow the Fibonacci sequence. The shell of the Nautilus twists into a Fibonacci spiral. The shell tries to maintain the same proportional shape, which allows it to maintain it throughout its life (unlike humans, who change proportions throughout life). Not all Nautiluses have a Fibonacci shell, but they all follow a logarithmic spiral.

Before you envy the math clams, remember that they don’t do this on purpose, it’s just that this form is the most rational for them.

5. Animals

Most animals have bilateral symmetry, which means they can be split into two identical halves. Even humans have bilateral symmetry, and some scientists believe that a person's symmetry is the most important factor that influences the perception of our beauty. In other words, if you have a one-sided face, you can only hope that it is compensated by other good qualities.

Some go to complete symmetry in an effort to attract a mate, such as the peacock. Darwin was positively annoyed by the bird, and wrote in a letter that "The sight of the tail feathers of a peacock, whenever I look at it, makes me sick!" To Darwin, the tail seemed cumbersome and made no evolutionary sense, as it did not fit with his theory of “survival of the fittest.” He was furious until he came up with the theory of sexual selection, which states that animals evolve certain features to increase their chances of mating. Therefore, peacocks have various adaptations to attract a partner.

There are about 5,000 types of spiders, and they all create a nearly perfect circular web with radial supporting threads at nearly equal distances and spiral webs for catching prey. Scientists aren't sure why spiders like geometry so much, as tests have shown that a round web won't lure food any better than an irregularly shaped web. Scientists theorize that radial symmetry evenly distributes the impact force when prey is caught in the net, resulting in fewer breaks.

Give a couple of tricksters a board, mowers, and the safety of darkness, and you'll see that people create symmetrical shapes, too. Due to the complexity of the design and incredible symmetry of crop circles, even after the creators of the circles confessed and demonstrated their skills, many people still believe that they were made by space aliens.

As the circles become more complex, their artificial origin becomes increasingly clear. It's illogical to assume that aliens will make their messages increasingly difficult when we couldn't even decipher the first ones.

Regardless of how they came to be, crop circles are a pleasure to look at, mainly because their geometry is impressive.

Even tiny formations like snowflakes are governed by the laws of symmetry, since most snowflakes have hexagonal symmetry. This occurs in part because of the way water molecules line up when they solidify (crystallize). Water molecules become solid by forming weak hydrogen bonds, they align in an orderly arrangement that balances the forces of attraction and repulsion, forming the hexagonal shape of a snowflake. But at the same time, each snowflake is symmetrical, but not one snowflake is similar to the other. This happens because as each snowflake falls from the sky, it experiences unique atmospheric conditions that cause its crystals to arrange themselves in a certain way.

9. Milky Way Galaxy

As we have already seen, symmetry and mathematical models exist almost everywhere, but are these laws of nature limited to our planet? Obviously not. A new section at the edge of the Milky Way Galaxy has recently been discovered, and astronomers believe that the galaxy is an almost perfect mirror image of itself.

10. Sun-Moon Symmetry

Considering that the Sun has a diameter of 1.4 million km and the Moon is 3,474 km in diameter, it seems almost impossible that the Moon can block sunlight and provide us with about five solar eclipses every two years. How does this work? Coincidentally, while the Sun is about 400 times wider than the Moon, the Sun is also 400 times farther away. Symmetry ensures that the Sun and Moon are the same size when viewed from Earth, so the Moon can obscure the Sun. Of course, the distance from the Earth to the Sun can increase, which is why we sometimes see annular and partial eclipses. But every one to two years, a precise alignment occurs and we witness a spectacular event known as a total solar eclipse. Astronomers don't know how common this symmetry is among other planets, but they think it's quite rare. However, we should not assume that we are special, as this is all a matter of chance. For example, every year the Moon moves about 4 cm away from the Earth, meaning that billions of years ago every solar eclipse would have been a total eclipse. If things continue like this, total eclipses will eventually disappear, and this will be accompanied by the disappearance of annular eclipses. It turns out that we are simply in the right place at the right time to see this phenomenon.

Symmetry (ancient Greek συμμετρία - symmetry) is the preservation of the properties of the arrangement of the elements of a figure relative to the center or axis of symmetry in an unchanged state during any transformations.

The word “symmetry” has been familiar to us since childhood. Looking in the mirror, we see symmetrical halves of the face; looking at the palms, we also see mirror-symmetrical objects. Taking a chamomile flower in our hand, we are convinced that by turning it around the stem, we can achieve the alignment of different parts of the flower. This is a different type of symmetry: rotational. There are a large number of types of symmetry, but they all invariably follow one general rule: with some transformation, a symmetrical object invariably combines with itself.

Nature does not tolerate exact symmetry . There are always at least minor deviations. Thus, our arms, legs, eyes and ears are not completely identical to each other, although they are very similar. And so on for each object. Nature was created not according to the principle of uniformity, but according to the principle of consistency and proportionality. It is proportionality that is the ancient meaning of the word “symmetry”. The philosophers of antiquity considered symmetry and order to be the essence of beauty. Architects, artists and musicians have known and used the laws of symmetry since ancient times. And at the same time, a slight violation of these laws can give objects a unique charm and downright magical charm. Thus, it is precisely by slight asymmetry that some art historians explain the beauty and magnetism of the mysterious smile of Mona Lisa by Leonardo da Vinci.

Symmetry generates harmony, which is perceived by our brain as a necessary attribute of beauty. This means that even our consciousness lives according to the laws of a symmetrical world.

According to Weyl, an object is called symmetrical if it is possible to perform some operation on it, resulting in the initial state.

Symmetry in biology is the regular arrangement of similar (identical) 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 nature

Objects and phenomena of living nature have symmetry. It allows living organisms to better adapt to their environment and simply survive.

In living nature, the vast majority of living organisms exhibit various types of symmetries (shape, similarity, relative location). Moreover, organisms of different anatomical structures can have the same type of external symmetry.

External symmetry can act as the basis for the classification of organisms (spherical, radial, axial, etc.) Microorganisms living in conditions of weak gravity have a pronounced symmetry of shape.

The Pythagoreans drew attention to the phenomena of symmetry in living nature back in Ancient Greece in connection with the development of the doctrine of harmony (5th century BC). In the 19th century, isolated works appeared on symmetry in the plant and animal world.

In the 20th century, through the efforts of Russian scientists - V. Beklemishev, V. Vernadsky, V. Alpatov, G. Gause - a new direction in the study of symmetry was created - biosymmetry, which, by studying the symmetries of biostructures at the molecular and supramolecular levels, allows us to determine in advance possible symmetry options in biological objects, strictly describe the external form and internal structure of any organisms.

Symmetry in plants

The specific structure of plants and animals is determined by the characteristics of the habitat to which they adapt and the characteristics of their way of life.

Plants are characterized by cone symmetry, which is clearly visible in any tree. Any tree has a base and a top, a “top” and a “bottom” that perform different functions. The significance of the difference between the upper and lower parts, as well as the direction of gravity, determine the vertical orientation of the rotary axis of the “wood cone” and the planes of symmetry. The tree absorbs moisture and nutrients from the soil through the root system, that is, below, and the remaining vital functions are performed by the crown, that is, at the top. Therefore, the directions “up” and “down” for a tree are significantly different. And directions in a plane perpendicular to the vertical are virtually indistinguishable for a tree: in all these directions, air, light, and moisture enter the tree in equal measure. As a result, a vertical rotary axis and a vertical plane of symmetry appear.

Most flowering plants exhibit radial and bilateral symmetry. A flower is considered symmetrical when each perianth consists of an equal number of parts. Flowers having paired parts are considered flowers with double symmetry, etc. Triple symmetry is common for monocotyledons, while quintuple symmetry is common for dicotyledons.

The leaves are characterized by mirror symmetry. The same symmetry is also found in flowers, but in them mirror symmetry often appears in combination with rotational symmetry. There are also frequent cases of figurative symmetry (acacia branches, rowan trees). It is interesting that in the floral world the most common is rotational symmetry of the 5th order, which is fundamentally impossible in the periodic structures of inanimate nature. Academician N. Belov explains this fact by the fact that the 5th order axis is a kind of instrument of the struggle for existence, “insurance against petrification, crystallization, the first step of which would be their capture by the grid.” Indeed, a living organism does not have a crystalline structure in the sense that even its individual organs do not have a spatial lattice. However, ordered structures are represented very widely in it.

Symmetry in animals

Symmetry in animals means correspondence in size, shape and outline, as well as the relative arrangement of body parts located on opposite sides of the dividing line.

Spherical symmetry occurs in radiolarians and sunfishes, whose bodies are spherical in shape, and parts are distributed around the center of the sphere and extend from it. Such organisms have neither front, nor back, nor lateral parts of the body; any plane drawn through the center divides the animal into equal halves.

With radial or radial symmetry, the body has the shape of a short or long cylinder or vessel with a central axis, from which parts of the body extend radially. These are coelenterates, echinoderms, and starfish.

With mirror symmetry, there are three axes of symmetry, but only one pair of symmetrical sides. Because the other two sides - abdominal and dorsal - are not similar to each other. This type of symmetry is characteristic of most animals, including insects, fish, amphibians, reptiles, birds, and mammals.

Insects, fish, birds, and animals are characterized by a difference between the directions “forward” and “backward” that is incompatible with rotational symmetry. The fantastic Tyanitolkai, invented in the famous fairy tale about Doctor Aibolit, seems to be an absolutely incredible creature, since its front and back halves are symmetrical. The direction of movement is a fundamentally selected direction, with respect to which there is no symmetry in any insect, any fish or bird, any animal. In this direction the animal rushes for food, in the same direction it escapes from its pursuers.

In addition to the direction of movement, the symmetry of living beings is determined by another direction - the direction of gravity. Both directions are significant; they define the plane of symmetry of a living creature.

Bilateral (mirror) symmetry is the characteristic symmetry of all representatives of the animal world. This symmetry is clearly visible in the butterfly; the symmetry of left and right appears here with almost mathematical rigor. We can say that every animal (as well as insects, fish, birds) consists of two enantiomorphs - the right and left halves. Enantiomorphs are also paired parts, one of which falls into the right and the other into the left half of the animal’s body. Thus, enantiomorphs are the right and left ear, right and left eye, right and left horn, etc.

Symmetry in humans

The human body has bilateral symmetry (external appearance and skeletal structure). This symmetry has always been and is the main source of our aesthetic admiration for the well-proportioned human body. The human body is built on the principle of bilateral symmetry.

Most of us view the brain as a single structure; in reality, it is divided into two halves. These two parts - the two hemispheres - fit tightly to each other. In full accordance with the general symmetry of the human body, each hemisphere is an almost exact mirror image of the other

Control of the basic movements of the human body and its sensory functions is evenly distributed between the two hemispheres of the brain. The left hemisphere controls the right side of the brain, and the right hemisphere controls the left side.

Physical symmetry of the body and brain does not mean that the right side and the left are equal in all respects. It is enough to pay attention to the actions of our hands to see the initial signs of functional symmetry. Few people have equal use of both hands; the majority has the leading hand.

Types of symmetry in animals

1. central

2. axial (mirror)

3. radial

4. bilateral

5. double beam

6. progressive (metamerism)

7. translational-rotational

Types of symmetry

There are only two main types of symmetry known - rotational and translational. In addition, there is a modification from the combination of these two main types of symmetry - rotational-translational symmetry.

Rotational symmetry. Every organism has rotational symmetry. For rotational symmetry, antimers are an essential characteristic element. It is important to know that when rotated by any degree, the contours of the body will coincide with the original position. The minimum degree of contour coincidence is for a ball rotating around the center of symmetry. The maximum degree of rotation is 360 0, when when turning by this amount the contours of the body coincide. If a body rotates around a center of symmetry, then many axes and planes of symmetry can be drawn through the center of symmetry. If a body rotates around one heteropolar axis, then through this axis one can draw as many planes as there are antimeres in the given body. Depending on this condition, one speaks of rotational symmetry of a certain order. For example, six-rayed corals will have sixth-order rotational symmetry. Ctenophores have two planes of symmetry, and they have second-order symmetry. The symmetry of ctenophores is also called biradial. Finally, if an organism has only one plane of symmetry and, accordingly, two antimeres, then such symmetry is called bilateral or bilateral. Thin needles extend in a radial manner. This helps the protozoa to “hover” in the water column. Other representatives of protozoa are also spherical - rays (radiolaria) and sunfishes with ray-shaped processes-pseudopodia.

Translational symmetry. For translational symmetry, the characteristic elements are metamers (meta - one after the other; mer - part). In this case, the parts of the body are not located mirror opposite to each other, but sequentially one after another along the main axis of the body.

Metamerism – one of the forms of translational symmetry. It is especially pronounced in annelids, whose long body consists of a large number of almost identical segments. This case of segmentation is called homonomic. In arthropods, the number of segments can be relatively small, but each segment is slightly different from its neighbors either in shape or appendages (thoracic segments with legs or wings, abdominal segments). This segmentation is called heteronomous.

Rotational-translational symmetry . This type of symmetry has a limited distribution in the animal kingdom. This symmetry is characterized by the fact that when turning at a certain angle, a part of the body moves forward a little and each subsequent one increases its size logarithmically by a certain amount. Thus, the acts of rotation and translational motion are combined. An example is the spiral chamber shells of foraminifera, as well as the spiral chamber shells of some cephalopods. With some conditions, non-chambered spiral shells of gastropods can also be included in this group

Mirror symmetry

If you stand in the center of the building and to your left there are the same number of floors, columns, windows as to your right, then the building is symmetrical. If it were possible to bend it along the central axis, then both halves of the house would coincide when superimposed. This symmetry is called mirror symmetry. This type of symmetry is very popular in the animal kingdom; man himself is tailored according to its canons.

The axis of symmetry is the axis of rotation. In this case, animals, as a rule, lack a center of symmetry. Then rotation can only occur around an axis. In this case, the axis most often has poles of different quality. For example, in coelenterates, hydra or anemone, the mouth is located on one pole, and the sole with which these motionless animals are attached to the substrate is located on the other. The axis of symmetry may coincide morphologically with the anteroposterior axis of the body.

With mirror symmetry, the right and left sides of the object change.

A plane of symmetry is a plane passing through the axis of symmetry, coinciding with it and cutting the body into two mirror halves. These halves, located opposite each other, are called antimers (anti - against; mer - part). For example, in Hydra, the plane of symmetry must pass through the mouth opening and through the sole. Antimeres of opposite halves should have an equal number of tentacles located around the hydra's mouth. Hydra can have several planes of symmetry, the number of which will be a multiple of the number of tentacles. In sea anemones with a very large number of tentacles, many planes of symmetry can be drawn. For a jellyfish with four tentacles on a bell, the number of planes of symmetry will be limited to a multiple of four. Ctenophores have only two planes of symmetry - pharyngeal and tentacle. Finally, bilaterally symmetrical organisms have only one plane and only two mirror antimeres - the right and left sides of the animal, respectively.

The transition from radial or radial to bilateral or bilateral symmetry is associated with the transition from a sedentary lifestyle to active movement in the environment. For sessile forms, the relationship with the environment is equal in all directions: radial symmetry exactly corresponds to this lifestyle. In actively moving animals, the front end of the body becomes biologically unequal to the rest of the body, the head is formed, and the right and left sides of the body become distinguishable. Due to this, radial symmetry is lost, and only one plane of symmetry can be drawn through the animal’s body, dividing the body into right and left sides. Bilateral symmetry means that one side of an animal's body is a mirror image of the other side. This type of organization is characteristic of most invertebrates, especially annelids and arthropods - crustaceans, arachnids, insects, butterflies; for vertebrates - fish, birds, mammals. Bilateral symmetry first appears in flatworms, in which the anterior and posterior ends of the body differ from each other.

In annelids and arthropods, metamerism is also observed - one of the forms of translational symmetry, when parts of the body are located sequentially one after another along the main axis of the body. It is especially pronounced in annelids (earthworms). Annelids get their name from the fact that their body consists of a series of rings or segments (segments). Both internal organs and body walls are segmented. So the animal consists of about a hundred more or less similar units - metameres, each of which contains one or a pair of organs of each system. The segments are separated from each other by transverse partitions. In an earthworm, almost all segments are similar to each other. Annelids include polychaetes - marine forms that swim freely in water and burrow in the sand. Each segment of their body has a pair of lateral projections bearing a dense tuft of bristles. Arthropods got their name from their characteristic jointed paired appendages (such as swimming organs, walking limbs, mouthparts). All of them are characterized by a segmented body. Each arthropod has a strictly defined number of segments, which remains unchanged throughout its life. Mirror symmetry is clearly visible in the butterfly; the symmetry of left and right appears here with almost mathematical rigor. We can say that every animal, insect, fish, bird consists of two enantiomorphs - the right and left halves. Thus, enantiomorphs are the right and left ear, right and left eye, right and left horn, etc.

Radial symmetry

Radial symmetry is a form of symmetry in which a body (or figure) coincides with itself when the object rotates around a specific point or line. Often this point coincides with the center of symmetry of the object, that is, the point at which an infinite number of axes of bilateral symmetry intersect.

In biology, radial symmetry is said to occur when one or more axes of symmetry pass through a three-dimensional being. Moreover, radially symmetrical animals may not have planes of symmetry. Thus, the Velella siphonophore has a second-order axis of symmetry and no planes of symmetry.

Usually two or more planes of symmetry pass through the axis of symmetry. These planes intersect along a straight line - the axis of symmetry. If the animal rotates around this axis by a certain degree, then it will be displayed on itself (coincide with itself).
There can be several such axes of symmetry (polyaxon symmetry) or one (monaxon symmetry). Polyaxonal symmetry is common among protists (e.g. radiolarians).

As a rule, in multicellular animals, the two ends (poles) of a single axis of symmetry are unequal (for example, in jellyfish, the mouth is located on one pole (oral), and the tip of the bell is on the opposite (aboral) pole. Such symmetry (a variant of radial symmetry) in comparative anatomy is called uniaxial-heteropole. In a two-dimensional projection, radial symmetry can be preserved if the axis of symmetry is directed perpendicular to the projection plane. In other words, the preservation of radial symmetry depends on the viewing angle.
Radial symmetry is characteristic of many cnidarians, as well as most echinoderms. Among them there is the so-called pentasymmetry, based on five planes of symmetry. In echinoderms, radial symmetry is secondary: their larvae are bilaterally symmetrical, and in adult animals, external radial symmetry is broken by the presence of a madrepore plate.

In addition to typical radial symmetry, there is biradial radial symmetry (two planes of symmetry, for example, in ctenophores). If there is only one plane of symmetry, then the symmetry is bilateral (bilaterally symmetrical people have such symmetry).

In flowering plants, radially symmetrical flowers are often found: 3 planes of symmetry (frogwort), 4 planes of symmetry (cinquefoil erect), 5 planes of symmetry (bellflower), 6 planes of symmetry (colchicum). Flowers with radial symmetry are called actinomorphic, flowers with bilateral symmetry are called zygomorphic.

If the environment surrounding an animal is more or less homogeneous on all sides and the animal is evenly in contact with it with all parts of its surface, then the shape of the body is usually spherical, and the repeating parts are located in radial directions. Many radiolarians that are part of the so-called plankton are spherical, i.e. a collection of organisms suspended in the water column and incapable of active swimming; spherical chambers contain a few planktonic representatives of foraminifera (protozoa, sea inhabitants, marine testate amoebae). Foraminifera are enclosed in shells of various, bizarre shapes. The spherical body of sunfish sends numerous thin, thread-like, radially arranged pseudopodia in all directions; the body is devoid of a mineral skeleton. This type of symmetry is called equiaxial, since it is characterized by the presence of many identical axes of symmetry.

Equiaxial and polysymmetric types are found mainly among low-organized and poorly differentiated animals. If there are 4 identical organs around the longitudinal axis, then radial symmetry in this case is called four-ray symmetry. If there are six such organs, then the order of symmetry will be six-rayed, etc. Since the number of such organs is limited (often 2,4,8 or a multiple of 6), several planes of symmetry can always be drawn, corresponding to the number of these organs. Planes divide the animal's body into equal sections with repeating organs. This is the difference between radial symmetry and the polysymmetric type. Radial symmetry is characteristic of sedentary and attached forms. The ecological significance of radial symmetry is clear: a sessile animal is surrounded on all sides by the same environment and must enter into relationships with this environment using identical organs that repeat in radial directions. It is a sedentary lifestyle that contributes to the development of radiant symmetry.

Rotational symmetry

Rotational symmetry is “popular” in the plant world. Take a chamomile flower in your hand. The combination of different parts of the flower occurs if they are rotated around the stem.

Very often flora and fauna borrow external forms from each other. Sea stars leading a vegetative lifestyle have rotational symmetry, and their leaves are mirror-like.

Plants confined to a permanent place clearly distinguish only the top and bottom, and all other directions are more or less the same for them. Naturally, their appearance is subject to rotational symmetry. For animals, it is very important what is in front and what is behind; only “left” and “right” remain equal for them. In this case, mirror symmetry prevails. It is curious that animals that exchange mobile life for immobile life and then return to mobile life again, move from one type of symmetry to another a corresponding number of times, as happened, for example, with echinoderms (starfish, etc.).

Helical or spiral symmetry

Helical symmetry is symmetry with respect to a combination of two transformations - rotation and translation along the rotation axis, i.e. there is movement along the axis of the screw and around the axis of the screw. There are left and right screws.

Examples of natural propellers are: tusk of a narwhal (a small cetacean that lives in the northern seas) - left propeller; snail shell – right screw; The horns of the Pamir ram are enantiomorphs (one horn is twisted in a left-handed spiral, and the other in a right-handed spiral). Spiral symmetry is not ideal, for example, the shell of mollusks narrows or widens at the end.

Although external helical symmetry is rare in multicellular animals, many important molecules from which living organisms are built - proteins, deoxyribonucleic acids - DNA have a helical structure. The true kingdom of natural screws is the world of “living molecules” - molecules that play a fundamentally important role in life processes. These molecules include, first of all, protein molecules. There are up to 10 types of proteins in the human body. All parts of the body, including bones, blood, muscles, tendons, hair, contain proteins. A protein molecule is a chain made up of individual blocks and twisted in a right-handed spiral. It is called the alpha helix. Tendon fiber molecules are triple alpha helices. Alpha helices twisted multiple times with each other form molecular screws, which are found in hair, horns, and hooves. The DNA molecule has the structure of a double right-handed helix, discovered by American scientists Watson and Crick. The double helix of the DNA molecule is the main natural screw.

Conclusion

All forms in the world are subject to the laws of symmetry. Even “eternally free” clouds have symmetry, albeit distorted. Freezing in the blue sky, they resemble jellyfish slowly moving in sea water, clearly gravitating towards rotational symmetry, and then, driven by the rising wind, they change symmetry to mirror one.

Symmetry, manifesting itself in a wide variety of objects of the material world, undoubtedly reflects its most general, most fundamental properties. Therefore, the study of the symmetry of various natural objects and the comparison of its results is a convenient and reliable tool for understanding the basic laws of the existence of matter.

Symmetry is equality in the broad sense of the word. This means that if there is symmetry, then something will not happen and, therefore, something will definitely remain unchanged, preserved.

Sources

1. Urmantsev Yu. A. “Symmetry of nature and the nature of symmetry.” Moscow, Mysl, 1974.

2. V.I. Vernadsky. Chemical structure of the Earth's biosphere and its environment. M., 1965.

3. http://www.worldnatures.ru

4. http://otherreferats

Symmetry (ancient Greek συμμετρία - symmetry) - maintaining the properties of the arrangement of the elements of a figure relative to the center or axis of symmetry in an unchanged state during any transformations.

Word "symmetry" familiar to us from childhood. Looking in the mirror, we see symmetrical halves of the face; looking at the palms, we also see mirror-symmetrical objects. Taking a chamomile flower in our hand, we are convinced that by turning it around the stem, we can achieve the alignment of different parts of the flower. This is a different type of symmetry: rotational. There are a large number of types of symmetry, but they all invariably follow one general rule: with some transformation, a symmetrical object invariably combines with itself.

Nature does not tolerate exact symmetry. There are always at least minor deviations. Thus, our arms, legs, eyes and ears are not completely identical to each other, although they are very similar. And so on for each object. Nature was created not according to the principle of uniformity, but according to the principle of consistency and proportionality. It is proportionality that is the ancient meaning of the word “symmetry”. The philosophers of antiquity considered symmetry and order to be the essence of beauty. Architects, artists and musicians have known and used the laws of symmetry since ancient times. And at the same time, a slight violation of these laws can give objects a unique charm and downright magical charm. Thus, it is precisely by slight asymmetry that some art historians explain the beauty and magnetism of the mysterious smile of Mona Lisa by Leonardo da Vinci.

Symmetry generates harmony, which is perceived by our brain as a necessary attribute of beauty. This means that even our consciousness lives according to the laws of a symmetrical world.

According to Weyl, an object is called symmetrical if it is possible to perform some operation on it, resulting in the initial state.

Symmetry in biology is the regular arrangement of similar (identical) 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 nature

Objects and phenomena of living nature have symmetry. It allows living organisms to better adapt to their environment and simply survive.

In living nature, the vast majority of living organisms exhibit various types of symmetries (shape, similarity, relative location). Moreover, organisms of different anatomical structures can have the same type of external symmetry.

External symmetry can act as the basis for the classification of organisms (spherical, radial, axial, etc.) Microorganisms living in conditions of weak gravity have a pronounced symmetry of shape.

The Pythagoreans drew attention to the phenomena of symmetry in living nature back in Ancient Greece in connection with the development of the doctrine of harmony (5th century BC). In the 19th century, isolated works appeared on symmetry in the plant and animal world.

In the 20th century, through the efforts of Russian scientists - V. Beklemishev, V. Vernadsky, V. Alpatov, G. Gause - a new direction in the study of symmetry was created - biosymmetry, which, by studying the symmetries of biostructures at the molecular and supramolecular levels, allows us to determine in advance possible symmetry options in biological objects, strictly describe the external form and internal structure of any organisms.

Symmetry in plants

The specific structure of plants and animals is determined by the characteristics of the habitat to which they adapt and the characteristics of their way of life.

Plants are characterized by cone symmetry, which is clearly visible in any tree. Any tree has a base and a top, a “top” and a “bottom” that perform different functions. The significance of the difference between the upper and lower parts, as well as the direction of gravity, determine the vertical orientation of the rotary axis of the “wood cone” and the planes of symmetry. The tree absorbs moisture and nutrients from the soil through the root system, that is, below, and the remaining vital functions are performed by the crown, that is, at the top. Therefore, the directions “up” and “down” for a tree are significantly different. And directions in a plane perpendicular to the vertical are virtually indistinguishable for a tree: in all these directions, air, light, and moisture enter the tree in equal measure. As a result, a vertical rotary axis and a vertical plane of symmetry appear.

Most flowering plants exhibit radial and bilateral symmetry. A flower is considered symmetrical when each perianth consists of an equal number of parts. Flowers having paired parts are considered flowers with double symmetry, etc. Triple symmetry is common in monocotyledons, and quintuple symmetry in dicotyledons.

The leaves are characterized by mirror symmetry. The same symmetry is also found in flowers, but in them mirror symmetry often appears in combination with rotational symmetry. There are also frequent cases of figurative symmetry (acacia branches, rowan trees). It is interesting that in the floral world the most common is rotational symmetry of the 5th order, which is fundamentally impossible in the periodic structures of inanimate nature. Academician N. Belov explains this fact by the fact that the 5th order axis is a kind of instrument of the struggle for existence, “insurance against petrification, crystallization, the first step of which would be their capture by the grid.” Indeed, a living organism does not have a crystalline structure in the sense that even its individual organs do not have a spatial lattice. However, ordered structures are represented very widely in it.

Symmetry in animals

Symmetry in animals means correspondence in size, shape and outline, as well as the relative arrangement of body parts located on opposite sides of the dividing line.

Spherical symmetry occurs in radiolarians and sunfishes, whose bodies are spherical in shape, and parts are distributed around the center of the sphere and extend from it. Such organisms have neither front, nor back, nor lateral parts of the body; any plane drawn through the center divides the animal into equal halves.

With radial or radial symmetry, the body has the shape of a short or long cylinder or vessel with a central axis, from which parts of the body extend radially. These are coelenterates, echinoderms, and starfish.

With mirror symmetry, there are three axes of symmetry, but only one pair of symmetrical sides. Because the other two sides - abdominal and dorsal - are not similar to each other. This type of symmetry is characteristic of most animals, including insects, fish, amphibians, reptiles, birds, and mammals.

Insects, fish, birds, and animals are characterized by a difference between the directions “forward” and “backward” that is incompatible with rotational symmetry. The fantastic Tyanitolkai, invented in the famous fairy tale about Doctor Aibolit, seems to be an absolutely incredible creature, since its front and back halves are symmetrical. The direction of movement is a fundamentally selected direction, with respect to which there is no symmetry in any insect, any fish or bird, any animal. In this direction the animal rushes for food, in the same direction it escapes from its pursuers.

In addition to the direction of movement, the symmetry of living beings is determined by another direction - the direction of gravity. Both directions are significant; they define the plane of symmetry of a living creature.

Bilateral (mirror) symmetry is the characteristic symmetry of all representatives of the animal world. This symmetry is clearly visible in the butterfly; the symmetry of left and right appears here with almost mathematical rigor. We can say that every animal (as well as insects, fish, birds) consists of two enantiomorphs - the right and left halves. Enantiomorphs are also paired parts, one of which falls into the right and the other into the left half of the animal’s body. Thus, enantiomorphs are the right and left ear, right and left eye, right and left horn, etc.

Symmetry in humans

The human body has bilateral symmetry (external appearance and skeletal structure). This symmetry has always been and is the main source of our aesthetic admiration for the well-proportioned human body. The human body is built on the principle of bilateral symmetry.

Most of us view the brain as a single structure; in reality, it is divided into two halves. These two parts - two hemispheres - fit tightly to each other. In full accordance with the general symmetry of the human body, each hemisphere is an almost exact mirror image of the other

Control of the basic movements of the human body and its sensory functions is evenly distributed between the two hemispheres of the brain. The left hemisphere controls the right side of the brain, and the right hemisphere controls the left side.

Physical symmetry of the body and brain does not mean that the right side and the left are equal in all respects. It is enough to pay attention to the actions of our hands to see the initial signs of functional symmetry. Few people have equal use of both hands; the majority has the leading hand.

Types of symmetry in animals

1. central
2. axial (mirror)
3. radial
4. bilateral
5. double-beam
6. progressive (metamerism)
7. translational-rotational

Types of symmetry

Only two main types of symmetry are known - rotational and translational. In addition, there is a modification from the combination of these two main types of symmetry - rotational-translational symmetry.

Rotational symmetry. Every organism has rotational symmetry. For rotational symmetry, antimers are an essential characteristic element. It is important to know that when rotated by any degree, the contours of the body will coincide with the original position. The minimum degree of contour coincidence is for a ball rotating around the center of symmetry. The maximum degree of rotation is 360 0, when when turning by this amount the contours of the body coincide. If a body rotates around a center of symmetry, then many axes and planes of symmetry can be drawn through the center of symmetry. If a body rotates around one heteropolar axis, then through this axis one can draw as many planes as there are antimeres in the given body. Depending on this condition, one speaks of rotational symmetry of a certain order. For example, six-rayed corals will have sixth-order rotational symmetry. Ctenophores have two planes of symmetry, and they have second-order symmetry. The symmetry of ctenophores is also called biradial. Finally, if an organism has only one plane of symmetry and, accordingly, two antimeres, then such symmetry is called bilateral or bilateral. Thin needles extend in a radial manner. This helps the protozoa to “hover” in the water column. Other representatives of protozoa are also spherical - rays (radiolaria) and sunfishes with ray-shaped processes-pseudopodia.

Translational symmetry. For translational symmetry, the characteristic elements are metamers (meta - one after the other; mer - part). In this case, the parts of the body are not located mirror opposite to each other, but sequentially one after another along the main axis of the body.

Metamerism - one of the forms of translational symmetry. It is especially pronounced in annelids, whose long body consists of a large number of almost identical segments. This case of segmentation is called homonomic. In arthropods, the number of segments can be relatively small, but each segment is slightly different from its neighbors either in shape or appendages (thoracic segments with legs or wings, abdominal segments). This segmentation is called heteronomous.

Rotational-translational symmetry . This type of symmetry has a limited distribution in the animal kingdom. This symmetry is characterized by the fact that when turning at a certain angle, a part of the body moves forward a little and each subsequent one increases its size logarithmically by a certain amount. Thus, the acts of rotation and translational motion are combined. An example is the spiral chamber shells of foraminifera, as well as the spiral chamber shells of some cephalopods. With some conditions, non-chambered spiral shells of gastropods can also be included in this group

Mirror symmetry

If you stand in the center of the building and to your left there are the same number of floors, columns, windows as to your right, then the building is symmetrical. If it were possible to bend it along the central axis, then both halves of the house would coincide when superimposed. This symmetry is called mirror symmetry. This type of symmetry is very popular in the animal kingdom; man himself is tailored according to its canons.

The axis of symmetry is the axis of rotation. In this case, animals, as a rule, lack a center of symmetry. Then rotation can only occur around an axis. In this case, the axis most often has poles of different quality. For example, in coelenterates, hydra or anemone, the mouth is located on one pole, and the sole with which these motionless animals are attached to the substrate is located on the other. The axis of symmetry may coincide morphologically with the anteroposterior axis of the body.

With mirror symmetry, the right and left sides of the object change.

The plane of symmetry is a plane passing through the axis of symmetry, coinciding with it and cutting the body into two mirror halves. These halves, located opposite each other, are called antimers (anti - against; mer - part). For example, in Hydra, the plane of symmetry must pass through the mouth opening and through the sole. Antimeres of opposite halves should have an equal number of tentacles located around the hydra's mouth. Hydra can have several planes of symmetry, the number of which will be a multiple of the number of tentacles. In sea anemones with a very large number of tentacles, many planes of symmetry can be drawn. For a jellyfish with four tentacles on a bell, the number of planes of symmetry will be limited to a multiple of four. Ctenophores have only two planes of symmetry - pharyngeal and tentacle. Finally, bilaterally symmetrical organisms have only one plane and only two mirror antimeres - the right and left sides of the animal, respectively.

The transition from radial or radial to bilateral or bilateral symmetry is associated with the transition from a sedentary lifestyle to active movement in the environment. For sessile forms, the relationship with the environment is equal in all directions: radial symmetry exactly corresponds to this lifestyle. In actively moving animals, the front end of the body becomes biologically unequal to the rest of the body, the head is formed, and the right and left sides of the body become distinguishable. Due to this, radial symmetry is lost, and only one plane of symmetry can be drawn through the animal’s body, dividing the body into right and left sides. Bilateral symmetry means that one side of an animal's body is a mirror image of the other side. This type of organization is characteristic of most invertebrates, especially annelids and arthropods - crustaceans, arachnids, insects, butterflies; for vertebrates - fish, birds, mammals. Bilateral symmetry first appears in flatworms, in which the anterior and posterior ends of the body differ from each other.

In annelids and arthropods, metamerism is also observed - one of the forms of translational symmetry, when parts of the body are located sequentially one after another along the main axis of the body. It is especially pronounced in annelids (earthworms). Annelids get their name from the fact that their body consists of a series of rings or segments (segments). Both internal organs and body walls are segmented. So the animal consists of about a hundred more or less similar units - metameres, each of which contains one or a pair of organs of each system. The segments are separated from each other by transverse partitions. In an earthworm, almost all segments are similar to each other. Annelids include polychaetes - marine forms that swim freely in water and burrow in the sand. Each segment of their body has a pair of lateral projections bearing a dense tuft of bristles. Arthropods got their name from their characteristic jointed paired appendages (such as swimming organs, walking limbs, mouthparts). All of them are characterized by a segmented body. Each arthropod has a strictly defined number of segments, which remains unchanged throughout its life. Mirror symmetry is clearly visible in the butterfly; the symmetry of left and right appears here with almost mathematical rigor. We can say that every animal, insect, fish, bird consists of two enantiomorphs - the right and left halves. Thus, enantiomorphs are the right and left ear, right and left eye, right and left horn, etc.

Radial symmetry

Radial symmetry is a form of symmetry in which a body (or figure) coincides with itself when the object rotates around a specific point or line. Often this point coincides with the center of symmetry of the object, that is, the point at which an infinite number of axes of bilateral symmetry intersect.

In biology, radial symmetry is said to occur when one or more axes of symmetry pass through a three-dimensional being. Moreover, radially symmetrical animals may not have planes of symmetry. Thus, the Velella siphonophore has a second-order axis of symmetry and no planes of symmetry.

Usually two or more planes of symmetry pass through the axis of symmetry. These planes intersect along a straight line - the axis of symmetry. If the animal rotates around this axis by a certain degree, then it will be displayed on itself (coincide with itself).
There can be several such axes of symmetry (polyaxon symmetry) or one (monaxon symmetry). Polyaxonal symmetry is common among protists (e.g. radiolarians).

As a rule, in multicellular animals, the two ends (poles) of a single axis of symmetry are unequal (for example, in jellyfish, the mouth is located on one pole (oral), and the tip of the bell is on the opposite (aboral) pole. Such symmetry (a variant of radial symmetry) in comparative anatomy is called uniaxial-heteropole. In a two-dimensional projection, radial symmetry can be preserved if the axis of symmetry is directed perpendicular to the projection plane. In other words, the preservation of radial symmetry depends on the viewing angle.
Radial symmetry is characteristic of many cnidarians, as well as most echinoderms. Among them there is the so-called pentasymmetry, based on five planes of symmetry. In echinoderms, radial symmetry is secondary: their larvae are bilaterally symmetrical, and in adult animals, external radial symmetry is broken by the presence of a madrepore plate.

In addition to typical radial symmetry, there is biradial radial symmetry (two planes of symmetry, for example, in ctenophores). If there is only one plane of symmetry, then the symmetry is bilateral (bilaterally symmetrical people have such symmetry).

In flowering plants, radially symmetrical flowers are often found: 3 planes of symmetry (frogwort), 4 planes of symmetry (cinquefoil erect), 5 planes of symmetry (bellflower), 6 planes of symmetry (colchicum). Flowers with radial symmetry are called actinomorphic, flowers with bilateral symmetry are called zygomorphic.

If the environment surrounding an animal is more or less homogeneous on all sides and the animal is evenly in contact with it with all parts of its surface, then the shape of the body is usually spherical, and the repeating parts are located in radial directions. Many radiolarians that are part of the so-called plankton are spherical, i.e. a collection of organisms suspended in the water column and incapable of active swimming; spherical chambers contain a few planktonic representatives of foraminifera (protozoa, sea inhabitants, marine testate amoebae). Foraminifera are enclosed in shells of various, bizarre shapes. The spherical body of sunfish sends numerous thin, thread-like, radially arranged pseudopodia in all directions; the body is devoid of a mineral skeleton. This type of symmetry is called equiaxial, since it is characterized by the presence of many identical axes of symmetry.

Equiaxial and polysymmetric types are found mainly among low-organized and poorly differentiated animals. If there are 4 identical organs around the longitudinal axis, then radial symmetry in this case is called four-ray symmetry. If there are six such organs, then the order of symmetry will be six-rayed, etc. Since the number of such organs is limited (often 2,4,8 or a multiple of 6), several planes of symmetry can always be drawn, corresponding to the number of these organs. Planes divide the animal's body into equal sections with repeating organs. This is the difference between radial symmetry and the polysymmetric type. Radial symmetry is characteristic of sedentary and attached forms. The ecological significance of radial symmetry is clear: a sessile animal is surrounded on all sides by the same environment and must enter into relationships with this environment using identical organs that repeat in radial directions. It is a sedentary lifestyle that contributes to the development of radiant symmetry.

Rotational symmetry

Rotational symmetry is “popular” in the plant world. Take a chamomile flower in your hand. The combination of different parts of the flower occurs if they are rotated around the stem.

Very often flora and fauna borrow external forms from each other. Sea stars leading a vegetative lifestyle have rotational symmetry, and their leaves are mirrored.

Plants confined to a permanent place clearly distinguish only the top and bottom, and all other directions are more or less the same for them. Naturally, their appearance is subject to rotational symmetry. For animals, it is very important what is in front and what is behind; only “left” and “right” remain equal for them. In this case, mirror symmetry prevails. It is curious that animals that exchange mobile life for immobile life and then return to mobile life again, move from one type of symmetry to another a corresponding number of times, as happened, for example, with echinoderms (starfish, etc.).

Helical or spiral symmetry

Helical symmetry is symmetry with respect to a combination of two transformations - rotation and translation along the rotation axis, i.e. there is movement along the axis of the screw and around the axis of the screw. There are left and right screws.

Examples of natural propellers are: tusk of a narwhal (a small cetacean that lives in the northern seas) - left propeller; snail shell - right screw; The horns of the Pamir ram are enantiomorphs (one horn is twisted in a left-handed spiral, and the other in a right-handed spiral). Spiral symmetry is not ideal, for example, the shell of mollusks narrows or widens at the end.

Although external helical symmetry is rare in multicellular animals, many important molecules from which living organisms are built - proteins, deoxyribonucleic acids - DNA have a helical structure. The true kingdom of natural screws is the world of “living molecules” - molecules that play a fundamentally important role in life processes. These molecules include, first of all, protein molecules. There are up to 10 types of proteins in the human body. All parts of the body, including bones, blood, muscles, tendons, hair, contain proteins. A protein molecule is a chain made up of individual blocks and twisted in a right-handed spiral. It is called the alpha helix. Tendon fiber molecules are triple alpha helices. Alpha helices twisted multiple times with each other form molecular screws, which are found in hair, horns, and hooves. The DNA molecule has the structure of a double right-handed helix, discovered by American scientists Watson and Crick. The double helix of the DNA molecule is the main natural screw.

Conclusion

All forms in the world are subject to the laws of symmetry. Even “eternally free” clouds have symmetry, albeit distorted. Freezing in the blue sky, they resemble jellyfish slowly moving in sea water, clearly gravitating towards rotational symmetry, and then, driven by the rising wind, they change symmetry to mirror one.

Symmetry, manifesting itself in a wide variety of objects of the material world, undoubtedly reflects its most general, most fundamental properties. Therefore, the study of the symmetry of various natural objects and the comparison of its results is a convenient and reliable tool for understanding the basic laws of the existence of matter.

Symmetry is equality in the broad sense of the word. This means that if there is symmetry, then something will not happen and, therefore, something will definitely remain unchanged, preserved.

Sources

1. Urmantsev Yu. A. “Symmetry of nature and the nature of symmetry.” Moscow, Mysl, 1974.
2. IN AND. Vernadsky. Chemical structure of the Earth's biosphere and its environment. M., 1965.

SYMMETRY IN LIVING NATURE. SYMMETRY AND ASYMMETRY.

Objects and phenomena of living nature have symmetry. It not only pleases the eye and inspires poets of all times and peoples, but allows living organisms to better adapt to their environment and simply survive.

In living nature, the vast majority of living organisms exhibit various types of symmetries (shape, similarity, relative location). Moreover, organisms of different anatomical structures can have the same type of external symmetry.

External symmetry can act as the basis for the classification of organisms (spherical, radial, axial, etc.) Microorganisms living in conditions of weak gravity have a pronounced symmetry of shape.

Asymmetry is already present at the level of elementary particles and manifests itself in the absolute predominance of particles over antiparticles in our Universe. The famous physicist F. Dyson wrote: “The discoveries of recent decades in the field of elementary particle physics force us to pay special attention to the concept of symmetry breaking. The development of the Universe from the moment of its origin looks like a continuous sequence of symmetry breaking.
At the moment of its emergence in a grandiose explosion, the Universe was symmetrical and homogeneous. As it cools, one symmetry after another is broken, which creates the possibility for the existence of an ever-increasing variety of structures. The phenomenon of life fits naturally into this picture. Life is also a violation of symmetry."
Molecular asymmetry was discovered by L. Pasteur, who was the first to distinguish “right-handed” and “left-handed” molecules of tartaric acid: right-handed molecules are like a right-handed screw, and left-handed ones are like a left-handed one. Chemists call such molecules stereoisomers. Stereoisomer molecules have the same atomic composition, the same size, the same structure - at the same time, they are distinguishable because they are mirror asymmetric, i.e. the object turns out to be non-identical with its mirror double. 67 Therefore, here the concepts of “right-left” are conditional.
It is now well known that the molecules of organic substances that form the basis of living matter are asymmetrical in nature, i.e. They enter into the composition of living matter only either as right-handed or left-handed molecules. Thus, each substance can be part of living matter only if it has a very specific type of symmetry. For example, the molecules of all amino acids in any living organism can only be left-handed, sugars - only right-handed.
This property of living matter and its waste products is called dissymmetry. It is completely fundamental. Although right- and left-handed molecules are indistinguishable in chemical properties, living matter not only distinguishes between them, but also makes a choice. It rejects and does not use molecules that do not have the structure it needs. How this happens is not yet clear. Molecules of opposite symmetry are poison for her.
If a living creature found itself in conditions where all food was composed of molecules of opposite symmetry that did not correspond to the dissymmetry of this organism, then it would die of starvation. In inanimate matter there are equal numbers of right- and left-handed molecules. Dissymmetry is the only property due to which we can distinguish a substance of biogenic origin from a nonliving substance. We cannot answer the question of what life is, but we have a way to distinguish living from non-living.
Thus, asymmetry can be seen as the dividing line between living and inanimate nature. Inanimate matter is characterized by the predominance of symmetry; during the transition from inanimate to living matter, asymmetry predominates already at the microlevel. In living nature, asymmetry can be seen everywhere. This was very aptly noted in the novel “Life and Fate” by V. Grossman: “In the large million Russian village huts there are not and cannot be two indistinguishably similar. All living things are unique.

Symmetry underlies things and phenomena, expressing something common, characteristic of different objects, while asymmetry is associated with the individual embodiment of this common thing in a specific object. The method of analogies is based on the principle of symmetry, which involves finding common properties in different objects. Based on analogies, physical models of various objects and phenomena are created. Analogies between processes allow them to be described by general equations.

SYMMETRY IN THE PLANT WORLD:

The specific structure of plants and animals is determined by the characteristics of the habitat to which they adapt and the characteristics of their way of life. Any tree has a base and a top, a “top” and a “bottom” that perform different functions. The significance of the difference between the upper and lower parts, as well as the direction of gravity, determine the vertical orientation of the rotary axis of the “wood cone” and the planes of symmetry.
The leaves are characterized by mirror symmetry. The same symmetry is also found in flowers, but in them mirror symmetry often appears in combination with rotational symmetry. There are also frequent cases of figurative symmetry (acacia branches, rowan trees). It is interesting that in the floral world the most common is rotational symmetry of the 5th order, which is fundamentally impossible in the periodic structures of inanimate nature.
Academician N. Belov explains this fact by the fact that the 5th order axis is a kind of instrument of the struggle for existence, “insurance against petrification, crystallization, the first step of which would be their capture by a lattice.” Indeed, a living organism does not have a crystalline structure in the sense that even its individual organs do not have a spatial lattice. However, ordered structures are represented very widely in it.

	Honeycomb- a real design masterpiece. They consist of a number of hexagonal cells.
This is the densest packaging, allowing the most advantageous placement of the larva in the cell and, with the maximum possible volume, the most economical use of the building material - wax.
The leaves on the stem are not arranged in a straight line, but surround the branch in a spiral. The sum of all previous steps of the spiral, starting from the top, is equal to the value of the next step A+B=C, B+C=D, etc.
The arrangement of achenes in the head of a sunflower or leaves in the shoots of climbing plants corresponds to a logarithmic spiral

SYMMETRY IN THE WORLD OF INSECTS, FISHES, BIRDS, ANIMALS

Types of symmetry in animals

1-central		3-radial	4-bilateral
5-double-beam	6-translational (metamerism)		7-translational-rotational

Axis of symmetry. The axis of symmetry is the axis of rotation. In this case, animals, as a rule, lack a center of symmetry. Then rotation can only occur around an axis. In this case, the axis most often has poles of different quality. For example, in coelenterates, hydra or sea anemone, the mouth is located on one pole, and the sole with which these immobile animals are attached to the substrate is located on the other (Fig. 1, 2,3). The axis of symmetry may coincide morphologically with the anteroposterior axis of the body.

Plane of symmetry. The plane of symmetry is a plane passing through the axis of symmetry, coinciding with it and cutting the body into two mirror halves. These halves opposite each other are called antimers (anti – against; mer – part). For example, in Hydra, the plane of symmetry must pass through the mouth opening and through the sole. Antimeres of opposite halves should have an equal number of tentacles located around the hydra's mouth. Hydra can have several planes of symmetry, the number of which will be a multiple of the number of tentacles. In sea anemones with a very large number of tentacles, many planes of symmetry can be drawn. For a jellyfish with four tentacles on a bell, the number of planes of symmetry will be limited to a multiple of four. Ctenophores have only two planes of symmetry - pharyngeal and tentacle (Fig. 1, 5). Finally, bilaterally symmetrical organisms have only one plane and only two mirror antimeres - the right and left sides of the animal, respectively (Fig. 1, 4, 6, 7).

Types of symmetry. There are only two main types of symmetry known - rotational and translational. In addition, there is a modification from the combination of these two main types of symmetry - rotational-translational symmetry.

Rotational symmetry. Any organism has rotational symmetry. For rotational symmetry, an essential characteristic element is antimers . It is important to know, when turning by what degree, the contours of the body will coincide with the original position. The minimum degree of contour coincidence is for a ball rotating around the center of symmetry. The maximum degree of rotation is 360, when when turning by this amount the contours of the body coincide.

If a body rotates around a center of symmetry, then many axes and planes of symmetry can be drawn through the center of symmetry. If a body rotates around one heteropolar axis, then through this axis one can draw as many planes as there are antimeres in the given body. Depending on this condition, one speaks of rotational symmetry of a certain order. For example, six-rayed corals will have sixth-order rotational symmetry. Ctenophores have two planes of symmetry, and they have second-order symmetry. The symmetry of ctenophores is also called biradial (Fig. 1, 5). Finally, if an organism has only one plane of symmetry and, accordingly, two antimeres, then such symmetry is called bilateral or bilateral (Fig. 1, 4). Thin needles extend in a radial manner. This helps the protozoa to “hover” in the water column. Other representatives of the protozoa are also spherical - rays (radiolaria) and sunfishes with ray-shaped processes-pseudopodia. “Looking at them, it seems that these lace plexuses are not part of living creatures, but the finest jewelry designed to decorate the outfits of sea

Translational symmetry. For translational symmetry, the characteristic elements are metamers (meta – one after another; mer – part). In this case, the parts of the body are not located mirror opposite to each other, but sequentially one after another along the main axis of the body.

Metamerism – one of the forms of translational symmetry. It is especially pronounced in annelids, whose long body consists of a large number of almost identical segments. This case of segmentation is called homonomous (Fig. 1, 6). In arthropods, the number of segments can be relatively small, but each segment is slightly different from its neighbors either in shape or appendages (thoracic segments with legs or wings, abdominal segments). This segmentation is called heteronomous.

Rotational-translational symmetry. This type of symmetry has a limited distribution in the animal kingdom. This symmetry is characterized by the fact that when turning at a certain angle, a part of the body moves forward a little and each subsequent one increases its size logarithmically by a certain amount. Thus, the acts of rotation and translational motion are combined. An example is the spiral chamber shells of foraminifera, as well as the spiral chamber shells of some cephalopods (modern nautilus or fossil ammonite shells, Fig. 1, 7). With some conditions, non-chambered spiral shells of gastropods can also be included in this group.

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Oh, symmetry! I sing your anthem! Oh, symmetry! I sing your anthem! I recognize you everywhere in the world. You are in the Eiffel Tower, in a small midge, You are in a Christmas tree near a forest path. With you in friendship are both a tulip and a rose, And a snow swarm - the creation of frost! The concept of symmetry is familiar and plays an important role in everyday life. Many human creations are deliberately given a symmetrical shape for both aesthetic and practical reasons. In ancient times, the word “symmetry” was used as “harmony”, “beauty”. Indeed, in Greek it means “proportionality, proportionality, uniformity in the arrangement of parts”

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Central and axial symmetries Central symmetry - A figure is called symmetrical with respect to point O if, for each point of the figure, a point symmetrical with respect to point O also belongs to this figure. Point O is called the center of symmetry of the figure. The figure is also said to have central symmetry. Axial symmetry - A figure is called symmetrical with respect to line a if for each point of the figure a point symmetrical with respect to line a also belongs to this figure. Straight line a is called the axis of symmetry of the figure. The figure is also said to have axial symmetry.

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The manifestation of symmetry in living nature Beauty in nature is not created, but only recorded and expressed. Let us consider the manifestation of symmetry from the “global”, namely from our planet Earth. The fact that the Earth is a ball became known to educated people in ancient times. The earth, in the minds of most well-read people before the era of Copernicus, was the center of the universe. Therefore, they considered the straight lines passing through the center of the Earth to be the center of symmetry of the Universe. Therefore, even the model of the Earth - the globe has an axis of symmetry.

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Almost all living beings are built according to the laws of symmetry; it is not for nothing that the word “symmetry” means “proportionality” when translated from Greek. Almost all living beings are built according to the laws of symmetry; it is not for nothing that the word “symmetry” means “proportionality” when translated from Greek. Among flowers, for example, there is rotational symmetry. Many flowers can be rotated so that each petal takes the position of its neighbor, the flower aligns with itself. The minimum angle of such rotation is not the same for different colors. For the iris it is 120°, for the bellflower – 72°, for the narcissus – 60°.

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There is helical symmetry in the arrangement of leaves on plant stems. Arranging in a screw along the stem, the leaves seem to spread out in different directions and do not block each other from the light), although the leaves themselves also have an axis of symmetry. In the arrangement of leaves on plant stems, screw symmetry is observed. Positioned like a screw along the stem, the leaves seem to spread out in different directions and do not obscure each other from the light), although the leaves themselves also have an axis of symmetry

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Considering the general plan of the structure of any animal, we usually notice a certain regularity in the arrangement of body parts or organs, which are repeated around a certain axis or occupy the same position in relation to a certain plane. This regularity is called body symmetry. The phenomena of symmetry are so widespread in the animal world that it is very difficult to indicate a group in which no symmetry of the body can be noticed. Both small insects and large animals have symmetry. Considering the general plan of the structure of any animal, we usually notice a certain regularity in the arrangement of body parts or organs, which are repeated around a certain axis or occupy the same position in relation to a certain plane. This regularity is called body symmetry. The phenomena of symmetry are so widespread in the animal world that it is very difficult to indicate a group in which no symmetry of the body can be noticed. Both small insects and large animals have symmetry.

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Manifestation of symmetry in inanimate nature Crystals bring the charm of symmetry to the world of inanimate nature. Each snowflake is a small crystal of frozen water. The shape of snowflakes can be very diverse, but they all have rotational symmetry and, in addition, mirror symmetry. What is a crystal? A solid body that has the natural shape of a polyhedron. Salt, ice, sand, etc. consist of crystals. First of all, Romeu-Delisle emphasized the correct geometric shape of crystals based on the law of constancy of angles between their faces. Why are crystals so beautiful and attractive? Their physical and chemical properties are determined by their geometric structure. In crystallography (the science of crystals) there is even a section called “Geometric Crystallography”. In 1867, artillery general, professor at the Mikhailovsky Academy in St. Petersburg A.V. Gadolin strictly mathematically derived all combinations of symmetry elements that characterize crystalline polyhedra. In total, there are 32 types of symmetries of ideal crystal shapes.

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