"Mandelbrot fractals" - There are several methods for obtaining algebraic fractals. The concept of fractal. Lots of Julia. The role of fractals in computer graphics today is quite large. Fractals. Let's turn to the classics - the Mandelbrot set. Sierpinski triangle. Gallery of fractals. Journey into the world of fractals. The second large group of fractals is algebraic.
"Sheet of paper" - A triangle is cut out of paper. In geometry, paper is used to: write, draw; cut; bend. The practical properties of paper give rise to a peculiar geometry. Geometry and sheet of paper. What paper actions can be used in geometry? Among the many possible actions with paper, an important place is occupied by the fact that it can be cut.
"Sine function" - The average time of sunset - 18h. The date. Miscellaneous trigonometry. Time. Using a tear-off calendar, it is easy to mark the moment of sunset. Target. Sunset chart. Conclusions. The process of sunset is described by the trigonometric sine function. Sunset.
"Geometry of Lobachevsky" - Euclidean axiom about parallel. It cannot be said that non-Euclidean geometry is the only correct one. "How does Lobachevsky's geometry differ from Euclid's geometry?". Is non-Euclidean geometry the only correct one? Riemannian geometry got its name after B. Riemann, who laid its foundations in 1854.
"Proof of the Pythagorean Theorem" - The Pythagorean Theorem. The simplest proof. geometric proof. The meaning of the Pythagorean theorem. Euclid's proof. "In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs." The Pythagorean theorem is one of the most important theorems in geometry. Proofs of the theorem. Statement of the theorem.
"Theorem of Pythagoras" - Creates a "Pythagorean" school around 510. BC. Aphorisms. Proof of the theorem. Divisibility of numbers. Here is the problem of an Indian mathematician of the 12th century. Bhaskara. The Pythagoreans had an oath number 36. Friendly numbers. Pythagoras began to depict numbers with dots. The number 3 is a triangle, the triangle defines the plane.
There are 13 presentations in total in the topic
Introduction.
Looking at different snowflakes, we see that they are all different in shape, but each of them represents a symmetrical body.
We call symmetrical bodies that consist of equal identical parts. The elements of symmetry for us are the plane of symmetry (mirror image), the axis of symmetry (rotation around an axis perpendicular to the plane). There is another element of symmetry - the center of symmetry.
Imagine a mirror, but not a big one, but a point one: a point where everything is displayed as in a mirror. This point is the center
Symmetries. With this display, the reflection is rotated not only from right to left, but also from the front to the wrong side.
Snowflakes are crystals, and all crystals are symmetrical. This means that in each crystalline polyhedron one can find symmetry planes, symmetry axes, symmetry centers and other symmetry elements so that the same parts of the polyhedron are aligned with each other.
Indeed, symmetry is one of the main properties of crystals. For many years, the geometry of crystals seemed to be a mysterious and insoluble riddle. The symmetry of crystals has always attracted the attention of scientists. Already in the year 79 of our era, Pliny the Elder mentions the flatness and straight-sidedness of crystals. This conclusion can be considered the first generalization of geometric crystallography.
FORMING SNOWFLAKES
In 1619, the great German mathematician and astronomer Johannes Kepler drew attention to the sixfold symmetry of snowflakes. He tried to explain it by the fact that the crystals are built from the smallest identical balls, closely attached to each other (only six of the same balls can be densely expanded around the central ball). Subsequently, Robert Hooke and M. V. Lomonosov followed the path outlined by Kepler. They also believed that the elementary particles of crystals can be likened to densely packed balls. In our time, the principle of the closest spherical packings underlies structural crystallography, only continuous spherical particles of ancient authors are now replaced by atoms and ions. Fifty years after Kepler, the Danish geologist, crystallographer and anatomist Nicholas Stenon first formulated the basic concepts of crystal formation: “The growth of a crystal does not occur from the inside, as in plants, but by imposing on the outer planes of the crystal the smallest particles brought from the outside by some liquid.” This idea about the growth of crystals as a result of the deposition of more and more new layers of matter on the faces has retained its significance to this day. For each given substance there is its own ideal form of its crystal, inherent only to it. This form has the property of symmetry, i.e., the property of crystals to be combined with themselves in various positions by means of rotations, reflections, and parallel transfers. Among the elements of symmetry, there are axes of symmetry, planes of symmetry, center of symmetry, mirror axes.
The internal structure of the crystal is represented as a spatial lattice, in the same cells of which, having the shape of parallelepipeds, the same smallest particles are placed according to the laws of symmetry - molecules, atoms, ions and their groups.
The symmetry of the external form of a crystal is a consequence of its internal symmetry - the ordered mutual arrangement of atoms (molecules) in space.
The law of constancy of dihedral angles.
Over the course of many centuries, material was accumulated very slowly and gradually, which made it possible at the end of the 18th century. discover the most important law of geometric crystallography - the law of constancy of dihedral angles. This law is usually associated with the name of the French scientist Romet de Lisle, who in 1783. published a monograph containing abundant material on measuring the angles of natural crystals. For each substance (mineral) studied by him, it turned out to be true that the angles between the corresponding faces in all crystals of the same substance are constant.
It should not be thought that before Romé de Lisle, none of the scientists dealt with this problem. The history of the discovery of the law of constancy of angles has come a long way, almost two centuries, before this law was clearly formulated and generalized for all crystalline substances. So, for example, I. Kepler already in 1615. indicated the preservation of angles of 60° between the individual rays of the snowflakes.
All crystals have the property that the angles between the corresponding faces are constant. The faces of individual crystals can be developed differently: the faces observed on some specimens may be absent on others - but if we measure the angles between the corresponding faces, then the values of these angles will remain constant regardless of the shape of the crystal.
However, with the improvement of the technique and the increase in the accuracy of measuring crystals, it turned out that the law of constancy of angles is justified only approximately. In the same crystal, the angles between faces of the same type differ slightly from each other. For many substances, the deviation of the dihedral angles between the corresponding faces reaches 10 -20', and in some cases even a degree.
DEVIATIONS FROM THE LAW
The edges of a real crystal are never ideal flat surfaces. Often they are covered with pits or growth tubercles, in some cases the faces are curved surfaces, for example, in diamond crystals. Sometimes flat areas are noticed on the faces, the position of which is slightly deviated from the plane of the very face on which they develop. These areas are called in crystallography vicinal faces, or simply vicinals. Vicinals can occupy most of the plane of a normal face, and sometimes even completely replace the latter.
Many, if not all, crystals break more or less easily along certain well-defined planes. This phenomenon is called cleavage and indicates that the mechanical properties of crystals are anisotropic, that is, they are not the same in different directions.
CONCLUSION
Symmetry manifests itself in the diverse structures and phenomena of the inorganic world and wildlife. 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 symmetry - rotational symmetry of the 6th order and, in addition, mirror symmetry. . A characteristic feature of this or that substance is the constancy of the angles between the corresponding faces and edges for all images of crystals of the same substance.
As for the shape of the faces, the number of faces and edges, and the size of snowflakes, they can differ significantly from each other, depending on the height from which they fall.
Bibliography.
1. “Crystals”, M. P. Shaskolskaya, Moscow “nauka”, 1978
2. “Essays on the properties of crystals”, M. P. Shaskolskaya, Moscow “nauka”, 1978
3. “Symmetry in nature”, I. I. Shafranovsky, Leningrad “Nedra”, 1985
4. “Crystallochemistry”, G. B. Bokiy, Moscow “science”, 1971.
5. “Living Crystal”, Ya. E. Geguzin, Moscow “science”, 1981.
6. “Essays on diffusion in crystals”, Ya. E. Geguzin, Moscow “nauka”, 1974.
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- Today, when I left the house, I stopped on the porch, looking around. The whole yard was as if bewitched. The whole earth, all the trees were covered with a white fluffy blanket. They seemed to fall asleep, wrapped in white down jackets and listening to the sonorous prelude of snowflakes. Read More ......
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Symmetry has always been the mark of perfection and beauty in classical Greek illustration and aesthetics. The natural symmetry of nature in particular has been the subject of study by philosophers, astronomers, mathematicians, artists, architects and physicists such as Leonardo Da Vinci. We see this perfection every second, although we do not always notice it. Here are 10 beautiful examples of symmetry that we ourselves are a part of.
Broccoli Romanesco
This type of cabbage is known for its fractal symmetry. This is a complex pattern where the object is formed in the same geometric figure. In this case, the entire broccoli is made up of the same logarithmic spiral. Broccoli Romanesco is not only beautiful, but also very healthy, rich in carotenoids, vitamins C and K, and tastes like cauliflower.
Honeycomb
For thousands of years, bees have instinctively produced perfectly shaped hexagons. Many scientists believe that bees produce honeycombs in this form in order to retain the most honey while using the least amount of wax. Others are not so sure and believe that this is a natural formation and wax is formed when the bees make their home.
sunflowers
These children of the sun have two forms of symmetry at once - radial symmetry, and numerical symmetry of the Fibonacci sequence. The Fibonacci sequence manifests itself in the number of spirals from the seeds of a flower.
Nautilus shell
Another natural Fibonacci sequence appears in the Nautilus shell. The shell of the Nautilus grows in a “Fibonacci spiral” in a proportional shape, which allows the nautilus inside to maintain the same shape throughout its lifespan.
Animals
Animals, like people, are symmetrical on both sides. This means there is a centerline where they can be split into two identical halves.
spider web
Spiders create perfect circular webs. The web web consists of equally spaced radial levels that spiral out from the center, intertwining with each other with maximum strength.
Crop Circles.
Crop circles don't happen "naturally" at all, but it's quite amazing the symmetry that humans can achieve. Many believed that crop circles were the result of UFO visits, but in the end it turned out that this was the work of man. Crop circles show various forms of symmetry, including Fibonacci spirals and fractals.
Snowflakes
You will definitely need a microscope to witness the beautiful radial symmetry in these miniature six-sided crystals. This symmetry is formed during the crystallization process in the water molecules that form the snowflake. When water molecules freeze, they create hydrogen bonds with the hexagonal shapes.
Milky Way Galaxy
Earth is not the only place that adheres to natural symmetry and mathematics. The Milky Way Galaxy is a striking example of mirror symmetry and is made up of two main arms known as the Perseus and Scutum Centaurus. Each of these arms has a nautilus shell-like logarithmic spiral with a Fibonacci sequence that starts at the center of the galaxy and expands.
Lunar-solar symmetry
The sun is much larger than the moon, in fact four hundred times larger. However, solar eclipse events occur every five years when the lunar disk completely blocks out sunlight. The symmetry happens because the Sun is four hundred times farther from the Earth than the Moon.
In fact, symmetry is inherent in nature itself. Mathematical and logarithmic perfection creates beauty around and within us.
Topic: "Snowflakes - the wings of angels that fell from heaven ..."
Place of work: MOU secondary school No. 9, grade 3, Irkutsk region, Ust-Kut
Scientific adviser:
1. Introduction.
2. Snowflakes - the wings of angels that fell from heaven:
History of the study of snowflakes;
Conditions for the birth of snowflakes;
The geometry of the snowflake
· Types of snowflakes;
· Physics of snow.
3. Entertaining and informative about snow and snowflake.
· Do you know that…;
· Snow fairy tales;
Snegurochka - a girl from the snow;
«Lantern for admiring the snow»;
· Excursion to the museum of snowflakes.
"Summer Snow Festival"
4. A small miracle with your own hands.
· Snowflake in 3D format;
· Quilling.
· How to cut a beautiful snowflake;
5. Conclusion.
Introduction.
"Nature is so about everything
Made sure that everywhere
You find something to learn."
Leonardo Da Vinci
Snow is a great miracle of nature. The legend about the very first snow tells that the Rebellious Angels at the moment of the fall lost their snow-white wings, which covered the earth with a white shiny carpet. So snow appeared, and the first winter came.
When it snows, this spectacle leaves no one indifferent. For some, the falling snow pleases, gives high spirits, while for others, on the contrary, it evokes sadness and sadness. Thanks to snow, every year we admire fabulous winter landscapes, but we love snow not only for this. Snow reserves affect the crop, the water level in the rivers. Snow is used to build winter roads and even airfields. But we do not even think about this useful role of snow. Snow for us is first of all a FAIRY TALE. Have you noticed that various monsters, mythical and fabulous, can live anywhere, but man has not settled them in the snow? But snow inspired a great many fairy tales to man.
The most amazing thing about snowflakes is that none of them repeats the other. Astronomer Johannes Kepler in his treatise "New Year's gift. About hexagonal snowflakes ”explained the shape of the crystals by the will of God. If you live in cold climes, you know firsthand about winter, then you have at least one reason to be proud of it: unlike residents of hot countries, you can admire snowflakes in natural conditions. Believe me, it is very interesting to look at snowflakes, if only because two identical ones have never fallen to the ground.
PURPOSE OF THE WORK:
· To get acquainted with the conditions of the birth of snowflakes;
Consider the division of snowflakes according to shape;
· Get acquainted with the geometry and physics of snowflakes;
· Learn myths, riddles, proverbs and sayings about snow;
Consider making unusual paper snowflakes.
THIS WORK CAN BE USED:
As an additional material in the lessons of the "World around" in the 3rd grade;
In the lessons of visual geometry;
· As material for messages;
· In additional and optional classes for younger students.
"Snowflakes are the wings of angels that have fallen from heaven..."
The history of the study of snowflakes.
It is difficult to say when a person first admired this miracle of nature. The forms of snowflakes are unusually diverse - there are more than five thousand of their variations.
Year | Personality | What was observed |
Archbishop Olaf Magnus of Uppsala, Sweden | For the first time I observed snowflakes with the naked eye. |
|
Johannes Kepler, German astronomer and mathematician.
| ||
French mathematician Rene Descartes | Wrote "Study on the shape of snowflakes", observed a 12-ray snowflake |
|
17th century | Robert Hooke | Concluded about six-pointed symmetry in the geometry of snowflakes |
17th century | Donat Rosetti, Italian priest and mathematician | The first to classify snowflakes |
17th century | William Scoresby, English whaler | first described snow crystals in the form of hexagonal pyramids, columns and their combinations |
Feudal ruler of the Land of the Rising Sun Tositsura Onakami Doi | made 97 drawings of "snow flowers". |
|
Wilson Bentley, American farmer Nicknamed "Snowflake"
| Got the first successful photo of a snowflake under a microscope |
|
Nikolai Vasilyevich Kaulbars, member of the Russian Geographical Society | For the first time, he sketched and described a snowflake of an unusual shape
|
|
Ukihiro Nogaya
| Carried out a classification, created a museum of ice crystals
|
|
Scientists at the University of Tokyo
| We started growing artificial snow for the Sapporo Olympics
|
|
International Commission on Snow and Ice
| Adopted the classification of snowflakes
|
|
Astronomer Kenneth Libbnecht |
Conditions for the birth of snowflakes.
Snowflakes develop from small ice crystals that are shaped like hexagons. During very severe frosts (at temperatures below 30 degrees), ice crystals fall out in the form of "diamond dust" - in this case, a layer of very fluffy snow is formed on the surface of the earth, consisting of thin ice needles. Usually, in the course of their movement inside the ice cloud, ice crystals grow due to the direct transition of water vapor into ice. How exactly this growth occurs depends on external conditions, in particular on temperature and humidity, as shown in the figure:
Under certain conditions, ice hexagons grow intensively along their axis, and then elongated snowflakes form - snowflakes-columns, snowflakes-needles. Under other conditions, hexagons grow mainly in directions perpendicular to their axis, and then snowflakes form in the form hexagonal plates or hexagonal stars. A drop of water can freeze to a falling snowflake - as a result, a snowflake irregular shape. We see, therefore, that the popular belief that snowflakes look like hexagonal stars is erroneous. Moving up and down, they fall into a layer of air with supercooled water droplets. Here, the future snowflake begins to intensively increase in size. In this case, the convex sections of the snowflake grow faster. So, a six-pointed asterisk grows from an originally hexagonal plate. Faced on its way with supercooled droplets, the snowflake is simplified in shape. If it collides with a large drop, it can turn into a small hailstone.
Snowflake geometry.
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"Star"
"Column"
"Plate"
"Triangle"
"Flat"
"Needle"
"Space Crystals"
"Fern Dendrites"
"Twelve Pointed Star"
Physics of snow.
Step on fluffy snow on a frosty day. Do you hear? It is the sound of a myriad of crystals breaking. The lower the temperature, the harder and more fragile the snowflakes, and the stronger the crunch underfoot. Can you tell the temperature by hearing the sound of breaking snowflakes?
After all, each temperature has its own creaking tone.
Despite the fact that snowflakes are small, by the end of winter, the mass of snow cover in the northern hemisphere of the planet reaches 13,500 billion tons. Snow reflects up to 90% of sunlight into space.
We are used to seeing white snow. And is he white? The fact is that the complex shape of the ice floes strongly refracts light. As a result, snow reflects white sunlight.
However, there are times when a different color of snow is pronounced for the human eye. So, for example, in the arctic and mountainous regions, pink or red snow, colored by algae living between its crystals, is considered common.
There are cases when blue, green, gray or black snow fell from the sky. So, on Christmas Day 1969, black snow fell on 16,000 square miles of Swedish territory. Most likely, this happened as a result of industrial waste emissions into the air.
In 1955, phosphorescent green snow fell near Dana, California. Some residents decided to try his flakes and soon died, the hands of those who dared only take it in their hands became covered with a rash, accompanied by severe itching. This phenomenon still creates controversy about the origin of snow. In the meantime, it is believed that the toxic fallout was the result of atomic tests in Nevada.
Wet snow in the mountains forms wet avalanches, which have tremendous destructive power and cementing action. Avalanches cause a lot of inconvenience to people, breaking down from the mountains at the most inopportune moment. Usually, avalanches form on slopes with a steepness of 25-45° (however, avalanches are known to descend from slopes with a steepness of 15-18°). On steeper slopes, snow does not accumulate in large quantities and rolls off in small doses as it accumulates. Any avalanches pose a threat, even with a volume of only a few cubic meters.
April 30" href="/text/category/30_aprelya/" rel="bookmark"> April 30, 1944 in Moscow. Caught on the palm, they covered almost the entire palm and resembled beautiful ostrich feathers. Scientists explained this phenomenon as follows: from near Franz Josef Land, a wave of cold air descended, the temperature dropped, the formation of snowflakes began in the clouds. But snowflakes could not immediately fall to the ground: they were held up in the air by warm streams rising from the heated earth. Snowflakes floated in the air layers and stuck together, forming large The earth cooled by evening, the ascending air currents weakened, and an amazing snowfall began.
Bulldozer" href="/text/category/bulmzdozer/" rel="bookmark">Bulldozer .
It is known that even in the air snowflakes are constantly changing. Depending on the weather conditions, "own" snow falls in different places. In the Baltics and in the central regions, for example, it often snows in the form of large, complexly shaped branched snowflakes, sometimes shaggy flakes.
The snow is slippery because under the pressure and friction of the runners of the sleigh or skis, the surface particles of the snow cover melt, and the resulting film of water serves as a lubricant. The "slipperiness" therefore depends on the temperature of the snow and on the speed of travel. The largest snowflake was recorded on January 28, 1887 in the USA in the state of Montana. It was 38 cm in diameter.
Entertaining and informative about snow and snowflakes.
Do you know that…
1. A snowflake is one of the most fantastic examples of the self-organization of matter from simple to complex.
2. The most amazing thing about snowflakes is that none of them repeats the other. Astronomer Johannes Kepler in his treatise "New Year's gift. About hexagonal snowflakes ”explained the shape of the crystals by the will of God.
3. Snowflakes are absolutely transparent. They only appear white to us due to the refraction of light at the edges of the crystals.
4. In the Japanese city of Kaga, the Museum of Snow and Ice was opened, made in the form of three hexagonal buildings.
6. Snowflakes are 95% air, which results in low density and relatively slow falling speed (0.9 km/h).
7. Snow can be eaten. True, the energy consumption for eating snow is many times greater than its calorie content.
8. More than half of the world's population has never seen snow, except in photographs.
9. It turns out that ice is not equally cold. There is very cold ice, with a temperature of about minus 60 degrees, this is the ice of some Antarctic glaciers. The ice of the Greenland glaciers is much warmer. Its temperature is approximately minus 28 degrees. Quite "warm ice" (with a temperature of about 0 degrees) lie on the tops of the Alps and the Scandinavian mountains.
10. A layer of one centimeter of snow packed over the winter gives 25-35 cubic meters of water per 1 ha.
11. The amount of water "conserved" in the glaciers of the globe is 50 times less than the entire mass of ocean waters, and 7 times more than land waters. If the glaciers completely melted, then the level of the world ocean would rise by 800 meters.
12. Two or three icebergs of medium size contain a mass of water equal to the annual flow of the Volga (the annual flow of the Volga is 252 cubic kilometers).
13. There are black icebergs. The first press report about them appeared in 1773. The black color of icebergs is caused by the activity of volcanoes - the ice is covered with a thick layer of volcanic dust, which is not washed away even by sea water.
14. The US Postal Service issued 4 snowflake stamps in October 2006.
15. There are people who can judge the temperature of the air by the way the snow creaks.
American scientists have spent $ $ on finding out the fact that snowflakes are formed directly from steam, bypassing the rain stage.
17. Residents of Norway, who call snowmen "white trolls", are not advised to look at the snow creature at night because of the curtain. And if you stumble upon someone else's snowman at night, you should bypass it.
18. The legend of the very first snow - The rebellious angels at the time of the fall lost their snow-white wings, which covered the earth with a white shiny carpet. So snow appeared, and the first winter came.
"Snow Tales"
https://pandia.ru/text/78/230/images/image042_2.jpg" alt="(!LANG:Image" align="left" width="193" height="125">Всем, конечно, знакомы сказки о снежных волшебниках. В русской народной сказке это Морозко, а в сказке Андерсена – Снежная Королева. Помните, какие они разные? Морозко - добрый и сердечный, и справедливый к тому же. Трудолюбивую девочку он щедро одарил, а ленивую да завистливую высмеял. Совсем иной предстает перед нами Снежная Королева из сказки Андерсена. В ее ледяном дворце холодно и неуютно, а разбрасываемые ею по свету льдинки вонзаются в человеческие сердца, и те становятся черствыми и злыми. Две сказки о властелинах снега – и такие они разные. Таким же разным может быть и сам снег. Когда снег идет, это зрелище никого не оставляет равнодушным. Кого – то идущий снег радует, дарит приподнятое настроение, на других, напротив, навевает печаль и грусть. Благодаря снегу мы каждый год любуемся сказочными зимними пейзажами, но любим снег не только за это. Запасы снега влияют на урожай, на уровень воды в реках. Из снега строят зимние дороги и даже аэродромы. Но о этой полезной роли снега мы даже не задумываемся. Снег для нас прежде всего СКАЗКА. Вы заметили, что разные чудовища, мифические и сказочные, могут жить где угодно, а вот в снегу человек их не поселил? Зато снег навеял человеку великое множество сказок. У снега и сказки есть одна общая черта. И сказки, и снег говорят нам о чудесных ПРЕВРАЩЕНИЯХ. Как Золушка превращается в принцессу, так и унылое черное поле под выпавшим снегом, как по волшебству, превращается в сверкающий на солнце великолепный ковер. Снег – один из удивительных феноменов природы. Его изменчивость почти таинственна.!}
Snegurochka - a girl from the snow.
The snow girl who comes to us on New Year's Eve is a unique phenomenon. In no other New Year's mythology, except for Russian, there is a female character! Meanwhile, we ourselves know little about her ... They say she is made of snow ... And melts with love. So, at least, the writer Alexander Ostrovsky introduced the Snow Maiden in 1873, who can be safely considered the foster dad of the ice girl.
The true roots of the relationship of the Snow Maiden go to the pre-Christian mythology of the Slavs. AT 
In the northern regions of pagan Russia, there was a custom to make idols from snow and ice. And the image of a revived ice girl is often found in the legends of those times. The parents of the Snow Maiden turned out to be Frost and Spring-Krasna. The girl lived alone, in a dark cold forest, not showing her face to the sun, yearning and reaching out to people. And one day she came out of the thicket to them. According to Ostrovsky's fairy tale, the icy Snow Maiden was distinguished by fearfulness and modesty, but there was not a trace of spiritual coldness in her. But if her heart falls in love and becomes hot, the Snow Maiden will die! She knew this, and yet she made up her mind: she begged from Mother Spring the ability to love passionately. How it looked was demonstrated by the artists Vasnetsov, Vrubel and Roerich. It was thanks to their paintings that we learned that the Snow Maiden wears a pale blue caftan and a cap with an edge, and sometimes a kokoshnik. This was the first time children saw her at the festive tree of 1937 in the Moscow House of Unions.
The Snow Maiden did not come to Santa Claus right away. Although even before the revolution, Christmas trees were decorated with figurines of a snow girl, girls dressed up in costumes of the Snow Maiden. In Soviet Russia, officially celebrating the New Year was allowed only in 1935. Christmas trees began to be set up all over the country and Santa Claus was invited. But suddenly an assistant appeared next to him - a sweet, modest girl with a scythe over her shoulder, dressed in a blue fur coat. First a daughter, then - it is not known why - a granddaughter. The first joint appearance of Father Frost and the Snow Maiden took place in 1937 - since then it has been the custom. The Snow Maiden leads round dances with children, conveys their requests to Grandfather Frost, helps distribute gifts, sings songs and dances with birds and animals.
And the New Year is not the New Year without the glorious assistant of the main wizard of the country.
"Yukimi - tora" - "Lantern for admiring the snow"
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a letter from heaven, written in secret hieroglyphs. "He was the first to create a classification of snowflakes. The only snowflake museum in the world, located on the island of Hokkaido, is named after Nakaya.
"Summer Snow Festival"
August 5" href="/text/category/5_avgusta/" rel="bookmark">August 5, on the day of the Feast of the Snow of Mary, during mass, white flowers fall on the worshipers from under the dome. A blizzard of a million white roses.
"A small miracle with your own hands." Master class on making snowflakes.
Snowflake in 3D.
To make one snowflake, you will need: 6 square pieces of paper of the same size , scissors, ruler, pencil, tape, stapler, thread or other material for hanging a snowflake.
Operating procedure:
Fold each piece of paper diagonally and draw future slots on it along the ruler: | We cut the intended slots and unfold the pieces of paper: |
We begin to twist the tubes to form paper snowflakes by taping them | The next "frame" of the future paper snowflake twist it to the other side. We alternate the sides, we get six blocks |
In each half of a paper snowflake that we make with our own hands, there will be three such blocks fastened with a stapler | We fasten the halves of the snowflake together, also with a stapler: |
Snowflakes can be made in different colors, textures and sizes, and the number of cuts can also be varied. It all depends on your requests, the interior and the amount of paper that you do not mind spending on decorating it. It is beautiful to make such snowflakes from colored paper, you can use the existing foil or colored film, and the finished snowflake can be covered with glitter hairspray! | Here is the result:
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Quilling.
Quilling, also known as paper rolling, is an art that has been practiced since the Renaissance. The technique is as follows: narrow strips of paper are twisted into rolls, shaped and glued with glue.
A similar type of creativity existed in medieval Europe. At the peak of its popularity, quilling was popular among noble ladies who occupied themselves with it during their leisure hours, and works of this art were often published in women's magazines of that time.
To perform these works, you will need white office paper. It must be cut into strips 5 mm thick along the short side. It is better to cut with a clerical knife along the ruler several sheets at once. For a small amount, you can cut with scissors. You can twist the strips with different tools. You can use an awl, a special slotted rod, a toothpick. To make a snowflake (pendant or applique), you need to prepare a variety of shapes from twisted strips. Forms can be closed, i.e. glued and open, where no glue is used. Both are suitable for applications. And for snowflake pendants, you can use only closed forms.
Scheme of work:
The results are also different:
https://pandia.ru/text/78/230/images/image053_0.jpg" alt="(!LANG: snowflake, quilling technique" width="194" height="146">!} 
How to cut a beautiful snowflake.
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Conclusion.
If you live in cold climes, you know firsthand about winter, then you have at least one reason to be proud of it: unlike residents of hot countries, you can admire snowflakes in natural conditions. And this is not at all as prosaic as it seems, you just need to dress warmer and go outside, taking with you the most ordinary magnifying glass or magnifying glass. Believe me, it is very interesting to look at snowflakes, if only because two identical ones have never fallen to the ground.
And in general, we advise you to carry a magnifying glass in your coat pocket all winter, because you never know when the most beautiful snowflake will fall from the sky.
Where did the snow come from? The legend says that the rebellious angels lost their snow-white wings at the time of the fall. And so the snow appeared. Do you know that more than half of the world's population has never seen snow? Or seen, but only in photographs. In the Eskimo language, there are more than 20 words for the name of snow, in the Yakut language - about 70. Most snowflakes weigh about a milligram. But billions of snowflakes can affect the speed of the Earth's rotation. When the white airy beauties descend to the ground, the fun begins. Under the influence of temperature, wind, relief, snowflakes turn into a wide variety of snow forms. Round dances begin to circle in snow blizzards, howl together in a snowstorm, wrap houses and roads in fluffy impassable snowdrifts. Struck by the extremely complex shape, perfect symmetry and endless variety of snowflakes, people from ancient times associated their outlines with the action of supernatural forces or divine providence.
While working on the project, I learned a lot of new and interesting things and realized that this is not all the information about snow and snowflakes. The forms of snowflakes are inexhaustible, which means that you can study them endlessly, as well as admire them.
Used literature and sources INTERNET:
1. Perelman tasks and experiments. D.: VAP, 1994.-547 p.
2. Physics in nature /: Book. for students. - M.: Enlightenment, 199p.: ill.
3. Literary reading [Text]: 3 cells. : Textbook. : At 2 o'clock / . - 3rd ed. - M .: Akademkniga / Textbook, 2009. - Ch 1: 192 ., 16 reprod. : ill.
4. http://wsyachina. *****/physics/snow_2.html
5. http://upovara. info/forum/index. php? s=a5a460fa2cee1883b817b0a74c55d896&showtopic=1888
6. http://brembola. pereslavl. info/b7.htm
7. http://www. *****/snezhinka_iz_paper
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9. http://go. *****/search? q=%D1%ED%E5%E3%20%E2%20%F1%EA%E0%E7%EA%E0%F5%2C%20%EF%EE%F1%EB%EE%E2%E8%F6 %E0%F5%2C%20%EF%EE%E3%EE%E2%EE%F0%EA%E0%F5%2C%20%EF%F0%E8%EC%E5%F2%E0%F5
10. http://news. *****/society/2254437
11. http://*****/archives/412
12. http://www. snowtale. *****/gallery. html
