Like a robiti unskinned tricoutnik from paper. Trikutnik Penrose: do-it-yourself with paper
kerivnik
mathematic teacher
1.Introduction ………………………………………………….……3
2. Historical review………………………………………..…4
3. The main part…………………………………………………….7
4. Proof of the impossibility of the Penrose trickster……9
5. Visnovki…………………………………………………..…………11
6. Literature……………………………………………….…… 12
Relevance: Mathematics is a subject that is taught from the first to the graduation class. We have a lot of learners in vvazhayut yoga, we don’t need it. But if you look behind the side of the assistant, read additional literature, mathematical sophistry and paradoxes, then the statement about mathematics will change, the message will appear more and more, school course mathematics.
Meta robots:
show that the basis of impossible articles expands one's horizons, develops open spaces, stagnates like mathematicians, and th artists.
manager :
1. Read literature on this topic.
2. Look at the impossibly figures, create a model of an impossibly tricot, make it clear that the impossibly tricot does not exist on the flat.
3. Zrobiti razgornennya impossibly trikutnik.
4. Take a look at the example of an impossibly tricoutine at the image-making art.
Entry
Historically, mathematics has played an important role in the image-creating art, zokrema with an image perspective, which conveys a realistic image of a trivial scene on a flat canvas or arch paper. It is obvious to the current glance, mathematics is Imaginative art in the distance, one kind of one discipline, the first one is analytical, the other one is emotional. Mathematics does not play an obvious role in most of the work of modern art, and, in fact, a lot of artists seldom invariably fail to create a victorious perspective. However, there are a lot of artists, like mathematicians, in the center of respect. A decade of significant articles in the image-creating mysticism paved the way for these individuals.
For some reason, they don’t follow the rules of the day, but they are limited to different topics in mathematical science, such as impossible figures, a line of Moebius, the creation of an immutable system of perspective, as well as fractals.
History of Impossible Figures
Impossible positions - a singing kind of mathematical paradoxes, which are from regular details, similar to an irregular complex. How to try to formulate the meaning of the term "impossible objects" vin bi, singsongly, sounding something like this - physically able to post, taken from an impotent looking. Ale marvel at them richly accepting, folding the appointment.
Spacious pardons were sung by artists and a thousand years ago. And first of all, who inspired and analyzed the impossible objects by right, the Swedish artist Oscar Reutersverd, who painted in 1934, is respected. the first impossibly tricoutnik, which was formed from nine cubes.
Trikutnik Reuterswerda
Independently from the Reuterswerd, the English mathematician and physicist Roger Penrose revisited the impossibly tricot and published his image in the British journal of psychology in 1958. In ilyuzii vikoristano "hibnu perspective". Sometimes such a perspective is called Chinese, but a similar way of painting, if the little clay is “two-valued”, is often painted in the robots of Chinese artists.
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Yesher Falls
At 1961. the Dutchman M. Escher, inspired by Penrose's impossibly tricky worker, creates the famous lithograph "Waterfall". The water in the picture is flowing incessantly, after the water wheel it won't pass far and drain at the exit point. In fact, the image of the eternal dvigun, but be it a try to really encourage this design, is doomed to failure.
One more example of impossibly articles of representations of the little "Moscow", which has a well-known scheme of the Moscow metro. On the back, we take the image as a whole, but with a simple glance, we look around the lines, we change our minds at the impossibility of our foundation.
«
Moscow”, graphics (carcass, olive), 50x70 cm, 2003.
The little “Three Ravliks” continues the tradition of another famous impossibly figure – an impossibly cube (box).
"Three Ravliks" Impossible Cube
You can know more about different objects even in the not so serious little "IQ" (intelligence coefficient). It’s clear that some people don’t perceive impossible objects through those that their knowledge is not capable of identifying flat pictures with trivial objects.
Donald Simanek made a thought that the understanding of visual paradoxes is one of the signs of the kind of creative potential that drives the best mathematicians and artists. A lot of work with paradoxical objects can be classified as "intellectual mathematical games". Modern science talk about the 7th world or the 26th world model of the world. It is possible to model such a world only with the help of mathematical formulas, a person to reveal yoga is simply not in his mind. And here there are corny impossible posts.
The third popular unimaginable figure is the nameless descend, created by Penrose. You will either climb up (against the Year's arrow) or go down (behind the Year's arrow). The Penrose model formed the basis of the famous painting by M. Yesher “Uphill and down” Nameless Go Penrose
Impossible trident
"Devil's Fork"
Іsnuє sche one group of ob'єktiv, realіzuvati yakі not vdas. The classic figure is the impossibly trident, or the "devil's fork". With respect for the picture, you can remember that three teeth step by step move from two to a single base, which leads to a conflict. Mi porіvnyuєmo kіlkіst prongs of the beast and below that comes to the visnovka about the impossibility of the object. If you close the upper part of the trident with your hand, then we get the whole picture - three round teeth. If you close the lower part of the trident, then we also get a more realistic picture - two straight-cut teeth. Ale, if you look at the whole figure as a whole, then you will see that three round teeth step by step turn into two straight ones.
In this way, you can argue that the front and back plans of this little one are in conflict. Tobto, those who are in the foreground go back, and the back plan (middle tooth) goes forward. Changes in the front and back plans for this little one have another effect - the flat edges of the upper part of the trident become round in the lower part.
Main part.
Trikutnik- a figure that is made up of three adjoining elements, as if behind the help of unacceptable elements of these elements, it creates an illusion from a mathematical point of view of an impossibly structure. Іnakshe tsey tribalochnik is called kutnik Penrose
The graphic principle, which is to be followed by the illusion, goiter to its formulas of the psychologist and son Roger, physicist. Kutnik Penruzov is folded from 3 bars in a square cut, cut in 3 mutually perpendicular lines; skin rushes from the approaching under a direct kut, everything is to be moved in a trivial space. The axis is a simple recipe, how to paint the isometric projection of the penruz cosin:
· Cut the kuti of the equal-sided tricoutnik along the lines, parallel sides;
· Draw the middle of the cut tricoutnik parallel to the sides;
· Shave the kuti again;
· Draw the middle parallel again;
· Show yourself in one of the huts of two possible cubes;
· Continue yoga L - figurative "thing";
· Prozhenіt tsyu design on stake.
· Yakbi mi chose another cube, then squint buv bi "twisting" into the next cube .
The fire of the impossibly trikutnik.
Line peregina
Rose line
What elements will be an impossibly trikutnik? More precisely, from some of the elements of the wines do we (get by ourselves!) wake up? The design is based on a straight-cut kutochok, which goes out under a straight kut of two identical rectangular bars. There are three pieces of such kutochkіv, and six pieces of bars. Qi kutochki required a singing rank of zorovo "z'ednati" one by one so that the stench would quell the closures of the lansyug. Those who are viide are an impossibly tricky one.
The first coil is placed near the horizontal plane. Before the new one, another little tuft arrives, directing one of the ribs uphill. Nareshti, up to the other fold, add the third fold so that the th rib was parallel to the outer horizontal plane. In this case, two ribs of the first and third coils will be parallel and directed in different sides.
And now let's try to marvel at the figure from different points of space (or create a real layout from the door). See, as if looking out from one point, from another, from a third ... When changing the point of caution (otherwise - the very same - when turning the structure in space), you will see that the two "final" edges of our kutochkiv move one to one. It doesn’t matter if you choose such a position, when the stench comes up (for sure, when the nearest little sliver is given to us, comrade, who has gone down).
But if you stand between the ribs a little less than the gap between the kutochkіv to the point where we can see our design, then insulting the ribs will make us the same comradeship, and because of the fact that these two ribs are really the continuation of one of one.
Until the speech, as if we were at once marveling at the reflection of the construction in the mirror, then the closed lansyug is not bogged down.
And from the point of guardianship mi on the vlasnі ochі bachim a miracle, scho vіdbulosya: є closures of the lancets from three kutochkіv. Just do not change the point of caution, so that the illusion (really the illusion!) does not collapse. Now you can paint a visible object or place it at the found point of the lens of the camera and take a photograph of an impossible object.
The first thing that came to mind was Penrosey. The stink victorious victoriousness, which is blamed for the appearance of a trivi- merous space and trivi- mer objects on a two-dimensional area (that is, when designing), that brought respect to the deuce of non-insignificance of the design - an open construction from three little folds can take on closures.
As has already been said, it is easy to prepare the simplest model, which in principle explains the effect, which is to be guarded. Take a straight piece of dart and divide it into three equal parts. Then let's bend the extreme parts so that the stinks make a straight cut from the middle part, and turn one at least one by 900. Now turn this figurine and watch over it with one eye. When deaky її stavishchi zdavatimeetsya, that she was made from a closed shmatka drotu. Having raised the floor lamp, you can watch for the tunnel that you fall on the table, as in the same way, when the figure is singed in the space, it transforms into a tricot.
Vtіm, tsyu osoblivіst proektuvannya can be poserіgati іnshіy situatsії. If we build a ring from a dart, and then we will open it at different sides, then we will see one turn of a cylindrical spiral. Tsej turn, zrozumіlo, rozіknuto. Ale, when projecting on a flat, you can take a closed line.
We once again exchanged words, but behind the projection on the flat, on the little one, the trivimir figure is ambiguous. So in the projection, there is a double meaning, lack of understanding, like a “impossible trickster”.
I can say that the "impossible trickster" of the Penroses, like a lot of others optical illusions stand in the same row with logical paradoxes and puns.
Proof of the impossibility of the Penrose trickster
Analyzing the features of a two-world image of trivi- cular objects on a flat surface, we realized how the features of this image can be reduced to an impossibly tricky one.
To bring that the impossibly tricoutnik is not used, it’s easy to cut it, even if the skin is straight, and the bag is more expensive 2700 instead of the “positions” 1800.
More than that, to wind up like an impossibly tricutnik, gluing from kutochkіv, less than 900, then you can bring it to the right angle, that the impossibly tricutnik is not used.
Let's look at one more tricot, which is made up of a lot of parts. As if a part, from which wines are added up, roztashuvati іnakshe, then we will see such a tricutnik itself, but with one small nedolіk. Not vistachatime one square. How is it possible? But still, it's an illusion.
https://pandia.ru/text/80/021/images/image016_2.jpg" alt="(!LANG:(!LANG:Impossible trickster" width="298" height="161">!}!}
A tribute to the phenomenon of sprinyattya
Can you somehow help the effect of impossibility? "Impossible" chi odnі objects, nizh іnshі? And here the special features of the human spirit come to the rescue. Psychologists have established that the eye starts to look at the object (picture) from the lower left corner, then we look to the right to the center and descends to the lower right corner of the picture. Such a trajectory, perhaps, is due to the fact that our forefathers, when struck by the enemy, marveled at the safest right hand, and then looked, moving to the left, at the disguise of that figure. In such a rank, the artist is naturally dependent on how the composition of the picture is going to be. This peculiarity of Serednyovichchi was clearly revealed during the preparation of tapestries: their little ones were mirrored in the original, and the attack, like the tapestries were vibrating that original, was resurrected.
Tsya power can be successfully victorious when creating creations with impossibly objects, increasing or changing the "steps of impossibility". There is also the prospect of taking tsіkavі compositions to the versatility of computer technologies or to the decals of pictures rotated (possibly, to the versatility different mind symmetrical) one way, which is created at the sight of different enemies in the object and more comprehension of the daily life I will think, or one thing, which turns (constantly with abbreviations) for the help of a simple mechanism of kuti.
Such a straight line can be called polygonal (rich-cut). The illustrations show images rotated one way or another. The composition was created in an offensive rank: little ones on paper, chiselling ink and olive, scanning, translating into digital form and turning it into a graphic editor. It is possible to indicate the regularity - the picture is rotated more "steps of impossibility", lower vyhіdna. This can be easily explained: the artist in the process of robotic work is not able to create a "correct" image.
Visnovok
The list of various mathematical articles and laws is not surrounded by more pointed butts. Respectfully watching all the pointing posts, you can know other things, not guessing at these statistics, geometric bodies and visual interpretation of mathematical laws.
Mathematical figurative art flourishes today, and a lot of artists create paintings in the style of Yesher and in their own style. Qi artists practice different directions, including sculpture, painting on flat and trivial surfaces, lithography and computer graphics. And the most popular topics of mathematical science are richly shaped, impossible positions, Möbius lines, creating system perspectives and fractals.
Visnovki:
1. From now on, the sight of impossibly figures develops our expanse of reality, helping to “go out” from the plane into a three-dimensional expanse, which is helpful when turning stereometry.
2. Models of impossibly figures help to see projections on the plane.
3. Looking at mathematical sophistry and paradoxes add interest to mathematics.
When vikonannі tsієї roboti
1. I recognized - like, if, de and kim bula was first looked at an impossible figure, that there are a lot of such figures, these figures are constantly depicted by artists.
2. I, at once from the tatom, having created a model of an impossibly tricoutnik, having looked at its projections on the plane, having recited the paradox of the position.
3. Having looked at the reproductions of artists, on which images these posts are
4. My studies made my classmates tick.
Nadalі otrimani znannya I vykoristovuvatim in the lessons of mathematics and me zatsіkavili, but what else paradoxes?
LITERATURE
1. Candidate of Technical Sciences D. RAKOV History of Impossible Figures
2. Impossible posts.- M.: Budvidav, 1990.
3. Aleksєva Ilyuzії · 7 Comments
4. J. Timothy Anrakh. - Amazing posts.
(TOV "Vidavnitstvo AST", TOV "Vydavnitstvo Astrel", 2002, 168 p.)
5. . - Graphics.
(Art-Spring, 2001)
6. Douglas Hofstadter. - Gödel, Escher, Bach: this inexhaustible garland. (Vidavnichy dim "Bahrakh-M", 2001)
7. A. Konenko - Mysteries of Impossible Figures
(Omsk:Livsha, 199)
Impossible is still possible. And this is clearly evidenced by Penrose's immature trickster. Vіdkritiy sche at the last century, vіn dosі often zustrichaєtsya in scientific literature. Even though it didn’t sound wonderful, but you can prepare yoga on your own. І zrobiti tse even simpler. A lot of lovers of little ones and picking origami could have done it a long time ago.
Meaning of the Penrose tricot
Іsnuє kіlka name of the figure. Some call її an impossibly tricoutnik, others - just a tribar. But most of all, you can use the "Penrose trickster" yourself.
Recognize one of the main impossibly figures with them. If you judge by the name, then it is impossible to take a similar figure for real. But in practice, it was brought to light that it is possible to work. The axis only accepts the shape of the tricot figure, as if marveling at it from the singing point under the necessary kut. On the other hand, the figure is entirely real. Vaughn is three edges of a cube. It is easy to prepare such a construction.
History
Penrose's tricutnik used as a tribute to the distant 1934 by the artist from Sweden Oskar Reutersvärd. The figure of the bula is represented by looking at selected cubes. Nadali of the artist began to be called "the father of impossible articles."
Possibly, the little ones of Reutersvärd are so deprived of small houses. In 1954 Swedish mathematician Roger Penrose wrote an article about impossible positions. Tse became other peoples of trikutnik. Truthfully, presenting yoga to a greater savvy mind. Vin vikoristav are not cubes, but beams. Three beams rolled between themselves at a 90 degree angle. Vіdminnіst takozh bula in the fact that Reutersvärd won a parallel perspective for painting. And Penrose zastosuvav perspective linear character, which gave the little one even more impossibility. Such a trickster was published in 1958 in one of the British journals about psychology.
In 1961, the artist Maurits Escher (Holland) created one of his most popular lithographs, Waterfall. It was created її under the enemy, as if it were a viklikana article about impossible positions.
In the 80s of the last century, tribars and other impossible positions were depicted on the sovereign postage stamps of Sweden. Trivalo lasted for a few years.
For example, the last century (more precisely, 1999) in Australia, a sculpture was created from aluminum, which depicted Penrose's immature trickster. Vaughn reached 13 meters. Similar sculptures, smaller behind the roses, are streaked in other lands.
Impossible really
As you can already guess, Penrose's tricot is really not a tricot for the greatest mind. Він є three faces of the cube. Ale, as if marveling at the singing kut, the illusion of a tricoutnik goes out behind the rahunok of the one that 2 kuti run on the flat. The near view of the dilyach and the distant kutia will be splendidly approached.
If we respect it, then we can guess that the tribar is nothing else, like an illusion. The real look of the figure can be seen shadow in it. She can see that really Kuti don't get upset. Well, obviously, everyone has become wiser, so take the figure in your hands.
Making figures with your own hands
Trikutnik Penrose can be chosen independently. For example, with paper and cardboard. І to help with the scheme. It’s more necessary to razdrukuvate and glue. There are two schemes presented on the Internet. One of them is light, the other is foldable, but popular. Offended by the presentation of the little one.
Penrose's trickster will become a tukavim virob, which is worthy of guests. Wine is definitely not left unmarked. The first stage of its creation is the preparation of the scheme. It will be transferred to paper (cardboard) for the help of a printer. And then everything is simpler. You just need to look at the perimeter. On the scheme there are all necessary lines. Better practice with a larger paper. As if the scheme was drawn up on a thin paper, but if you want a wider one, the blank is simply applied to the selected material and folded along the contour. So that the scheme does not collapse, you can attach it with violins.
Further, it is necessary to designate those lines, with which the preparation will be made. As a rule, the scheme is represented by a dotted line. We're bending the detail. Dali vyznaєmo mіstsya, scho pіdlyagayut gluing. The stench is smeared with PVA glue. The detail will merge into a single figure.
The detail can be rozfarbuvat. And you can use a bunch of vicoristate colored cardboard.
Impossible is still possible. And this is clearly evidenced by Penrose's immature trickster. Vіdkritiy sche at the last century, vіn dosі often zustrichaєtsya in scientific literature. Even though it didn’t sound wonderful, but you can prepare yoga on your own. І zrobiti tse even simpler. A lot of lovers of little ones and picking origami could have done it a long time ago.
Meaning of the Penrose tricot
Іsnuє kіlka name of the figure. Some call її an impossibly tricoutnik, others - just a tribar. But most of all, you can use the "Penrose trickster" yourself.
Recognize one of the main impossibly figures with them. If you judge by the name, then it is impossible to take a similar figure for real. But in practice, it was brought to light that it is possible to work. The axis only takes shape, as if marveling at it from the singing point under the required cut. On the other hand, the figure is entirely real. Vaughn is three edges of a cube. It is easy to prepare such a construction.
History
Penrose's tricutnik used as a tribute to the distant 1934 by the artist from Sweden Oskar Reutersvärd. The figure of the bula is represented by looking at selected cubes. Nadali of the artist began to be called "the father of impossible articles."
Possibly, the little ones of Reutersvärd are so deprived of small houses. In 1954 Swedish mathematician Roger Penrose wrote an article about impossible positions. Tse became other peoples of trikutnik. Truthfully, presenting yoga to a greater savvy mind. Vin vikoristav are not cubes, but beams. Three beams rolled between themselves at a 90 degree angle. Vіdminnіst takozh bula in the fact that Reutersvärd won a parallel perspective for painting. And Penrose zastosuvav perspective linear character, which gave the little one even more impossibility. Such a trickster was published in 1958 in one of the British journals about psychology.
In 1961, the artist Maurits Escher (Holland) created one of his most popular lithographs, Waterfall. It was created її under the enemy, as if it were a viklikana article about impossible positions.
In the 80s of the last century, tribars and other impossible positions were depicted on the sovereign postage stamps of Sweden. Trivalo lasted for a few years.
For example, the last century (more precisely, 1999) in Australia, a sculpture was created from aluminum, which depicted Penrose's immature trickster. Vaughn reached 13 meters. Similar sculptures, smaller behind the roses, are streaked in other lands.
Impossible really
As you can already guess, Penrose's tricot is really not a tricot for the greatest mind. Він є three faces of the cube. Ale, as if marveling at the singing kut, the illusion of a tricoutnik goes out behind the rahunok of the one that 2 kuti run on the flat. The near view of the dilyach and the distant kutia will be splendidly approached.
If we respect it, then we can guess that the tribar is nothing else, like an illusion. The real look of the figure can be seen shadow in it. She can see that really Kuti don't get upset. Well, obviously, everyone has become wiser, so take the figure in your hands.
Making figures with your own hands
Trikutnik Penrose can be chosen independently. For example, with paper and cardboard. І to help with the scheme. It’s more necessary to razdrukuvate and glue. There are two schemes presented on the Internet. One of them is light, the other is foldable, but popular. Offended by the presentation of the little one.
Penrose's trickster will become a tukavim virob, which is worthy of guests. Wine is definitely not left unmarked. The first stage of its creation is the preparation of the scheme. It will be transferred to paper (cardboard) for the help of a printer. And then everything is simpler. You just need to look at the perimeter. On the scheme there are all necessary lines. Better practice with a larger paper. As if the scheme was drawn up on a thin paper, but if you want a wider one, the blank is simply applied to the selected material and folded along the contour. So that the scheme does not collapse, you can attach it with violins.
Further, it is necessary to designate those lines, with which the preparation will be made. As a rule, a detail is shown on the scheme. Dali vyznaєmo mіstsya, scho pіdlyagayut gluing. The stench is smeared with PVA glue. The detail will merge into a single figure.
The detail can be rozfarbuvat. And you can use a bunch of vicoristate colored cardboard.
Slightly impossibly figure
The Penrose trickster can also be painted. A simple square is drawn on the back of the arch. Rosemary yoga has no meaning. From the base on the lower side of the square, a trikutnik is painted. At the yoga kutah in the middle, small rectangles are painted. It will be necessary to erase these sides, leaving only those that are sleeping with a tricot. As a result, the tricoutnik is to blame for the truncated kutami.
From the left part of the lower upper kut, a straight line is drawn. The same line, but a little short, is drawn from the lower left kut. Parallel to the base of the tricutnik, a line is drawn to exit the right kut. Enter another world.
Behind the principle of the other, there is a third world. Only in times all are directly primed on the kuti of the figure of the first, and the other in the world.
Vіdoma so nіd names impossibly tricoutnikі tribar.
History
The figure gained wide popularity after the publication of articles about impossible figures in British Journal of Psychology English mathematician Roger Penrose in 1958 roku. In this article, the impossibly tricot of images in the largest double form - in the sight of three beams, connected one by one with straight kuta. Under the infusion of stats from the Dutch artist Maurits Escher having created one of his famous lithographs « waterfall ».
sculptures
A 13-meter sculpture of an impossibly tricot with aluminum was sporudzhen in 1999 rock in the city Perth (Australia)
Deutsches Technikmuseum Berlin February 2008 0004.JPG
The same sculpture when changing the point of review
Other figures
Although it is possible to create analogs of the Penrose tricot on the basis of the correct bagatokutniks, the visual effect in them is less damaging. With an increase in the number of sides, the object is simply twisted and twisted.
Div. also
- Three hares (English three hares )
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A trick that characterizes the Penrose tricot
Having hung up everything that he was punished, Balashev said that Emperor Oleksandr bazhaє peace, but do not start negotiations otherwise, as if from your mind, sob ... Here Balashev hesitated: having guessed those words, like the emperor Oleksandr did not write on the sheet, ale yakі Obov'yazkovo ordering to insert into the rescript to Saltikov and ordering Balashev to hand over to Napoleon. Balashev remembered the words: “as long as it is possible to destroy the enemy not to be deprived of the Russian land”, but even more folded, it was almost as easy as yoga. Vіn did not have a moment to say tsikh sіv, hoch i hоtіv tse robiti. Vіn zam'yavsya and saying: for the mind, schob French vojska stood up for Nyoman.Napoleon commemorating the siege of Balashev at the hour of the speech of the remaining words; the appearance of yoga shuddered, the lion's calf began to tremtiti peacefully. Not coming from the month, in a voice that is greater and faster, lower earlier, starting to speak. At the hour of the advancing promotion, Balashev, repeatedly lowering his eyes, inadvertently caught a tremton іkri in the left nose of Napoleon, as if they were more fond of him, that they were more guilty, raising their voice.
- I bless the world no less than Emperor Oleksandr, - pochav vіn. - Why have I not been working for eighteen months to do yoga? I have been checking for an explanation for eighteen months. Ale, in order to have a conversation, why should you look out for me? - having said wine, frowning and rolyachi energetically nourishing gesture with his small white and plump hand.
- Vіdstup vіysk for Niman, sir, - said Balashev.
- For Neman? repeated Napoleon. “So now you want to step up for the Neman—only for the Newman?” repeated Napoleon, glancing at Balashev.
Balashev cocked his head in a shrewd way.
The deputy may have come a few months ago from the room, now they have only come out of the Neman. Napoleon quickly turned around and began to walk around the room.
- You seem to want me to take the entrance to Nyoman for the beginning of negotiations; but in the meantime, just two months ago, I stepped across the Oder and the Vistula, and, regardless of those who were able to negotiate.
Vіn movchki proyshov vіd one kіmnati kіmnati kіmnati to іnshhogo i zupinivsya again against Balashev. The appearance of yoga nibi zakam'yanіlo at its sharp expression, and the lion's leg tremtila more swidden, lower earlier. Tse tremtinnya left іkri Napoleon knowing behind him. La tremtinnya my levoї іkri є a great sign, - saying wine with luck.
