All that we see in reality, perceive as a given. Whether it is a rainbow after the rain, a smile of a child or gradually the lighting sea away. But it is worth it to start watching the clouds-changing shape, and familiar images appear, items ... At the same time, we rarely think about how it turns out and what operations occur in our brain. In science, such a phenomenon received an appropriate definition - the optical illusions of the eye. At such moments, visually we perceive one picture, and the brain protests and decrypts it differently. We will get acquainted with the most popular visual illusions and try to explain them.
general description
The illusions for the eyes have long been the object of curiosity of psychologists and artists. In scientific definition, they are perceived as inadequate, distorted perception of objects, error, delusion. In ancient times, the cause of illusion was considered the wrong work of the human visual system. Today, the impact is a concept of deeper, associated with brain processes that help us "decipher", understand the surrounding reality. The principle of human view is due to the recreating on the retina of the eyes of a three-dimensional image of visible objects. Due to this, you can determine the size, depth and remoteness of them, the principle of perspective (parallelism and perpendicularity of lines). The eyes read the information, and the brain processes it.
The illusion of eye deception may differ in several parameters (size, color, perspective). Let's try to explain them.
Depth and size
The simplest and usual for human vision is a geometric illusion - distortion of perception of size, length or depth of the object of reality. In reality, this phenomenon can be observed, looking at the railway. Near the rails are parallel to each other, the sleepers are perpendicular to the rails. In the future, the picture changes: the tilt or bending appears, the lines parallel. The further the road goes, the harder it is to determine the distance of any of its plot.
The Italian psychologist Mario Ponto in 1913 was told about this illusion for the eyes (with explanations, everything as it should be) for the first time in 1913. The usual decrease in the size of the item with its remoteness is a stereotype for human vision. But there are intentional distortions of these prospects that destroy the holistic image of the subject. When the staircase throughout the length saves parallelism of lines, it becomes incomprehensible, a person descends or rises. At the grandfather itself, the construction has a narrow expansion of the book or up.
In terms of depth, there is a disparativity concept - the different position of points on the retina of the left and right eye. Due to this, the human eye perceives the subject concave or convex. The illusion of this phenomenon can be observed in 3D pictures when there are volumetric images on flat objects (sheet of paper, asphalt, wall). Due to the correct location of forms, shadows and light, the picture is mistakenly perceived by the brain as real.
Color and contrast
One of the most important properties of the human eye is the ability to distinguish colors. Depending on the illumination of objects, perception can be varied. This is due to the optical irradiation - the phenomenon of "flowing" of light from brightly illuminated to dark areas of the image on the retina. This explains the loss of sensitivity to distinguishing red and orange colors and an increase in it in relation to blue and purple at the twilight time of the day. In this regard, optical illusions may occur.
Contrasts play an important role. Sometimes a person mistakenly judges the saturation of the color of one or another object on a black background. Conversely, a bright contrast mild colors near the subjects.
The illusion of the color can be observed in the shade, where brightness and saturation are also not manifested. There is a concept "color shadow". In nature, it can be observed when the fire sunset stains in red at home, the sea, with themselves with contrasting shades. This phenomenon can also be found to the illusion for the eyes.
Contours
The next category is the illusion of contour perception, outlines of objects. In the scientific world, she received the name of the phenomenon of perceptual readiness. Sometimes what we see is not so, or has a double interpretation. Currently, fashion for the creation of dual images appeared in the visual arts. Different people look at the same "encrypted" picture and read different characters in it, silhouettes, information. A vivid example of this in psychology is a test with spots of Rorschah. According to experts, the visual perception in this case is equally, but the answer in the form of a interpretation depends on the characteristics of the personality of a person. In evaluating qualities, it is necessary to take into account localization, form, content, and originality / popularity of reading such illusions.
Calling
This type of eye illusion is also popular in art. The trick is that in one position of the image the human brain reads one image, and in the opposite - the other. The most famous translations are the princess-old woman and duck-hare. From the point of view of perspective and colors, there are no distortion here, but perceptual readiness is present. But to distinguish the picture should be turned over. A similar example in reality may be monitoring clouds. When the same form from different positions (vertically, horizontally) can be associated with different objects.
Eix room
An example of 3D illusion for the eyes is the Eix Room invented in 1946. It is designed in such a way that at the sight of the front seems to be ordinary room with parallel walls, perpendicular to the ceiling and floor. In fact, this room is a trapezoidal. The long wall in it is located so that the right angle is blunt (closer), and the left is sharp (further). Illusion enhance chess cells on the floor. The man in the right corner is visually perceived by the giant, and in the left - dwarf. Of interest is the movement of a person around the room - a person, fast growing or, on the contrary, decreasing.
Experts argue that for such an illusion it is not necessary for the presence of walls and ceiling. A sufficiently visible horizon, which only seems as relative to the appropriate background. The illusion of the Eix room is often used in cinema to create a special effect of dwarf giant.
Moving illusions
Another type of eye illusion is a dynamic picture, or autocainetic movement. This phenomenon occurs when, when considering a flat image, the shapes on it begin to literally revive. The effect is enhanced if the person alternately approaches / removes from the picture, he looks at the right left and vice versa. In this case, the distortion occurs due to a certain selection of color, circular location, incorrectness or "vector vector" forms.
"Tracking" paintings
Probably, each person at least once had to face the auditorium when the portrait or image on the poster literally watches the movements of his room. Legendary "Mona Lisa" Leonardo da Vinci, "Diones" Caravaggio, "Portrait of an unknown" cramor or ordinary portrait photos - bright examples of this phenomenon.
Despite the mass of mystical stories, which this effect is enveloped, there is nothing unusual in it. Scientists and psychologists, reflecting how to make the illusion of "tracking eyes", brought a simple formula.
- The face of the model should look straight on the artist.
- The more the cloth, the stronger the impression.
- Emotions of the face model are important. An indifferent expression does not cause an observer of curiosity and fear of persecution.
With the right location of the light and shadow, the portrait will acquire a three-dimensional projection, the volume, and when moving it will seem that the eyes are watching from the picture behind a person.
Illusion - illusion.
Types of deception of view:
illusion on the basis of color perception;
illusion on the basis of contrast;
curvaturing illusions;
optical deception of the perception of depth;
optical deception of size perception;
contour illusion;
illustrate "transverse";
ames Room;
moving optical illusions.
stereo illusions, or, as they are also called: "3D pictures", stereo circuits.
Illusion of the size of the ball
Is it wrong, the size of these two balls is different? Top ball greater than Lower?
In fact, this is an illustrate: these two balls are completely equal. You can use a ruler to check. By creating the effect of a removing corridor, the artist managed to deceive our vision: the top ball seems to us more, because Our consciousness perceives it as a longer object.
Illusion of A. Einstein and M.Mro
If you look at a picture from a close distance, you see the brilliant physics of A. Einstein.
Now try to move away a few meters, and ... a miracle, in the picture M.Mro. It seems to be everything without a deception of sight. But how?! No one painted the mustache, eyes, hair. Just from far vision does not perceive some trifles, and more accent does for large details.
The optical effect that creates a false idea from the viewer about the location of the seat is due to the original design of the chair invented by the French studio IBRIDE.
Peripheral vision turns beautiful faces in monsters.
Which way is the wheel spinning?
See, not blinking, in the middle of the image 20 seconds, and then transfer a look at someone's face or just a wall.
Wall face illusion with window
Which part of the building is the window? With left, maybe with the right?
Again our eyesight was deceived. How did it become possible? It is very simple: the railway part of the window is depicted, as the window located on the right side of the building (we look, as if from the bottom), and the lower part - with the left (we look at the top). And the middle of sight perceives, according to the desired consciousness. That's all deception.
Illusion of bars
Take a look at these bars. Depending on what end you are looking, two pieces of wood will be or located nearby, or one of them will lie on the other.
Cube and two identical cups
Optical illusion created by Chris Westoll. On the table there is a cup, next to which there is a cube with a small cup. However, with a more detailed consideration, we can see that in fact the cube is drawn, and the cups are absolutely the same size. Such effect is noticed only at a certain angle.
The illusion of the "Cafe Wall"
Carefully look into the image. At first glance it seems that all lines are curved, but in fact they are parallel. Illusion was discovered by R. Gregory in a Wall cafe in Bristol. Hence the name of her name.
Illusion of the Pisa Tower
Above you see two pictures of the Pisan Tower. At first glance it seems that the tower on the right leans more than the tower on the left, but in fact both these pictures are the same. The reason lies in the fact that the visual system considers two images as part of a single scene. Therefore, it seems to us that both photos are not symmetrical.
Illusion of wavy lines
It does not even have a doubt that the shifted wavy lines.
Remember how the section is called - an area of \u200b\u200bview. You are right it is straight, parallel lines. And this is a curvatiming illusion.
Ship or arch?
This illusion is a real work of art. The picture drew Rob Gonzalves - Canadian artist, a representative of the magic realism genre. Depending on where you look, you can see or the arch of the long bridge or the ship's sail.
Illusion - Graffiti "Letter"
Now you can relax, and do not think that there will be another illusion. Let's admire the artist's fantasy.
Such graffiti made a wonderful artist in the subway surprisingly to all passersby.
Effect of Cretiful
Look at the picture and say, in which part red lines are brighter and contrast. Right not?
In fact, red lines in the picture are no different from each other. They are absolutely identical, again illusion. This is the effect of Cretiful, when we perceives in different ways of color, depending on its neighborhood with other colors.
Illusion of color change
Is the color of the horizontal gray line change in a rectangle?
The horizontal line in the picture does not change all over and remains equally gray. Do not believe, right? This is an illicit. To make sure this is the closeup of the paper surrounding its rectangle.
Illusion of a decreasing sun
This magnificent photo of the Sun made the American Space Agency NASA. It shows two spots in the sun directed directly to the ground.
Much more interesting is another. If you pass around around the edge of the sun, you will see how it is compressed. This is really great - without cheating, good illusion!
Solner Illusion
Do you see that the lines of the Christmas tree in the picture are parallel?
I also do not see. But they are parallel - check the ruler. My vision also turned out to be deceived. This is the famous classic Solner Illusion, existing from the 19th century. Because of the "needles" on the lines it seems to us that they are not parallel.
Illusion-jesus christ
Look at the picture 30 seconds (it may be necessary and more), then transfer the view to the lightly smooth surface, for example, on the wall.
Before your eyes, you saw the image of Jesus Christ, the image is similar to the famous Turin shroud. Why does this effect arise? In the eye, a person has cells that call wizards and sticks. Columns are responsible for the transfer of color image to the human brain with good sanctification, and sticks help to see a person in the dark and are responsible for the transfer of black and white low-definition image. When you look at a black and white image of Jesus, the wands "tired" due to long and intensive work. When you take a look from the image, these "tired" cells do not cope and cannot transfer new information to the brain. Therefore, the image remains before your eyes, and disappears when the sticks "will come to themselves."
ILLUSION. Three squares
Sit down closer and look at the picture. Do you see that the sides of all three squares curves?
I also see curves lines, despite the fact that the sides of all three squares are perfectly smooth. When you move away from the monitor for some distances, everything falls into place - the square looks perfect. This is due to the fact that the rear background makes our brain perceive lines of curves. This is an optical illusion. When the background merges and we do not clearly see it, the square seems even.
ILLUSION. Black figures
What do you see in the picture?
This is a classic illusion. Throwing a quick glance, we see some incomprehensible figures. But looking just longer, we begin to distinguish the word lift. Our consciousness is used to seeing black letters on a white background, and also continues to perceive this word. It is very unexpected for our brain reading white letters on a black background. In addition, most people first glance thrown into the center of the picture, and this still complicates the challenge to the brain, because he used to read the word from left to right.
ILLUSION. Illusion of Uchucha
Look at the center of the picture and you will see the "dancing" ball.
This is a cult optical illusion, invented in 1973 by the Japanese artist Ouchi and named after him. There are several illusions in this picture. First, it seems that the ball moves a bit from side to the side. Our brain cannot understand that this is a flat image and perceives it as a volume. Another deception of the illusion of Ouchi -Printing that we look through the round keyhole on the wall. Finally, the size of all rectangles in the picture is the same, and they are located strictly in the rows without apparent displacement.
State budget general education
institution Secondary school № 000
Moscow District St. Petersburg
Research work in mathematics
Geometrical illusions "Do not believe our eyes ..."
Nomination: Informational - Mathematical
Performed:
Kopach Anna
Momzina Valery
GBOU SOSH № 000
Moscow District
Leader:
mathematic teacher,
informatics
St. Petersburg
I. Introduction 3.
II. Main part
2.1. Illusions of visual perception. five
2.2. Optical geometric illusions. 6.
2.3. Violation of perspective 7.
2.4. The phenomenon of irradiation. nine
2.5. Illusions of information processing. 10
2.6. Revaluation of vertical lines. 13
2.7. Using visual illusions in human life 14
III. Research part 20.
IV. Conclusion. 31.
V. List of literature used. 32.
application
Introduction
In the lessons of geometry, we often face such a problem: considering the properties of geometric figures, some students sometimes be based on the drawing, on their visual perception. But this approach to solving the problem often leads to erroneous conclusions, and therefore the incorrect decision. We used to trust our own vision, but it often deceives us, showing what does not actually exist. At such moments we are faced with visual illusions - errors of visual perception. Scientists and artists created a lot of deceptive pictures, clearly demonstrating, however, the possibilities of human eyes are limited.
Human vision has a complex nature, and because of its nature sometimes gives a false idea that a person sees actually. How often are intuitive considerations to sum up us, we will be convinced today when considering some optical-geometric illusions.
Consider several examples. The first displays the illusion of volume on a flat asphalt.
On the second, the picture is presented, on which the items located closer to us seem less than those that are further from us, in fact they are exactly the same.
In the third drawing it can easily seem that the spiral is depicted, but it is again just an illusion - depicted circles! ( see Appendix 1)
Why is this happening? Why is the same thing visible to the naked eye, it seems larger than when we look at it from afar? Why, in order to see the details hanging on the wall of the picture, are we approaching her closer? Why do "running" in the distance parallel rails seem intersecting in an imaginary point? Answers to these and others "why" we tried to find in our work. therefore the object of our study are visual illusions, and subject - Studying the causes of illusions.
Purpose of work:
Ø aboutto devour the causes of visual illusions from the point of view of geometry
Hypothesis.Spectatical illusions can be explained using the laws of geometry.
Research tasks:
Ø learn theoretical material on this issue;
Ø Consider examples of using geometric illusions.
Ø Conduct studies related to geometric and visual illusions, explain and prove them from the point of view of geometry.
II.. Main part
Looking at the world, it is impossible not to be surprised.
K. rods.
2.1. Illusions of visual perception
Word "illusion" Comes from Latin Illusere - to deceive. Optical-geometric illusions - visual illusions, due to which the distortion of the spatial ratios of the signs of perceived objects occurs.
We perceive the surrounding us as a given: a sunbeam playing glare on the surface of the water, overflows of the paints of the autumn forest, a smile of a child ... We have no doubt that the real world is exactly what we see it. But is it really? Why sometimes vision fails? How does the human brain interprets perceived objects? Replies to these and many other questions we will try to reveal in our work.
Is the visible world illusory? A person perceives most of the world information due to vision, but few people think about exactly how it happens. Most often, the eye is considered to be similar to a camera or a camera that projects external objects on the retina, which is a photosensitive surface. The brain "looks" to this picture and "sees" everything that surrounds us. However, not all so simple.
First, the image on the retina is inverted.
Secondly, due to the imperfect optical properties of the eye, the picture on the retina is defocused or smeared.
Thirdly, the eye makes permanent movements, that is, the image is in constant dynamics.
Fourthly, the eye blinks approximately 15 times a minute, which means that the image every 5-6 seconds ceases to be projected onto the retina.
So what "sees" the brain?
Since a person has a binocular vision, then in fact he sees two blurred, twitching and periodically endangered images, which means that the problem of combining information coming through the right and left eye arises.
Another paradox of our vision should be noted. Imagine an engineer before the task is to create a device that displays the light information about the external world. How would he arrange photosensitive elements? Most likely, they would be oriented towards falling light. The engineer named "Nature" focused our photosensitive elements - wands and mesh columns - not a "face", but "back" to falling light. What for? There are quite a lot of such issues when analyzing research of visual perception. There are many scientific directions that, using various experimental techniques, are trying to understand how we perceive the world around us. One of the most interesting ways to study is a study of visual illusions.
2.2. Optical geometric illusions.
Many researchers were engaged in studying the causes of illusions. The main question , Of interest not only psychologists, but also artists, - as based on a two-dimensional image, a three-dimensional visible world is recreated on the retina.
Perhaps the visual system uses certain signs of depth and remoteness, for example, the principle of perspective, which assumes that all parallel lines converge at the horizontal level, and the dimensions of the object as it removes it from the observer is proportionally decreased.
Illusions of the distortion of perception of size.
One of the most famous optical geometric illusions - illusion of Muller Lyer.
Illusion of Muller Lyer in everyday life
We are surrounded by a lot of rectangular items: rooms, windows, at home, the typical outlines of which can be seen in the picture. Therefore, the image on which the lines diverge can be perceived as an angle of the building, located on the observer, while the drawing on which the lines converge are perceived as the angle of the building located closer.
2.3. Violation of perspective
We often see converging in the distance along parallel lines (canvas of the railway, highway, etc.). This phenomenon is called the prospect. To portray a certain part of the space, filled with objects, so that the picture makes the impression of reality, it is necessary to be able to use the laws of perspective. All lines on this figure, which is actually parallel to the surface, should be depicted converging at some point of the horizon, called the "dot". The lines going at different angles should converge on the other side of the "point of departure", the farther from it than at a large angle to the line of direct vision they pass. From these points, the point is especially wonderful where the lines going at an angle of 45 degrees to the line of direct view are converged; This point is called a "dot dot". It is wonderful in that if it is opposite it to place the eye at a distance equal to the distance from the "point of departure" to the "dot point", the drawing makes the impression of the volume. The promising perception of space developed by the centuries-old evolution of vision, a person transfers to the pictures and photographs in question and photographs in which equidistant items are depicted. In the picture, the corridor seems volumetric precisely thanks to the future: the corridor on it goes deep into it, and the floor consists of rectangles.
Illusion perspective. Many theories were proposed explaining such distortions. One of the most interesting hypotheses assumes that a person interprets both pictures as flat images in perspective. The alignment of oblique rays at one point create signs of perspective, and the person seems to be segments located at different depths regarding the observer.
Given these signs, as well as the same projection of segments on the retina, the visual system is forced to conclude that they are different sizes. Those fragments of the pattern that seem more remotely perceived large in size.
An example of how you can destroy the holistic image of the object, serve so-called "impossible", contradictory figures, paintings with a violated perspective.
"Impossible "Penrose Staircase. Look at the drawing and answer the question: Does man move upwards?
Each individual span stairs tells us that a person climbs up, however, after passing four spans, it turns out to be in the same place from which he began his way. The "impossible" staircase is not perceived as a whole, since there is no consistency between its individual fragments. Once at once we follow the gaze behind the steps leading up, trying to find a way to solve this problem, and do not find it.
https://pandia.ru/text/78/016/images/image006_116.gif "align \u003d" left "width \u003d" 367 "height \u003d" 140 src \u003d "\u003e Example of this is the given drawing: the cube seems to be visible from above, then on the side; the opened book then seems to be shown to us, then the root from us. This happens both at our desire and involuntarily and sometimes even by our desire.
2.4 Phenomenon of Irradiaration
Which of the inner squares is greater? Black or white?
The irradiation phenomenon is that bright items on a dark background seem more increased against their real sizes and, as it were, capture part of the dark background. When we consider a light surface on a dark background, due to the imperfection of the lens, as it were, the boundaries of this surface are moved, and this surface seems to us more than their true geometric sizes. In the figure, due to the brightness of the colors, white square seems, significantly, large relative to the black square on a white background.
It is curious to note that knowing about this property of black color to english sizes, the duelists in the XIX century preferred to shoot in black suits in the hope that the enemy misses when shooting.
The following example: We will see afar on the drawing and answer how many black circles could fit in the free interval between the lower circle and one of the top circles - four or five? Most likely, you will answer that four mugs will fit freely, but for the fifth, perhaps the places will not remain.
In fact, exactly three mug is placed in the interval. However, if you take paper, a circuit or a ruler, you can make sure that it is so.
This strange illusion, by virtue of which black areas seem to be less than white, are called "irradiation". It depends on the imperfection of our eye, which as an optical apparatus does not fully meet the strict optics requirements. Its refractive media do not give on the retina of those sharp contours that are obtained on the matte glass of a well-set photographic apparatus: due to the so-called spherical aberration, each light contour is surrounded by a bright border, which increases its dimensions on the mesh shell of the eye. As a result, bright areas always seem more to us than equal to it black.
2.5 Illusion of Information Processing
Some illusions arise in connection with the processing of incoming information. A person sometimes sees the world is not like that, what is it really, but as I would like to see it, give up to the formed habits, hidden dreams or passionate desires. It is looking for the right form, color or other distinguishing quality of the object among those represented in the outside world. This property of selectivity is called phenomenon of perceptual readiness.
Look at the drawing. Symbol in the center - letter or digit? If we consider the horizontal visual row, consisting of letters, in the center will be "in" - the observer is prepared alphabet. If you look at the vertical row, it turns out that this is not the letter at all, and the number 13 - the numbers pushed to this solution.
Such illusions are due to a higher level of information processing, when the nature of the task is determined by the fact that he perceives a person in the surrounding world. Interesting features of selectivity of perception. If you say a person: there is your last name in this book, he will be able to, very quickly spilling a page, find a mention of himself. And no one reads about the reading of the text of the speech.
Such skills have proofreaders, incomprehensiblely mixed in the text of the error, imperceptible to the usual reader. In this case, we are talking about professional skills purchased in the process of activity.
Very many erroneous visual impressions are due to the fact that we are perceived by us figures and their parts are not separately, but always in some relationship with their surrounding other figures, some background or atmosphere. With this, the largest number of visual illusions occurring in practice is connected. All of them can be divided into five groups.
Firstly, Comparing two figures, of which one is valid less than the other, we mistakenly perceive all parts of a smaller figure smaller, and all parts are large - large ("a whole more - more and its parts"). This is determined by the psychological aspect of perception.
In two other figures, the right figures are greater than the left (figures in general), however, the parts of these figures marked with the letters are equal to the parts of the left figures marked with the letters, although they seem significantly larger. This is because the properties of the figure we are mistaken to carry on it.
https://pandia.ru/text/78/016/images/image011_75.gif "width \u003d" 564 "height \u003d" 128 src \u003d "\u003e
Thirdly,the illusions are known, the cause of which lies in the approach (assimilation) of one part of the figure of another. The figure is straight, tangent to all mugs of different radii seems to be a curve, since we involuntarily like it to the upper curvilinear border. (Thompson).
https://pandia.ru/text/78/016/images/image013_37.jpg "Alt \u003d" (! Lang: Parall3.gif" align="left" width="280" height="131 src=">Аксиома" href="/text/category/aksioma/" rel="bookmark">аксиомами , теоремами, доказывать! Большая часть обманов зрения зависит исключительно от того, что мы не только видим, но и бессознательно рассуждаем, причём невольно вводим себя в заблуждение. Это – обманы суждения, а не чувств.!}
2.7. Use of visual illusions in human life
Ø Optical illusions on the road.
https://pandia.ru/text/78/016/images/image016_30.jpg "Align \u003d" Left "width \u003d" 136 "height \u003d" 160 src \u003d "\u003e
The woman on the right seems slimmer.
Sometimes it happens that the costume space filled with decor and parts seems more than equal to it unfair.
https://pandia.ru/text/78/016/images/image018_53.gif "align \u003d" left "width \u003d" 311 "height \u003d" 208 "\u003e Methods for optical change of room space.
Vertical stripes: lengthen the wall, the room seems to be higher. The wider stripes, the stronger the effect.
The transverse strips push the walls, and the room is done below.
non-existent. "Visually contradictory configuration creates an unresolved conflict between the actual form and the form visible.
If in nature we see beauty even where the chaos reigns and there is no rhythm, then op-art, like a person seeking to transform nature, is looking for beauty and expressiveness in a clear, but complex for our perception of a geometric figure, making chaos in our feeling of form and spaces and thus achieving a certain effect. Our perception seeks to organize a visible eye an image of chaotic scattered colored spots into a simple system, op-art, on the contrary, using strict geometric constructions, destroys the integrity of perception (See Appendix 4).
Ø 3D drawings on asphalt. Street art on asphalt.
Imagine: You go around the city, and suddenly the cleft appears before your eyes, from which the sacchadge of hell is trying to escape! Or suddenly on the asphalt you notice a completely ordinary apple, that's just touching it does not work - it is drawn! When you first look at the surround pictures on the asphalt, you can not believe that it is really just a drawing. This type of street art is called Street Painting (in English), or Madonnari (ITal.). In essence, the modern art of Street Painting (or Madonnari) originated in the XVI century, when street artists in religious holidays near churches and temples depicted paintings by biblical plots. Among the images most often dominated the image with the Virgin (Madonna).
To create a surround image on asphalt, artists use a special distortion, while the picture looks volumetric when looking at a certain point. One picture leaves for about three days.
Art actively uses the ability to vision to self-deception for their own purposes. The perspectives or reproduction of the volume effect on the flat figure are already named. Using new-fashioned terms, this effect can be called the "virtual volume effect". It turns out that our vision is capable of perceiving the volumetric paintings and perceive them as real when in fact is just an illusion. (See Appendix 5).
The picture - the illusion of the "raging waterfall" on the asphalt helps mentally move away from the pisceing heat, where there is water and coolness. The main secret of the image of the volumetric pictures, they need to "stretch". This is the skill of the artist. If you apply in conventional proportions, it will not be possible to achieve such an effect. Moreover, it falls several hours.
III. Research part
Research work on identifying and explaining the illusions and their evidence.
To the right thing, many of you have a question: why spend time on proof of what is so clear?
And in fact, why prove that the angles at the base of an equifiable triangle are equal to each other? Or that the amount of even numbers is obligatory?
After all, the equality of angles can be seen from the drawing, and how many times there are even numbers, you always get an even amount ... maybe it's true, evidence is needed only to teachers of mathematics?
However, many centuries of the development of science and art have accumulated many examples showing that it is not always necessary to trust what you see, especially on the first impression. What seems the same may turn out to be different, and the fact that first seemed different - it turns out to be the same.
1. Compare sizes.
1.1 Consider the illusion of Baldwin distortion of size perception
In the above examples, segments are also equal to each other.
1.2 We offered school students to draw the vertical and horizontal line of the same length, and in most cases the drawn vertical lines were shorter than horizontal.
Vertical parallel lines with significant lengths usually seem to be slightly divergent, and horizontal - converging.
2. View of the sizes of figures (revaluation of vertical lines)
https://pandia.ru/text/78/016/images/image024_46.gif "alt \u003d" (! Lang: D: \\ Svetlana \\ Illusion \\ New" align="left" width="212" height="137 src=">!} 2.2 Cafe illusion
Lines in this picture are also parallel
2.3. The illusion of vertgeimer-koffki.https://pandia.ru/text/78/016/images/image026_14.jpg "alt \u003d" (! Lang: Circlet.gif (826 bytes)" align="left hspace=12" width="272" height="163">!} 2.4 Ebbigauz Illusion (1902).
What circle more? One that is surrounded by small circles
or is the one that is surrounded by big?
https://pandia.ru/text/78/016/images/image028_11.jpg "Alt \u003d" (! Lang: Description:" align="left" width="164" height="163">!} 2.6 Consider the figure composed of rhombuses and triangles. Is it true that the width is less than the height?
Output:Nevertheless, they are the same, and if we connect the tops of sharp corners, then we get a square.
2.7 Compare the relative dimensions of several objects in the field of view.
If the items are removed from the eyes on the same distance and are close to each other quite close, they are easy to compare them. In this case, we are rarely mistaken in our assessment: a higher item is visible at a large angle, therefore it seems above.
Complete the task. Place the items at different distances from the eye, including the items of different sizes. Then their visible sizes seem the same.
https://pandia.ru/text/78/016/images/image031_10.jpg "width \u003d" 293 "height \u003d" 144 "\u003e. jpg" align \u003d "left" width \u003d "276 height \u003d 141" height \u003d " 141 "\u003e
3. The illusion of perspective
This method of images of objects in space, consistent with the peculiarities of human vision.
3.1
Illusion Ponsto - Also illustrates distortion of size perception. What is a blue or red feature - longer?
In 1913, Mario Bowno showed that sometimes our brain defines the size of the object, based on the background behind him.
The lines applied to the following photos have the same length, parallel and equal to each other.
Nevertheless, the closest lines seems shorter than the distant.
3.2 Consider two "runaway" from us parallel lines (tram or rail). They seem converging at some point of the horizon. At the same time, the point itself seems to us infinitely remote and inaccessible. Vision seems to be trying to convince us that contrary to the laws of geometry parallel direct intersect.
Evidence: This illusion is explained by us above the feature of visual perception. The object (sleeper), located at different distances from the observer, visible at different angles of view and as it removed along parallel straight lines (rails), its angular size decreases, which leads to a visible reduction in the distance between the lines (in this case it is determined by the sleeper). Obviously, when the angle of view reaches some "critical" size, the eye ceases to distinguish between the removing object as a body having dimensions, and the straight "merge" for it in one point.
Output: There is the limit value of the angle of view - the smallest value in which the eye is able to see separately two points .
3.3 Look at the cars. Which one is more?
https://pandia.ru/text/78/016/images/image040_26.gif "align \u003d" left hspace \u003d 12 "width \u003d" 217 "height \u003d" 227 "\u003e
The most interesting thing is that the parallelepipeds and these three cars are the same !!!
Thanks to the signs of perspective, the right parallelepiped seems to be more remote than the rest. Since the sign of the remoteness "launches the mechanism" of the constancy of the perception of the magnitude, the observer seems that the right parallelepiped is greater than the rest, although they are identical.
Output: if two objects whose images are equal in magnitude, seem to be an observer located at different distances from it, that of them that seems more remote, will always seem large in magnitude. This dependence is called the apparent remoteness hypothesis.
4. Deceptible volumes.
Flat images of spatial bodies, of course, always contain some conventions: it's just some flat pieces that help us imagine the location of the body in space.
It sometimes it turns out that different bodies can have the same flat image. And then we can not decide: what are we still visible in front of them?
4.1 The simplest image consists of a rhombus with a short diagonal spent in it. If we are one half an adhesion, we can see or image a pyramid, or an image of a rectangular hole in the floor.
4.2.
Consider the drawing from top to bottom, we can see a cube, in which two adjacent faces are continued down, and if the eye moves from the bottom up - you can see the same cube that has two faces are continued upwards.
4.3 Consider a cube. As it seems to us, the blue edge of the cube is
ahead or rear? And this is how to see.
Sometimes it seems that there is ahead, and sometimes - rear.
https://pandia.ru/text/78/016/images/image045_8.jpg "Alt \u003d" (! Lang: Description:" align="left" width="171" height="171 src=">На левом мы можем видеть большой куб, из которого в углу вырезан маленький кубик, помещенный в углу то ли комнаты, то ли коробки. А теперь сосчитайте кубики на правом рисунке. Иногда у вас получиться 7 (с черными гранями, обращенными к нам), а иногда – 6 (с черными гранями сверху).!}
5. "Impossible objects"
Probably, when you met such words. What do they mean? Word itself an objectmeans some item that can be viewed, touching, learn. How can he not exist?
Drawing "Href \u003d" / Text / Category / Cherchenie / "REL \u003d" Bookmark "\u003e The correct elements were incorrectly connected .
All three figures shown below are composed of very simple, quite existing parts. But these parts are interconnected by some plausible, but absolutely impossible.
https://pandia.ru/text/78/016/images/image050_2.jpg "Alt \u003d" (! Lang: Description:" align="left" width="200" height="102 src=">С этой фигурой мы входим с самую сердцевину и суть «невозможного». Может быть, это самый многочисленный класс невозможных объектов.!}
This notorious impossible object with three (or two-time) teeth became popular with engineers and puzzle lovers in 1964. The first publication dedicated to an unusual figure appeared in December 1964. The author called her "bracket consisting of three elements." Perception and permission (if it is only possible) inconsistencies in this new type of ambiguous figure requires a real shift of visual fixation. From a practical point of view, this strange trident or a mechanism in the form of a bracket is absolutely not applicable. Some call it just a "annoying mistake." One of the representatives of the aerospace industry proposed to use its properties when constructing interdimal spacecaps.
6. Trust, but check!
All the examples reviewed above, convinced you that the first impression of the image can be deceptive. And therefore, do not rush to say: "Well, it's clearly seen from the figure!" It is possible that one can see one, and the other is completely different.
And it happens that what is painted, and does not happen at all!
So, before drawing conclusions from the drawing, it is useful to think about it.
https://pandia.ru/text/78/016/images/image052_25.gif "Alt \u003d" (! Lang: Description:" align="left hspace=12 alt=" width \u003d."290" height="147">Отношения длин соответствующих сторон синего и красного треугольников не равны друг другу (2/3 и 5/8), поэтому эти треугольники не являются подобными, а значит, имеют разные углы при соответствующих вершинах. Назовём первую фигуру, являющуюся вогнутым четырёхугольником, и вторую фигуру, являющуюся вогнутым восьмиугольником, псевдотреугольниками. Если нижние стороны этих псевдотреугольников параллельны, то гипотенузы в обоих псевдотреугольниках 13×5 на самом деле являются ломаными линиями (на верхнем рисунке создаётся излом внутрь, а на нижнем - наружу). Если наложить верхнюю и нижнюю фигуры 13×5 друг на друга, то между их «гипотенузами» образуется параллелограмм, в котором и содержится «лишняя» площадь. На рисунке этот параллелограмм приведён в верных пропорциях. «Гипотенуза» на самом деле является ломаной линией.!}
Conclusion.
The material presented in the work expands the horizons of students, replenishes theoretical knowledge and explains many optical illusions. Geometric illusions create rich opportunities for artists, photographers, fashion designers. However, engineers and mathematicians have to be careful with drawings and reinforce the "obvious" accurate calculations.
We have shown that our eyemetic estimates of geometric real values \u200b\u200bare very highly dependent on the nature and background of the image. Errors arising from optical illusions can be very large.
Thus, our study showed how wide and multifaceted human activity, such and different requirements for the form and content of images. Some of them should produce the same impression on the human eye as the image itself, and in other words, the image should have sufficient visibility. In another case, the image must be, first of all, geometrically equivalent to the original, it should give a complete geometric and dimensional characteristic of the item depicted.
In the process of working on the theme "Do not believe our eyes ..." - Geometric illusions We:
Ø studied theoretical material on this issue;
Ø We considered examples of using geometric illusions.
Ø conducted studies associated with optical-geometric and visual illusions, explained and proved them from the point of view of geometry.
And they came to the conclusion: in mathematics, when solving problems, it is impossible to rely only on the drawing, it is necessary to confirm all its statements to confirm the properties, axioms, theorems.
Thus, the hypothesis of our research is confirmed.
Bibliography
1. S. Twevsky, "Optical Illusions". - M.: Mir, 1967. - P. 128.
2. O. Ruthersvard , "Impossible figures." - M.: Stroyzdat, 1990.
3. P. Dyubin, "Physical Experiments and Psychological Illusions." - M., 2006.
4. H. Schiffman, "Feeling and Perception". - St. Petersburg., 2003.
5., "Illusions of view", ed.3 - M., Science, 1969
6., "Entertaining physics". - M., AST, 2010
7. O. Ruthersvard, "Impossible Figures". - M., Stroyzdat, 1990.
8., "Designed geometry", M.1963
9., "Perspective in geometry and painting", M 1998
10., "Live Mathematics", M.2006
11. R. L Gregory, "Reasonable Eyes", M.2003g
12., "Geometry and Mareselza", M.1986
13. Large electronic encyclopedia Cyril and Kagirov Methodius
14. N. M Carpunin, "Unexpected Mathematics", M.2003g
15. E. Rubin, "Items and Images", Encyclopedia for Children 2000
16.P Francesca, "On the picturesque perspective", Encyclopedia 2000
17. Children's encyclopedia in mathematics "I will know the world"
18. I. I am the Depman, behind the pages of the textbook of mathematics. M-1988.
19. Do not believe your eyes // Kvant-1970.-№10-s. 18-20.
Internet resources.
http: // www. illusion. / main / index / index. PHP - visual illusions and phenomena
http: // www. ***** / 2004/6 / OCHEVIDNOE. Shtml - illusions of visual perception. Obvious-incredible. Journal "In the World of Science", June 2004 № 6
http: // www. ***** / Book / Gregory. HTM - "Reasonable Eye"
Deception is called such effects of visual perception, which arise involuntarily or consciously in a person observing certain images.
Such effects are also called optical illusions - errors of the visual perception caused by the inaccuracy or inadequacy of the processes occurring with an unconscious correction of visual images. In addition, the physiological features of the organs of vision and psychological aspects of visual perception are also involved in the process of optical illusions.
Optical illusionSubmitted in this section of the site is to distort the perception by improper estimation of the length of the segments, the size of the angles, the colors of the visible object, etc. Its most popular types are the illusions of the perception of depth, flippers, stereo pairs and illusions of movement.
The illusions of the perception of depth include inadequate reflection of the depicted object. The most famous examples of such illusions are two-dimensional contour pictures - with observation, they are unconsciously perceived by the brain as simply connected. In addition, distortion in the perception of depth is capable of improperly evaluating geometric sizes (in some cases, an error reaches 25%).
Optical illusion Crawling lies in the image of this picture, the perception of which depends on the direction of the view.
Stereo pairs allow you to observe a stereoscopic image by overlaying them to periodic structures. Focusing look at the picture leads to the observation of the stereoscopic effect.
Moving illusions are periodic images, a continuous view of which leads to visual perception of movement from individual parts.
See the frog and horse to this deception of sight?
This picture is very famous. Turn it over to see how men see women, skipping 6 bottles of beer.
Mysterious face found on Mars. This is a real photo of the surface of Mars, made by Viking 1 in 1976.
Peer in four black dots in the image price of about 30-60 seconds. Then quickly close your eyes and turn to something bright (to the lamp or to the window). Valued to see the white circle with the image inside.
Beautiful illusion of a moving bike (© Akiyoshi Kitaoka: Used with a resolution).
Illusion of moving curtains (© Akiyoshi Kitaoka: Used with a resolution).
Interesting illusion of vision with perfect squares (© Akiyoshi Kitaoka: Used with a resolution).
And once again perfect squares (© Akiyoshi Kitaoka: Used with a resolution).
This is a classic - no need to explain.
In this picture there must be 11 persons. The middle manner sees 4-6, attentive - 8-10. The best see all 11, schizophrenics and paranoids 12 and more. And you? (Do not take this test too seriously, I heard that there may be 13 people.)
Do you see your face in this pile of coffee beans? Do not hurry, it really is there.
Do you see squares or rectangles? In fact, here only straight lines in different directions, but our brain perceives them quite differently!
We used to perceive the world around us as a givenness, so we do not notice how our brain is deceiving its own owners.
The imperfection of our binocular vision, unconscious false judgments, psychological stereotypes and other distortion of worldview serve as a reason for the emergence of optical illusions. Their huge set, but we tried to collect the most interesting, insane and incredible and incredible of them.
Impossible figures
At one time, this graphics genre received such widespread that even received its own name - impusilism. Each of these figures seems quite real on paper, but there can be no simplicity in the physical world.Impossible trident
Classic Billine is perhaps the most vivid representative of optical drawings from the category "Impossible Figures". No matter how trying to determine where the middle prong originates, it will not work.
Another bright example is an impossible triangle of Penrose.
He is in the form of the so-called "endless staircase".
And also the "impossible elephant" Roger Shepard.
Eix room
Optical illusions questions were interested in Adelbert Amesa Jr. from early childhood. Becoming an ophthalmologist, he did not stop his research on the perception of depth, the result of which the famous Eix Room became. 
How the Eix Room works
In a nutshell, the effect of the Eix room can be conveyed like this: it seems that two people stand in the left and right corner of its rear wall - dwarf and giant. Of course, this is an optical trick, and in fact these people are quite ordinary growth. In fact, the room has an elongated trapezoidal form, but because of the false perspective it seems to us rectangular. The left corner is stronger from the sight of visitors than the right, and therefore the person standing there seems so small. 
Illusions of Movement
This category of optical tricks is the greatest interest for psychologists. Most of them are based on the intricacies of the combination of colors, brightness of objects and their repetition. All these tricks are misleading our peripheral vision, as a result of which the perception mechanism is knocked down, the retina fixes the image intermittently, jumps like, and the brain activates the bark sites responsible for the motion recognition.Floating Star
It is difficult to believe that this picture is not an animated GIF format, but an ordinary optical illusion. The drawing was created by the Japanese artist Kaya Nao in 2012. A pronounced illusion of motion is achieved due to the opposite direction of patterns in the center and at the edges. 
There are quite a lot of similar illusions of movement, that is, static images of apparent movable. For example, the famous rotating circle.
Or Yellow arrows on a pink background: with a close look it seems that they are pegged there and here.
Caution, this image can cause a row or dizziness in people with a weak vestibular apparatus.
Honestly, this is the usual picture, and not a gif! Psychedelic spirals seem to be tightened somewhere in full of oddities and wonders of the universe.
Illusions-transverse
The most numerous and cheerful genre of drawing-illusions is based on the change of direction of view on the graphic object. The most simple pictures need to simply deploy 180 or 90 degrees. 
Two classic illusions-invertes: nurse / old woman and beauty / urodin.
A more highly artistic picture with a trick - when turning 90 degrees, the frog turns into a horse.
Other "double illusions" have a more subtle background.
Girl / old woman
One of the most popular dual images was published in 1915 in the PUCK caricature magazine. Signature to the picture read: "My wife and mother-in-law". 
Old men / Mexicans
Elderly couple or mexicants singing under the guitar? Most of the first sees old people, and only then their eyebrows turn into Sombrero, and their eyes in the face. Authorship belongs to the Mexican artist Octavio Okampo, who created a lot of pictures of illusions of this character. 
Lovers / Dolphins
Surprisingly, the interpretation of this psychological illusion depends on the age of a person. As a rule, the children seemed to see children - their brain, not yet familiar with sexual relationships and their symbols, simply does not extend in this composition of two lovers. A older people, on the contrary, first see a couple, and then the dolphins. 
The list of such dual pictures can continue infinitely:
In the picture above, most people see the face of the Indian first, and then the look left to the left and distinguish the silhouette in the fur coat. The image below is usually interpreted by everyone as a black cat, and only then the mouse appears in its circuits.
Very simple picture-transverse - something like this can be easily made with your own hands.
Illusions of color and contrast
Alas, the human eye is imperfect, and in their assessments we have seen (without noticing themselves) often rely on the color environment and brightness of the background of the object. This leads to very interesting optical illusions.Gray squares
Optical illusions of colors - one of the most popular types of deception. Yes, yes, squares a and b are painted in the same color. 
Such a trick is possible thanks to the peculiarities of our brain. The square B drops the shadow without sudden boundaries. Due to the darker "surrounding" and a smooth gradient of the shadow it seems that it is significantly the lighter square A.
Green spiral
In this photo, only three colors: pink, orange and green. Do not believe? This is what happens if replaced with pink and orange on black. 
Dress white and gold or blue-black?
However, the illusion color based on the perception is not uncommon. Take for example, at least the white-golden or black and blue dress in 2015. What color actually was a mysterious dress, and why did different people perceived it differently?Clarification of the phenomenon dresses is very simple: as in the case of gray squares, it all depends on the imperfect chromatic adaptation of our bodies of vision. As you know, the retina of a person consists of two types of receptors: sticks and colodes. Wands better fix light, and columns - color. Each person has a ratio of colums and chopsticks, therefore, the definition of the color and shape of the object differs slightly depending on the dominance of this or that type of receptors.
Those who saw a white-golden dress drew attention to a brightly lit back background and decided that the dress was in the shade, which means that the white color should be darker than the usual. If the dress seemed to you blue-black, it means that your eye first drew attention to the main color of the dress, which in this photo really has a blue shade. Then your brain judged that the golden shade is black, brightening because of the sun rays and poor quality photo.
In fact, the dress was blue with black lace.
But another photo that put millions of users who could not solve the wall in front of them or a lake.
Optical illusions on video
Ballerina
This insane optical illusion is misleading: it is difficult to determine which foot shape is supporting and, as a result, to understand which way the ballerina rotates. Even if you managed it, while watching a video, the reference foot can "change" and the girl as if starting to rotate in the other side.Popular optical illusion of "ballerina"
If you easily able to fix the direction of the ballerina, it speaks of a rational, practical warehouse of your mind. If the ballerina rotates in different directions, it means that you have a stormy, not always a consistent imagination. Contrary to popular belief, on the principle of the right or left hemisphere it does not affect.
Face Monsters
Interest for lovers of unusual things represents the chair of the design of Chris Duffy. It seems that it relies exclusively on the front legs. But risking to sit on him, you will understand that the shadow, discarded by the chair, is its main support.
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