The pictures are an optical illusion. Why optical illusions trick our brain

We are used to taking the world around us for granted, so we do not notice how our brain deceives its own masters.

The imperfection of our binocular vision, unconscious false judgments, psychological stereotypes and other distortions of world perception serve as a pretext for the emergence of optical illusions. There are a lot of them, but we tried to collect for you the most interesting, crazy and incredible of them.

Impossible figures

At one time, this genre of graphics was so widespread that it even got its own name - impossibilism. Each of these figures seems quite real on paper, but simply cannot exist in the physical world.

Impossible Trident


The classic blevet is perhaps the brightest representative of optical drawings from the category of “impossible figures”. No matter how hard you try, you will not be able to determine where the middle prong originates.

Another striking example is the impossible Penrose triangle.


It is in the form of the so-called "endless staircase".


And also Roger Shepard's "impossible elephant".


Ames room

The questions of optical illusions interested Adelbert Ames Jr. early childhood. After becoming an ophthalmologist, he did not stop his research on depth perception, which resulted in the famous Ames Room.


How the Ames room works

In a nutshell, the effect of the Ames room can be conveyed as follows: it seems that two people are standing in the left and right corners of its back wall - a dwarf and a giant. Of course, this is an optical trick, and in fact these people are of quite ordinary height. In reality, the room has an elongated trapezoidal shape, but because of the false perspective, it seems to us rectangular. The left corner is farther away from the visitors' view than the right corner, and therefore the person standing there seems so small.


Illusions of movement

This category of optical tricks is of most interest to psychologists. Most of them are based on the subtleties of color combinations, the brightness of objects and their repetition. All these tricks mislead our peripheral vision, as a result of which the perception mechanism goes astray, the retina captures the image intermittently, spasmodically, and the brain activates the areas of the cortex responsible for detecting movement.

floating star

It's hard to believe that this picture is not an animated gif-format, but an ordinary optical illusion. The drawing was created by Japanese artist Kaya Nao in 2012. A pronounced illusion of movement is achieved due to the opposite direction of the patterns in the center and along the edges.


There are quite a few such illusions of motion, that is, static images that appear to be in motion. For example, the famous spinning circle.


Or yellow arrows on a pink background: when you look closely, it seems that they are swaying back and forth.


Beware, this image may cause eye pain or dizziness in people with weak vestibular apparatus.


Honestly, this is a regular picture, not a GIF! Psychedelic spirals seem to drag somewhere into the universe full of oddities and wonders.


Illusions-shifters

The most numerous and fun genre of drawings-illusions is based on a change in the direction of looking at a graphic object. The simplest upside-down drawings just need to be rotated 180 or 90 degrees.


Two classic shifter illusions: nurse/old woman and beauty/ugly.


A more highly artistic picture with a catch - when rotated 90 degrees, the frog turns into a horse.


Other "double illusions" are more subtle.

Girl / old woman

One of the most popular dual images was published in 1915 in the cartoon magazine Puck. The caption to the drawing read: "My wife and mother-in-law."


old people / mexicans

An elderly couple or guitar-singing Mexicans? Most see old people first, and only then do their eyebrows turn into a sombrero, and their eyes into faces. The authorship belongs to the Mexican artist Octavio Ocampo, who created many pictures-illusions of a similar nature.


Lovers / dolphins

Surprisingly, the interpretation of this psychological illusion depends on the age of the person. As a rule, children see dolphins frolicking in the water - their brain, not yet familiar with sexual relationships and their symbols, simply does not isolate two lovers in this composition. Older people, on the contrary, first see a couple, and only then dolphins.


The list of such dual pictures is endless:


In the picture above, most people first see the face of an Indian, and only then look to the left and distinguish a silhouette in a fur coat. The image below is usually interpreted by everyone as a black cat, and only then does a mouse appear in its contours.


A very simple upside-down picture - something like this can be easily done with your own hands.


Illusions of color and contrast

Alas, the human eye is imperfect, and in our assessments of what we see (without noticing it ourselves) we often rely on the color environment and the brightness of the background of the object. This leads to very interesting optical illusions.

gray squares

Optical illusions of colors are one of the most popular types of optical illusion. Yes, yes, squares A and B are painted in the same color.


Such a trick is possible due to the peculiarities of how our brain works. A shadow without sharp borders falls on square B. Thanks to the darker "environment" and smooth shadow gradient, it appears to be significantly lighter than square A.


green spiral

There are only three colors in this photo: pink, orange and green. Don't believe? Here's what happens when you replace pink and orange with black.


Is the dress white and gold or blue and black?

However, illusions based on the perception of color are not uncommon. Take, for example, the white-gold or black-and-white that conquered the Internet in 2015. blue dress. What color was this mysterious dress, and why did different people perceive it differently?

The explanation for the dress phenomenon is very simple: as in the case of gray squares, it all depends on the imperfect chromatic adaptation of our organs of vision. As you know, the human retina consists of two types of receptors: rods and cones. Rods capture light better, while cones capture color. Each person has a different ratio of cones and rods, so the definition of the color and shape of an object is slightly different depending on the dominance of one or another type of receptor.

Those who saw the white-and-gold dress drew attention to the brightly lit background and decided that the dress was in the shade, which means that the white color should be darker than usual. If the dress seemed blue-black to you, then your eye first of all paid attention to the main color of the dress, which in this photo really has a blue tint. Then your brain judged that the golden hue was black, brightened due to the rays of the sun directed at the dress and the poor quality of the photo.


In fact, the dress was blue with black lace.


And here is another photo that baffled millions of users who could not decide if there was a 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 leg of the figure is the supporting one and, as a result, to understand in which direction the ballerina is spinning. Even if you succeeded, while watching the video, the supporting leg can “change” and the girl seems to start to rotate in the other direction.

The most popular optical illusion "Ballerina"

If you could easily fix the direction of the ballerina's movement, this indicates a rational, practical mindset. If the ballerina rotates in different directions, this means that you have a stormy, not always consistent imagination. Contrary to popular belief, this does not affect the dominance of the right or left hemisphere.

monster faces


Of interest to fans of unusual things is the chair designed by Chris Duffy. It seems that it relies solely on the front legs. But if you dare to sit on it, you will realize that the shadow cast by the chair is its main support.



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Optical illusions are created through simple manipulations of lines, colors and patterns to confuse our brains. With each passing day, optical illusions are being used more and more in the arts, entertainment, and audience-focused scientific research. Since time immemorial, artists have come up with new ideas and techniques that require full sensory interaction with viewers - something that would give their brains a big boost. Here is a list of 10 such optical illusion setups that simply and literally confuse you.

18 PHOTOS

1. Invisible trolleybuses.
2. Optical illusion of Casa Ceramica.
3. This illusion makes people afraid to fall off the moment they enter the room. This dizzying floor system was designed by British company Casa Ceramica. Floors with this design are for the specific purpose of slowing people down as they walk across it.
4. 3D zebra.
5. Zebra that will make you feel like you are floating in the air. It can be seen in the quaint fishing town of Isafjordur in Iceland. It was created in September this year as a collaboration between the city's environmental commissioner Ralkom Trulla and the street art firm Vegi GIH. They tried to reinforce both the aesthetic value of the city and remind motorists to slow down at crosswalks and in narrow streets.
6. Large-scale geometric illusions by Felice Varini in Paris.
7. La Villette En Suites is an exhibition of the same name by Swiss artist Felice Varini opened in 2015. When viewed from one point, a strange feeling is created.
8. Varini, being an architecture enthusiast, uses unconventional spaces with different depths to create new ones. geometric shapes, which are basically paintings. These installations were available both inside and outside the Grande Halle de la Villette at the Parc de la Villette from 15 April to 13 September 2015.
9. Retro city of optical illusions.
10. Photographed by Michael Paul Smith.
11. Green planet.
12. If you look at the composition from a certain angle and at a certain height, it looks like a globe with several trees on top of it. In reality, however, this is a 1,500 square meter wide installation.
13. 3D gummy bears.
14. Optical illusions on buildings.
15. Mind-bending room settings.
16. Want to experience how simple lines can make you tipsy? There is Peter Kogler from Austria for you with his mind-blowing, psychedelic optical illusions. Kogler loves to bend time and space, which is what he does most interestingly. It turns the flat floors and white walls of galleries into something strange. It uses fully two-dimensional, simple lines and bold graphics to fool perspective and change your own architecture concepts.
17. Interactive installation by Leandro Erlich.
18. This is another art to get rid of your sense of coordination completely. Leandro Erlich, an artist from Argentina, gives an interactive experience to participants who get the illusion of sitting on the ledges of buildings. Known as the Dalston House, it allowed people young and old to experience the thrill of performing the wildest stunts while staying safe on the ground.

Optical illusion refers to such effects of visual perception that occur involuntarily or consciously in a person observing certain images.

Such effects are also called optical illusions - errors in visual perception, the cause of which is the inaccuracy or inadequacy of the processes occurring during the unconscious correction of visual images. In addition, the physiological characteristics of the organs of vision and the psychological aspects of visual perception also take part in the process of the emergence of optical illusions.

Optical illusion, presented in this section of the site, is to distort perception by incorrectly estimating the length of segments, the size of the angles, the colors of the visible object, etc. Its most popular types are depth perception illusions, flips, stereo pairs and motion illusions.

Illusions of depth perception include inadequate reflection of the depicted object. The most famous examples of such illusions are two-dimensional contour pictures - when they are observed, they are unconsciously perceived by the brain as one-convex. In addition, distortions in the perception of depth can lead to incorrect estimation of geometric dimensions (in some cases, the error reaches 25%).

Optical illusion The flipper consists in the image of such a picture, the perception of which depends on the direction of view.

Stereopairs make it possible to observe a stereoscopic image by superimposing them on periodic structures. Focusing the eye behind the picture leads to the observation of a stereoscopic effect.

Moving illusions are periodic images, a long look at which leads to a visual perception of movement from separate parts.

See the frog and the horse in this optical illusion?

This picture is very famous. Flip it over to see how men see women after 6 beers.

Mysterious face found on Mars. This is a real photograph of the surface of Mars taken by Viking 1 in 1976.

Stare at the four black dots in the center of the image for about 30-60 seconds. Then quickly close your eyes and turn to something bright (a lamp or a window). You should see a white circle with an image inside.

Beautiful illusion of a moving bike (© Akiyoshi Kitaoka: Used with permission).

Illusion of moving curtains (© Akiyoshi Kitaoka: Used with permission).

Interesting optical illusion with perfect squares (© Akiyoshi Kitaoka: used with permission).

And once again perfect squares (© Akiyoshi Kitaoka: used with permission).

This is a classic - no need to explain.

There should be 11 faces in this picture. The average layman sees 4-6, attentive - 8-10. The best see all 11, the schizophrenics and paranoids 12 or more. And you? (Don't take this quiz too seriously, I've heard there might be 13 faces.)

Can you see the face in this pile of coffee beans? Don't rush, it's really there.

Do you see squares or rectangles? In fact, there are only straight lines in different directions, but our brain perceives them in a completely different way!

An optical illusion is a hoax human vision. Observations of some images leave visual illusions in our minds.

Optical illusion is an unreliable perception of certain visual information. A person, looking at an illusion, incorrectly assesses its size or shape, creating a deceptive image in the mind.

The reason for erroneous perception is the peculiarity of the structure of our visual organ. The physiology and psychology of vision allow us to make an incorrect final result, and instead of round shapes, a person is able to see square ones, and large pictures will seem small.

Illusion - an error of visual perception

Optical illusion can be divided into several main types:

  • wrong color perception
  • misperception based on contrast
  • misperception of the size of an object
  • misperception of image depth
  • twisted illusion
  • "changeling"
  • illusions that move
  • 3D pictures
  • optical illusion contour

The human brain is capable of deceptively responding to certain images. It seems that the image moves or even changes its color only due to the fact that the brain perceives the visible light of some pictures.

Moving pictures optical illusion, photo

One of the most popular are the so-called moving pictures. The secret of this type lies in color and contrast perception.

moving picture

It is enough to look at the center of this picture for a few seconds, then look away at one of the sides of the salad frame of the image, as the picture literally “floats”.



moving illusion "wall"

This illusion can be attributed to two types of "curvature of the form" and "moving illusion". Firstly, the uneven placement of the cubes allows us to conclude that the lines are crooked.

However, they are absolutely equal. Secondly, if you move the picture up and down using the slider on your monitor on the right, you can see how the cubes move and run.



moving illusion

Thanks to the textured image, it creates the feeling that the squares in the center of the picture are moving.



illusion that moves

Due to the contrasting image of round discs, it seems that they are moving in different directions: clockwise and counterclockwise.



the illusion is moving

The patterns in the picture are of different sizes and stand out with bright contrasting colors. That is why it creates the feeling that the lines and curves are moving.

What are the pictures for optical illusion for children?

  • Visual illusions are one of the most popular intellectual entertainment for children. Observations of such pictures allow you to develop the thinking of the child.
  • He tries to understand why it happens that the desired is not presented as real.
  • In addition, groups are exercising eye muscles. This helps to improve blood circulation to the visual channel, which means it serves as a kind of prevention of blindness and other problems.

During the observation of illusions, the child exercises his logical thinking and develops the brain.

The most popular illusions for children:



animalistic shapeshifter

Such an illusion helps the baby understand which animal is shown in the picture: a cat or a dog. The child analyzes all the external features and remembers the characteristics, in addition, he tries to visually turn the image around, which trains his eye muscles.



volumetric illusion

This illusion gives the child the opportunity to see a three-dimensional image. In order to do this, you need to bring your face closer to the image, direct your gaze to the middle, scatter your vision for five seconds, and then quickly focus. Such an activity intensively trains the muscles of the eyes and allows the child to develop vision.



mirror illusion

Monotonous prints, arranged mirror to each other, allow the baby to find common features of external parameters in different animals.



optical illusion

This image allows you to develop abstract thinking: in the proposed picture you can see a simple branching tree. But if you read the contours correctly, the image of a newborn child will appear to your eyes.

What is an optical illusion hypnosis pictures?

Some images are called “pictures of hypnosis” because they can be misleading and a kind of trance when a person diligently tries to understand what is the secret of the drawn objects and why they move.



hypnosis picture

There is a belief that if you look at the center of a moving image for a long time, a person imagines how he plunges into a deep tunnel without a bottom and an edge. It is this immersion that distracts him from other thoughts and his trance is comparable to hypnosis.

Illusion pictures in black and white, optical illusion in contrasts

Black and white colors are absolutely opposite. These are the most contrasting colors of all. Looking at such a picture, the human eye literally “doubts” which of the colors to pay the main attention to and that is why it turns out that the pictures “dance”, “float”, “move” and even appear in space.

The most popular black and white illusions:



parallel black and white lines

The secret of the image is that the dashes on the lines are depicted in different directions and that is why it seems that the lines are not parallel at all.



black and white illusions

These images allow us to see two images in one picture. The drawing is built on the principle of contour and contrasts.

black and white illusion based on concentration

In this illusion, for the effect, you need to peer at the red dot located on the image for a long time.

One minute will be enough. After that, the gaze is taken to the side and on any object you see what you previously observed only on the monitor.

What is optical illusion pictures 3d?

This type of illusion allows a person to literally “break the brain”. This is because the picture displays the arrangement of objects in such a way that, firstly, they become voluminous on a plane, and secondly, sometimes they are too difficult to understand.



simple 3d illusion

This picture makes the location of objects incomprehensible to a person: their sides and surfaces. Nevertheless, the picture is perceived in volume.



complex illusion picture in 3D

More complex images involve a person peering into the depth of the picture for a long time. It is necessary to completely disperse and split vision and after a while sharply restore it.

On a completely flat picture, a three-dimensional figure (in this case, a woman) with clear contours will appear.

Optical illusion pictures

Optical illusions of vision are errors that can occur in our vision. The causes of optical illusions are perceptual errors.

While viewing the picture, inexplicable movements, disappearances and appearances may occur. All this is justified by the physiological and psychological aspect visual perception.



optical illusion "black dot"

The secret of the illusion is that when we notice a small black object in the center, we do not pay attention to the surroundings.



elephant optical illusion

Not a clear image of the contours allows you to see the elephant instead of four - eight legs.



optical illusion "sun"

Contrasting colors and indistinct borders of the picture allow the image to literally vibrate at the moment when we look at it and remain immobilized when we look at something else.



optical illusion "one picture - two images"

Based on a mirror image with an exact repetition of all forms.

Image Illusion: Dress, Illusion Explained

  • The famous network "virus" and the joke "blue or gold dress" are based on the perception of vision, depending on individual features each person
  • Once upon a time, everyone received a picture from friends in social networks with the caption “What color is the dress?”. And many of your friends answered this question in completely different ways: either blue or gold
  • The secret of the perception of the picture lies in the way your visual organ What are the conditions under which you are viewing this image?
  • In the retina of the human eye in each case there is a certain number of cones and rods. It is the quantity that plays the role of perception: for some it will be blue, for others it will be golden.


optical illusion "dress"

It is important to pay attention to the fact of lighting. look at the image in bright light - you will see a blue dress. Leave for half an hour in a dark room and then look back at the picture - most likely you will see a golden dress.

Double pictures optical illusion, what's the secret?

As mentioned earlier, the secret of this illusion is hidden in the complete repetition of the lines of the picture when it is mirrored. Of course, this can not be done in practice with every picture, but if you clearly choose the shape, you get quite an interesting result.



classic double picture "old or young woman?"

looking at this image, you need to decide for yourself: “What do you see first of all?” Of the possible options, you will see a young girl turned in profile with a feather in her headdress, or an old woman with a long chin and a big nose.



modern double image

Of the more modern versions of the double image, paintings can be distinguished that simultaneously depict two separate drawings. In such cases, the features of one image are read in different lines.

Video: “Five most incredible optical illusions. Optical illusion"

Petrova Oksana

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Slides captions:

Why are mistakes made in evaluating and comparing the lengths of a segment, the magnitude of the angles, in the perception of the shape of objects, etc.? performed by the observer under certain conditions. Relevance

Explain the visual illusion in terms of geometry and conduct social research. Target

1 Study the theoretical material on the topic. 2 show the application of the use of illusions in art, in mathematics, in real life. 3 Conduct a study showing the limitations of our eyes. Challenges

Illusions Drawings Subject of study Subject of study Hypothesis If our perception is deceptive, then the simplest things, if you look at them, are fraught with the most unexpected discoveries. Visual illusions can be explained using the laws of geometry.

1 Study 3 analysis, generalization Research methods 2 search 4 synthesis, classification

Varieties of illusions

Optical Illusions Optical illusions are, simply put, an optical illusion of our brain. When our eye receives a picture, a huge number of processes in our brain turn on.

optical illusions

Consider a figure made up of rhombuses and triangles. Is it true that the width is smaller than the height? Conclusion: However, they are the same, and if we connect the vertices of sharp corners, we get a square.

The Illusion of Movement The perception of movement is a very complex process, the nature of which has not yet been fully elucidated. If an object is objectively moving in space, then we perceive its movement due to the fact that it leaves the area of ​​​​best vision and thereby forces us to move our eyes or head in order to fix our gaze on it again.

illusions of movement on which the principle of cinematography is based. Look at the center of the picture (on the right). Violet and blue rings will flicker. Some also notice a circular rotation. And in the picture on the left, look closely at the ball in the center. It seems that the pattern on it is moving from side to side. Without taking your eyes off the center of the circle, move your head. There was an illusion that the pattern around the ball is shifting.

Vertical-horizontal illusion. The vertical line is perceived as longer. If you look at the drawing with one eye, then the effect is somewhat reduced. The feeling of vertical and horizontal directions depends not only on visual impressions, legs and stereotypes formed in the human brain

Vertical-horizontal illusion. The students were asked to determine "by eye" which of the lines is longer: vertical or horizontal. Vertical length Equal in length I know this effect Total 18 (75%) 4 (18%) 2 (7%) 24 (100%)

Illusion by Franz Müller-Lyer. The arrows at the ends of the segments create the illusion of length distortion, so the same segments are perceived as unequal. But in fact the segments are equal.

Children (20) Adults (10) Total (30) Line segments equal 4 (20%) 4 (40%) 8 (27%) Blue line greater than 16 (80%) 6 (60%) 22 (73%) Muller Illusion- Layer Verno was correctly identified by 20% of children and 40% of adults.

Poggendorff illusion. An amazing impression is made by a picture with two parallel intersecting oblique lines. If the right line is continued, then it will intersect the left one at its upper end. The apparent intersection point is somewhat to the right.

Continuation of line A Continuation of line B Between lines A and B Total 3 (17%) 4 (23%) 10 (60%) 17(100%) Poggendorff illusion The students were asked the question: "Which line is continued by line C?"

Illusion of parallelograms. A striking illusion is created by angles - obtuse and sharp; the diagonals AB and AC of the two parallelograms are equal, although the diagonal AC seems to be much shorter.

Illusion of parallelograms

Impossible Tiles. How many tiles are shown in the picture below? Seen from the left, there are four. If you look to the right, then three.

Area of ​​two triangles In the picture below you see 2 triangles. Triangles are made up of four shapes. The area of ​​the figures that make up the triangles is the same. What is at the top, what is at the bottom (you can cut it out of paper and check). What happens if the figures are mixed a little?

Illusion of lopsided squares. Very interesting optical focus. Looking at this picture, our brain assures us that the blue squares in the center of this picture are slightly skewed, and they tend to tilt to the side every now and then. But having defocused my eyes or simply moving away from the computer image a little, I understand that these are regular quadrangles, and that this is just an illusion.

The effect of perceptual readiness If you look at the picture below, it is not immediately clear which symbol is depicted in the center. This example clearly demonstrates the so-called perceptual readiness effect. Its essence lies in the fact that, depending on where you started reading from, you are ready to see different characters. If from top to bottom, then the number is 13. If from left to right, then the letter “B”.

Relief image. The brain, perceiving an object, distorts the relief image that we see. The following figure serves as an example of this: the cube now seems to be visible from above, then from the side; the open book now seems to be depicted with the spine towards us, then with the spine away from us. This happens both at our will, and involuntarily, and sometimes even contrary to our desire. The fact is that any image can be interpreted in different ways, but the human visual system prefers the most familiar and likely interpretation.

Impossible figures. Figures that do not exist in nature, but exist in our imagination An analysis of the proposed explanation of optical-geometric illusions shows that, firstly, all the parameters of the visual image are interconnected, due to which a holistic perception arises, an adequate picture of the external world is recreated. Secondly, perception is influenced by stereotypes formed by everyday experience. An example of how an integral image of an object can be destroyed is the so-called "impossible", contradictory figures, for example, the impossible trident of Norman Mingo and the impossible Penrose stairs

Illusion through the eyes of artists H Some artists change the logic of images of space, getting various illusions. By the "logic" of space, we mean those relationships between physical objects that are common in the real world, and in violation of which visual paradoxes arise, also called optical illusions. Most artists who experiment with the logic of space change these relationships between objects based on their intuition, like Picasso for example. Beautiful mountain landscape. Turn the picture to the right: now you have a praying mother and son. Changeling "Baby and Grandpa"

Tasks. Selfridge illusion. If you are even slightly familiar with English language, then it will not be difficult for you to read the name of the pet in the picture below. As the name suggests, Selfridge was the first to describe this optical illusion (Selfridge, 1955). Its essence lies in the fact that, depending on the context, the same character is perceived as “H” or as “A”? Answer: look carefully, because the picture says abracadabra THE CHT, not THE CAT.

Bucket illusion. Are the inner circle on the lid of the bucket equal to the circle that forms the bottom of the bucket? Answer: The inner circle on the lid of the bucket appears to be smaller than the circle that forms the bottom of the bucket. However, these circles are equal, and it is difficult to get rid of the idea that the lower one is larger than the upper one. The presence of an outer bordering oval creates the illusion that the oval enclosed in it is smaller than the lower one. Which segment is longer: AB or CD? Answer: they are equal.

illusion in real life. Optical illusions on the road. Visual illusions in clothes. The woman on the right appears slimmer. The vertical stripes lengthen the walls of the room and make it seem taller. The driver sees the painted objects and thinks there is a barrier on the road, he slows down to drive over it, when in fact it is a completely flat surface.

Consider the problem of constructing a perspective image of a figure. The figure shows how an image of an arbitrary point M of the plane α is obtained (numbers 1-4 indicate the order of drawing straight lines). If the point K does not lie in the object plane, then first a perpendicular is lowered from it to α (in the figure this is the KM segment), then constructions 1-3 are performed for its base (point M). Finally, a straight line is drawn, the intersection of which with the π plane is the image of the point K.

Let's compare the relative sizes of several objects in the field of view. If the objects are the same distance from the eyes and are close enough to each other, it is easy to compare them. In this case, we rarely make mistakes in our assessment: a higher object is seen at a greater angle, and therefore it seems higher. Let's complicate the task. We will place objects at different distances from the eye, including objects of different sizes. Then their visible sizes seem to be the same.

Conclusion. And this means that regardless of the shape of objects, the observed phenomenon should be described “in the language of mathematics” by the same law, in which such parameters as the linear size and distance to the object probably play a key role.

Determine the height of the pole (tower, tree, etc.) Let's move away from the pole at a distance at which the thumb of the outstretched hand will completely cover it (that is, their visible dimensions will become the same), while counting the number of steps taken. For an adult, the average distance from the eye to thumb the length of the outstretched arm is 60 cm, the length of the finger itself is 7 cm, and the length of the step is 65 cm. Using these data, it is easy to calculate the approximate height of the pillar. Similarly, the distance to an inaccessible object is determined by its known height. Note that the described method is reliable for estimating relatively close distances up to several hundred meters; the smaller the object and the farther it is, the higher the measurement error.

Conclusion: From the point of view of geometry, in all the examples given, we are dealing with similar figures or corresponding segments, namely, heights of figures of different shapes; moreover, in each case we encounter a transformation of a homothety whose center coincides with the observer's eye. Therefore, it can be argued that if two objects are seen from the same angle of view, then their linear dimensions differ by the same factor as the distance to the object differs):

Consider two parallel lines (tram or railway) running away from us. They seem to converge at some point on 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 lines intersect. Proof: this illusion is explained by the peculiarity of visual perception discussed above. There is a limit to the angle of view - smallest value, at which the eye is able to see two points separately.

Conclusion: There is a limit value of the angle of view - the smallest value at which the eye is able to see two points separately.

Social studies. Experiment No. 2 When perceiving a figure and a background, we tend to see, first of all, spots of a smaller area, as well as brighter “protruding” spots, and most often the background seems to us to lie farther from us, behind the figure. The greater the brightness contrast, the better the object is visible and the more clearly its outline and shape are visible. We decided to conduct an experiment to test this conclusion. We showed the respondents the following drawing and asked them to say what they saw. In the drawing, most people were supposed to see the vase first, and then the two silhouettes, according to the theory. Rubin's vase During the experiment, our assumption was not justified, as can be seen from the table: Figure and ground perception

Children (20) Adults (10) Total (30) Seeing a vase 10 (50%) 2 (20%) 12 (40%) Seeing faces 8 (40%) 4 (40%) 12 (40%) Seeing a vase and faces 2 (10%) 4 (40%) 6 (20%) Figure and ground perception If we consider children separately from adults, we get the following picture: 8 people (40%) of students and 4 people (40%) of adults did not see the vase .

Experiment #4. The Impossible Penrose Staircase. Children (20) Adults (10) Total (30) Moving 11 (55%) 8 (80%) 19 (63%) Standing - 7 (35%) 2 (10%) 1 (10%) 1 (10%) 8 (27%) 3 (10%) stereotypes formed by everyday experience affect the perception of adults to a greater extent than children

Conclusion Starting to study the geometric illusion, I asked myself this question: can we always trust our vision? It turns out not! Scientists have come up with and built many deceptive pictures that clearly demonstrate how limited the possibilities of our eyes are. In the course of my work, I realized that Geometric illusions create rich opportunities for artists, photographers, fashion designers. However, engineers and mathematicians have to be careful with drawings and back up the “obvious” with accurate calculations.