Mathematical figures in my life drawings. Geometric shapes in pictures and their names for children

At the same time as learning colors, you can start showing your child cards of geometric shapes. On our website you can download them for free.

How to study figures with your child using Doman cards.

1) You need to start with simple shapes: circle, square, triangle, star, rectangle. As you master the material, begin to study more complex shapes: oval, trapezoid, parallelogram, etc.

2) You need to work with your child using Doman cards several times a day. When demonstrating a geometric figure, clearly pronounce the name of the figure. And if during classes you also use visual objects, for example, collecting inserts with figures or a toy sorter, then your child will master the material very quickly.

3) When the child remembers the name of the shapes, you can move on to more complex tasks: now showing the card, say - this is a blue square, it has 4 equal sides. Ask your child questions, ask him to describe what he sees on the card, etc.

Such activities are very useful for the development of a child’s memory and speech.

Here you can download Doman's cards from the series “Flat geometric shapes” There are 16 pieces in total, including cards: flat geometric shapes, octagon, star, square, ring, circle, oval, parallelogram, semicircle, rectangle, right triangle, pentagon, rhombus, trapezoid, triangle, hexagon.

Classes according to Doman cards develop perfectly visual memory, attentiveness, child's speech. This is a great exercise for the mind.

You can download and print everything for free Doman cards flat geometric shapes

Right-click on the card and click “Save Image As...” so you can save the image to your computer.

How to make Doman cards yourself:

Print cards on thick paper or cardboard, 2, 4 or 6 pieces per sheet. To conduct classes using the Doman method, the cards are ready, you can show them to your child and say the name of the picture.

Good luck and new discoveries to your baby!

Educational video for children (toddlers and preschoolers) made according to the Doman method “Prodigy from the cradle” - educational cards, educational pictures on various topics from part 1, part 2 of the Doman method, which can be watched for free here or on our Channel Early childhood development on youtube

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards based on Glen Doman's method with pictures of flat geometric shapes for children

Educational cards geometric shapes according to Glen Doman's method with pictures of flat geometric shapes for children

Educational cards geometric shapes according to Glen Doman's method with pictures of flat geometric shapes for children

Educational cards geometric shapes according to Glen Doman's method with pictures of flat geometric shapes for children

More of our Doman cards using the “Prodigy from the Diaper” method:

1. Domana Cards Tableware
2. Doman cards National dishes

In this post I will show several pictures drawn using mathematical formulas. The purpose of these drawings is not just to draw something on the screen (there is computer graphics for this), but to suggest simple formula, defining the drawing.

The first picture shows a lotus. The figure was created in Wolfram Mathematica.

Code

phi = 0; dphi = 2*Pi/7; theta := 0.4*r; theta1 := 1*r; theta2 := 0.7*r; Show[ ParametricPlot3D[(r*Cos, r*Sin, 0), (r, 0, 0.8), (phi, 0, 2 Pi), PlotStyle -> Darker, Mesh -> None], ParametricPlot3D[(r*Cos , r*Sin, 0.02), (r, 0, 0.15), (phi, 0, 2 Pi), PlotStyle -> Yellow, Mesh -> None], ParametricPlot3D[ Join[ Table[ (r*Cos]*Cos[ (i*dphi) + t*dphi/2*r*(1 - r)^1.5*5], r*Cos]*Sin[(i*dphi) + t*dphi/2*r*(1 - r )^1.5*5], r*Sin]), (i, 0, 6)], Table[(r*Cos]*Cos[(i*dphi) + t*dphi/2*r*(1 - r )^1.5*5], r*Cos]*Sin[(i*dphi) + t*dphi/2*r*(1 - r)^1.5*5], r*Sin]), (i, 0, 6)], Table[(r*Cos]* Cos[(dphi/2 + i*dphi) + t*dphi/2*r*(1 - r)^1.5*5], r*Cos]* Sin[ (dphi/2 + i*dphi) + t*dphi/2*r*(1 - r)^1.5*5], r*Sin]), (i, 0, 6)]], (r, 0, 1), (t, -1, 1), PlotStyle -> Directive, 20], RGBColor, Lighting -> (("Directional", Darker, (2, 0, 2)), ("Ambient", Darker)) ], Mesh -> None], PlotRange -> ((-0.85, 0.85), (-0.85, 0.85), (0, 0.8))]

The next drawing is a cute flower. The formula is given in a spherical coordinate system, and the compression transformation along the axis is also done z.

Code

r := If[(Pi/2 - Abs< Pi/8), 0.25*Sin, Sin*Cos]; Show*Cos*Cos, r*Cos*Sin, r*Sin/Sqrt}, {theta, -Pi/2, Pi/2}, {phi, 0, 2*Pi}, Mesh ->None, PlotStyle -> Orange, PlotRange -> All, MaxRecursion -> 4], SphericalPlot3D]

Here's another flower.

Code

xx := 0; yy := -0.75 t*(1 - t); zz := -3 t; rr = 0.05; x1 := 0; y1 := -0.15 + 0.5 t; z1 := -1.6 + 0.5 t; r := If[(Pi/2 - Abs< Pi/8), 0.25*Sin, Sin*Cos]; Show*Cos*Cos, r*Cos*Sin, r*Sin/Sqrt}, {theta, -Pi/2, Pi/2}, {phi, 0, 2*Pi}, Mesh ->None, PlotStyle -> Orange, PlotRange -> All, MaxRecursion -> 4], SphericalPlot3D, ParametricPlot3D[(xx[t] + rr*Cos, yy[t] + rr*Sin, zz[t]), (t, 0, 1), (phi, 0, 2 Pi), Mesh -> None, PlotStyle -> Green], ParametricPlot3D[(x1[t] + phi*t*(1 - t), y1[t] - 0.5 phi *t*(1 - t)^3, z1[t]), (t, 0, 1), (phi, -1, 1), Mesh -> None, PlotStyle -> Green], Boxed -> False, Axes -> None]

This figure shows balls obtained as a surface of revolution for some function.

Code

x1 = 0; y1 = 0; z1 = -0.2; x2 = 0.8; y2 = 0.3; z2 = 0; x3 = -0.8; y3 = 0.5; z3 = 0.1; f := z*(1 - z); f := 0.3 z^0.5*Exp; gz := -0.6 t; gy := 0.1 t*(1 - t); gx := 0.05 Sin; Show*Cos, y1 + f*Sin, z1 + z), (z, 0, 1), (phi, 0, 2*Pi), PlotStyle -> Directive, 30], Lighter, Lighting -> (("Directional ", White, (1.5, 0, 3)), ("Ambient", Darker))], Mesh -> None], ParametricPlot3D[(x1 + gx[t], y1 + gy[t], z1 + gz[ t]), (t, 0, 1), PlotStyle -> Directive, Lighter]], ParametricPlot3D[(x2 + f*Cos, y2 + f*Sin, z2 + z), (z, 0, 1), ( phi, 0, 2*Pi), PlotStyle -> Directive, 30], Lighter, Lighting -> (("Directional", White, (1.5, 0, 3)), ("Ambient", Darker))], Mesh -> None], ParametricPlot3D[(x3 + f*Cos, y3 + f*Sin, z3 + z), (z, 0, 1), (phi, 0, 2*Pi), PlotStyle -> Directive, 30] , Lighter, Lighting -> (("Directional", White, (1.5, 0, 3)), ("Ambient", Darker))], Mesh -> None], ParametricPlot3D[(x2 + gx, y2 + gy, z2 + gz), (t, 0, 1), PlotStyle -> Directive, Lighter]], ParametricPlot3D[(x3 + gx[t], y3 + gy, z3 + gz), (t, 0, 1), PlotStyle -> Directive, Lighter]], PlotRange -> All]

Now I’ll give you a few holiday drawings.

Here is a drawing made on New Year. This is a Christmas tree built using segments.

Code

a = 1; b = 0.5; c = 1.5; h = 3.5; dr := b + (c - b)/n*k; dz := -(a - a/n*k); z := h - h*k/n; cnt = 0; Do = dr[i]*Cos; ldy = dr[i]*Sin;

Code

ldz = dz[i]; lz = z[i], (j, 1, m)], (i, 1, n)] ParametricPlot3D[ Table[(ldx[i]*t, ldy[i]*t, lz[i] + ldz[ i]*t), (i, 1, cnt)], (t, 0, 1), PlotStyle -> Directive, Thickness]

gamma = Pi/10; rho = 1; p = rho*Sin; k := Floor[(phi + 0.2*Pi)/(0.4*Pi)]; s := Sign*Pi]; alpha := s*(Pi/2 - gamma) + 0.4*k*Pi; PolarPlot], (phi, 0, 2*Pi), PlotStyle -> Directive]]
By the way, the parameter (half the angle of the star's ray) can be varied. This star corresponds to the value .
When we get an asterisk, similar to a starfish:

When we get a pointed star:

Here's a picture that fits Valentine's Day.

Code

f := x^2 + (y - (x^2)^(1/3))^2 - 1; h1 := (x^2)^(1/3) + Sqrt; h2 := (x^2)^(1/3) - Sqrt; Do = 1 - (i - 1)/6; y0[i] = h1]; k[i] = 4 + i, (i, 1, 6)];<= 0) || (f[(x + x0[i])*k[i], (y - y0[i])*k[i]] <= 0), {i, 1, 7}] || Or @@ Table[(f[(x - xx0[i])*kk[i], (y - yy0[i])*kk[i]] <= 0) || (f[(x + xx0[i])*kk[i], (y - yy0[i])*kk[i]] <= 0), {i, 1, 7}], {x, -1.5, 1.5}, {y, -2.5, 2.5}, PlotStyle ->x0 = 0; y0 = h1; k = 7; xx0 = 0.95; yy0 = h2; kk = 6; Do = 1.1 - 0.15*i; yy0[i] = h2];

kk[i] = 4 + i, (i, 2, 6)] xx0 = 0; yy0 = h2; kk = 6; RegionPlot[ Or @@ Table[(f[(x - x0[i])*k[i], (y - y0[i])*k[i]]

Red, AspectRatio -> 0.9, PlotRange -> All, MaxRecursion -> 5]

You can even make a mathematical confession:

Here's another math heart. An autonomous system of 2 differential equations of the 1st order is considered. A phase portrait of this system is constructed (trajectories of the system are drawn for various initial conditions) and the general integral of the system is found.

This system can be obtained by differentiating the general integral with respect to t. In this way (by solving a system of differential equations) you can build graphs of equations.

And this is a mathematical postcard for March 8th. The figure shows an abstract computer that has generated a graph of the Bernoulli lemniscate.
When needed: to identify personality types: leader, performer, scientist, inventor, etc.

TEST

“Constructive drawing of a man from geometric shapes”

Instructions

Please draw a human figure made up of 10 elements, which may include triangles, circles, and squares. You can increase or decrease these elements (geometric shapes) in size and overlap each other as needed.

It is important that all these three elements are present in the image of a person, and the sum of the total number of figures used is equal to 10. If you used more figures when drawing, then you need to cross out the extra ones, but if you used less than 10 figures, you need to complete the missing ones.

Key to the test “Constructive drawing of a person from geometric shapes”

Description

The employee needs to draw a human figure on each sheet, made up of 10 elements, which may include triangles, circles, and squares. An employee can increase or decrease these elements (geometric shapes) in size and overlap each other as needed. It is important that all these three elements are present in the image of a person, and the sum of the total number of figures used is equal to 10.

If an employee used a larger number of shapes when drawing, then he needs to cross out the extra ones, but if he used fewer than 10 shapes, he needs to complete the missing ones.

If the instructions are violated, the data will not be processed.

Example of drawings made by three assessees

Processing the result

Count the number of triangles, circles and squares used in the image of a man (for each picture separately). Write the result as three-digit numbers, where:

• hundreds indicate the number of triangles;
• tens – number of circles;
• units – number of squares.

These three-digit numbers make up the so-called drawing formula, according to which those drawing are assigned to the corresponding types and subtypes.

Interpretation of the result

Our own empirical studies, in which more than 2000 drawings were obtained and analyzed, showed that the ratio various elements V design drawings not by chance. The analysis allows us to identify eight main types, which correspond to certain typological characteristics.

The interpretation of the test is based on the fact that the geometric shapes used in the drawings differ in semantics:

• the triangle is usually referred to as a sharp, offensive figure associated with the masculine principle;
• circle – a streamlined figure, more in tune with sympathy, softness, roundness, femininity;
• a square, a rectangle are interpreted as a specifically technical structural figure, a technical module.

Typology based on the preference for geometric shapes allows us to form a kind of system of individual typological differences.

Types

Type I – leader

Drawing formulas: 901, 910, 802, 811, 820, 703, 712, 721, 730, 604, 613, 622, 631, 640. Dominance over others is most severely expressed in subtypes 901, 910, 802, 811, 820; situationally - at 703, 712, 721, 730; when influencing people with speech - verbal leader or teaching subtype - 604, 613, 622, 631, 640.

Typically, these are people with a penchant for leadership and organizational activities, focused on socially significant norms of behavior, and may have the gift of good storytellers, based on a high level of speech development. They have good adaptation to social sphere, dominance over others is kept within certain boundaries.

It must be remembered that the manifestation of these qualities depends on the level of mental development. At a high level of development, individual developmental traits are realizable and quite well understood.

At low levels they may not be detected in professional activity, and to be present situationally is worse if it is inadequate to the situations. This applies to all characteristics.

Type II – responsible executor

Drawing formulas: 505, 514, 523, 532, 541, 550.

This type of person has many traits of the “leader” type, being disposed towards it, however, there are often hesitations in making responsible decisions. Such a person is focused on the ability to get things done, high professionalism, has a high sense of responsibility and demands on himself and others, highly values ​​being right, that is, he is characterized by increased sensitivity to truthfulness. Often he suffers from somatic diseases of nervous origin due to overexertion.

Type III – anxious and suspicious

Drawing formulas: 406, 415, 424, 433, 442, 451, 460.

This type of people is characterized by a variety of abilities and talents - from fine manual skills to literary talent. Usually these people are cramped within one profession, they can change it to a completely opposite and unexpected one, and also have a hobby, which is essentially a second profession. Physically they cannot tolerate clutter and dirt. They usually conflict with other people because of this. They are characterized by increased vulnerability and often doubt themselves. Need encouragement.

In addition, 415 - “poetic subtype” - usually persons who have such a drawing formula have poetic talent; 424 – a subtype of people recognized by the phrase “How can you work poorly? I can’t imagine how it could work poorly.” People of this type are particularly careful in their work.

IV type – scientist

Drawing formulas: 307, 316, 325, 334, 343, 352, 361, 370.

These people easily abstract from reality, have a conceptual mind, and are distinguished by the ability to develop all their theories. They usually have peace of mind and rationally think through their behavior.

Subtype 316 is characterized by the ability to create theories, mainly global ones, or carry out large and complex coordination work.

325 – a subtype characterized by a great passion for knowledge of life, health, biological disciplines, and medicine. Representatives of this type are often found among people involved in synthetic arts: cinema, circus, theatrical and entertainment directing, animation, etc.

Type V – intuitive

Drawing formulas: 208, 217, 226, 235, 244, 253, 262, 271, 280.

People of this type have strong sensitivity nervous system, its high depletion. They work more easily by switching from one activity to another; they usually act as advocates for the minority. They have increased sensitivity to novelty. Altruistic, often caring for others, with good manual skills and imaginative skills, which gives them the ability to engage technical types creativity. They usually develop their own moral standards and have internal self-control, that is, they prefer self-control, reacting negatively to attacks on their freedom.

235 – often found among professional psychologists or people with an increased interest in psychology;

244 – has the ability for literary creativity;

217 – has the ability for inventive activity;

226 – has a great need for novelty, usually sets very high standards of achievement for himself.

Type VI – inventor, designer, artist

Drawing formulas: 109, 118, 127, 136, 145, 019, 028, 037, 046.

Often found among people with a technical streak. These are people with a rich imagination, spatial vision, and often engage in various types technical, artistic and intellectual creativity. More often they are introverted, just like the intuitive type, they live by their own moral standards, and do not accept any outside influences other than self-control. Emotional, obsessed with their own original ideas.

The following subtypes are also distinguished:

019 – found among people who have good command of the audience;

118 is the type with the most pronounced design capabilities and ability to invent.

VII type – emotive

Drawing formulas: 550, 451, 460, 352, 361, 370, 253, 262, 271, 280, 154, 163, 172, 181, 190, 055, 064, 073, 082, 091.

They have increased empathy towards others, have a hard time dealing with cruel scenes of the film, and can be unsettled for a long time and shocked by cruel events. The pains and worries of other people find in them participation, empathy and sympathy, on which they spend a lot of their own energy, as a result it becomes difficult to realize their own abilities.

Type VIII – the opposite of emotive

Drawing formulas: 901, 802, 703, 604, 505, 406, 307, 208, 109.

This type of people has the opposite tendency to the emotive type. Usually does not feel the experiences of other people, or treats them with inattention, or even increases pressure on people. If this is a good specialist, then he can force others to do what he considers necessary. Sometimes it is characterized by callousness, which arises situationally when, for some reason, a person becomes isolated in the circle of his own problems.

Little children are ready to learn everywhere and always. Their young brain is able to capture, analyze and remember so much information that is difficult even for an adult. What parents should teach their children has generally accepted age limits.

Children should learn basic geometric shapes and their names between the ages of 3 and 5 years.

Since all children are learning differently, these boundaries are only conditionally accepted in our country.

Geometry is the science of shapes, sizes and arrangement of figures in space. It may seem like it's difficult for kids. However, the objects of study of this science are all around us. This is why having basic knowledge in this area is important for both children and elders.

To get children interested in learning geometry, you can use funny pictures. Additionally, it would be nice to have aids that the child can touch, feel, trace, color, and recognize with his eyes closed. The main principle of any activities with children is to keep their attention and develop a craving for the subject using game techniques and a relaxed, fun atmosphere.

The combination of several means of perception will do its job very quickly. Use our mini-tutorial to teach your child to distinguish geometric shapes and know their names.

The circle is the very first of all shapes. In nature, many things around us are round: our planet, the sun, the moon, the core of a flower, many fruits and vegetables, the pupils of the eyes. A volumetric circle is a ball (ball, ball)

It is better to start studying the shape of a circle with your child by looking at drawings, and then reinforce the theory with practice by letting the child hold something round in his hands.

A square is a shape in which all sides have the same height and width. Square objects - cubes, boxes, house, window, pillow, stool, etc.

It is very easy to build all sorts of houses from square cubes. It’s easier to draw a square on a checkered piece of paper.

A rectangle is a relative of a square, which differs in that it has equal opposite sides. Just like a square, a rectangle's angles are all 90 degrees.

You can find many objects shaped like a rectangle: cabinets, Appliances, doors, furniture.

In nature, mountains and some trees have a triangle shape. From the immediate environment of children, we can cite as an example the triangular roof of a house and various road signs.

Some ancient structures, such as temples and pyramids, were built in the shape of a triangle.

An oval is a circle elongated on both sides. For example, eggs, nuts, many vegetables and fruits have an oval shape, human face, galaxies, etc.

An oval in volume is called an ellipse. Even the Earth is flattened at the poles - elliptical.

Rhombus

A rhombus is the same square, only elongated, that is, it has two obtuse angles and a pair of acute ones.

You can study a rhombus using visual aids- a drawn picture or three-dimensional object.

Memorization techniques

Geometric figures It's easy to remember the names. You can turn their study into a game for children by applying the following ideas:

• Buy a children's picture book that has fun and colorful drawings of shapes and their analogies from the world around them.

• Cut out a lot of different figures from multi-colored cardboard, laminate them with tape and use them as construction sets - you can create a lot of interesting combinations by combining different figures.

• Buy a ruler with holes in the shape of a circle, square, triangle and others - for children who are already familiar with pencils, drawing with such a ruler is a very interesting activity.

You can think of many ways to teach kids to know the names of geometric shapes. All methods are good: drawings, toys, observing surrounding objects. Start small, gradually increasing the complexity of the information and tasks. You will not feel how time flies, and the baby will definitely please you with success in the near future.