Volumetric geometric shapes and their names. Geometric figures. Let's play geometric lotto

Geometric figures are a complex of points, lines, solids or surfaces. These elements can be located both on the plane and in space, forming a finite number of straight lines.

The term “figure” implies several sets of points. They must be located on one or more planes and at the same time limited to a specific number of completed lines.

The main geometric figures are the point and the straight line. They are located on a plane. In addition to them, among simple figures there is a ray, a broken line and a segment.

Dot

This is one of the main figures of geometry. It is very small, but it is always used to build various shapes on a plane. The point is the main figure for absolutely all constructions, even the highest complexity. In geometry, it is usually denoted by a letter of the Latin alphabet, for example, A, B, K, L.

From a mathematical point of view, a point is an abstract spatial object that does not have such characteristics as area or volume, but at the same time remains a fundamental concept in geometry. This zero-dimensional object simply has no definition.

Straight

This figure is completely placed in one plane. The straight line has no specific mathematical definition, since it consists of a huge number of points located on one endless line, which has no limit or boundaries.

There is also a segment. This is also a straight line, but it starts and ends from a point, which means it has geometric restrictions.

The line can also turn into a directional beam. This happens when a straight line starts from a point, but does not have a clear ending. If you put a point in the middle of the line, then it will split into two rays (additional), and oppositely directed to each other.

Several segments that are sequentially connected to each other by ends in common point and are not located on the same straight line, it is usually called a broken line.

Corner

Geometric figures, the names of which we discussed above, are considered key elements used in the construction of more complex models.

An angle is a structure consisting of a vertex and two rays that extend from it. That is, the sides of this figure connect at one point.

Plane

Let's consider another primary concept. A plane is a figure that has neither end nor beginning, as well as a straight line and a point. When considering this geometric element, only its part, limited by the contours of a broken closed line, is taken into account.

Any smooth bounded surface can be considered a plane. This could be an ironing board, a piece of paper, or even a door.

Quadrilaterals

A parallelogram is a geometric figure whose opposite sides are parallel to each other in pairs. Among the particular types of this design are diamond, rectangle and square.

A rectangle is a parallelogram in which all sides touch at right angles.

A square is a quadrilateral with equal sides and angles.

A rhombus is a figure in which all sides are equal. In this case, the angles can be completely different, but in pairs. Each square is considered a diamond. But in the opposite direction this rule does not always apply. Not every rhombus is a square.

Trapezoid

Geometric shapes can be completely different and bizarre. Each of them has a unique shape and properties.

A trapezoid is a figure that is somewhat similar to a quadrilateral. It has two parallel opposite sides and is considered curved.

Circle

This geometric figure implies the location on one plane of points equidistant from its center. In this case, a given non-zero segment is usually called a radius.

Triangle

This is a simple geometric figure that is very often encountered and studied.

A triangle is considered a subtype of a polygon, located on one plane and limited by three edges and three points of contact. These elements are connected in pairs.

Polygon

The vertices of polygons are the points connecting the segments. And the latter, in turn, are considered to be parties.

Volumetric geometric shapes

prism;
sphere;
cone;
cylinder;
pyramid;

These bodies have something in common. All of them are limited to a closed surface, inside of which there are many points.

Volumetric bodies are studied not only in geometry, but also in crystallography.

Curious facts

Surely you will be interested in reading the information provided below.

Geometry was formed as a science back in ancient times. This phenomenon is usually associated with the development of art and various crafts. And the names of geometric figures indicate the use of the principles of determining similarity and similarity.
Translated from ancient Greek, the term “trapezoid” means a table for a meal.
If you take various figures, the perimeter of which will be the same, then the circle is guaranteed to have the largest area.
Translated from Greek language the term "cone" refers to a pine cone.
There is a famous painting by Kazemir Malevich, which, since the last century, has attracted the views of many painters. The work “Black Square” has always been mystical and mysterious. The geometric figure on the white canvas delights and amazes at the same time.

Exists a large number of geometric shapes. They all differ in parameters, and sometimes even surprise in shape.

Chukur Lyudmila Vasilievna
Geometric figures. Peculiarities of children's perception of the shape of objects and geometric figures

« GEOMETRIC FIGURE.

FEATURES OF CHILDREN'S PERCEPTION

Prepared: Art. teacher Chukur L. IN.

1. Concept « geometric figure» . Features of the development of ideas about the shape of objects in preschool children

One of the properties of those around objects is their shape. Shape of objects received a generalized reflection in geometric shapes.

Figure - Latin word, means "image", "view", "mark"; it is a part of a plane bounded by a closed line, or a part of space bounded by a closed surface. This term came into general use in the 12th century. Before this, another Latin word was more often used - « form» , also meaning "external appearance", "external outline subject» .

Watching objects of the surrounding world, people have noticed that there is some general property, allowing you to combine items in one group. This property was named geometric figure. A geometric figure is a standard for determining the shape of an object, any non-empty set of points; generalized abstract concept.

Self The definition of the concept of a geometric figure was given by the ancient Greeks. They determined, What geometric figure is the internal region bounded by a closed line on the plane. Euclid actively used this concept in his work. The ancient Greeks classified everything geometric figures and gave them names.

Mention of the first geometric shapes found among the ancient Egyptians and ancient Sumerians. Archaeological scientists found a papyrus scroll with geometric problems , which mentioned geometric figures. And each of them was called something a certain word.

Thus, idea of geometry and studied by this science figures people have had since ancient times, but the name « geometric figure» and names for everyone geometric shapes given by ancient Greek scientists.

Nowadays, getting to know geometric shapes begins in early childhood and continues throughout the educational process. Preschoolers learning the world, face diversity shapes of objects, learn to name and distinguish them, and then get acquainted with the properties geometric shapes.

Form- this is the external outline subject. A bunch of endless forms.

Ideas about the shape of objects occur in children quite early. In the research of L. A. Wenger, it becomes clear whether it is possible to distinguish shapes of objects by children who have not yet the act of grasping has formed. As an indicator, he used the approximate reaction of a child aged 3-4 months.

For children were presented two volumetric bodies of the same steel color and size (a prism and a ball, one of them was suspended above the arena to extinguish the indicative reaction; then the pair was suspended again figures. To one of them (prism) reaction extinguished, different (ball)- new. The kids turned their attention to the new figure and fixed it with their gaze for a longer time than the old one.

L. A. Wenger also noticed that what on geometric figure with a change in spatial orientation, the same visual concentration arises as on a new one geometric figure.

Research by M. Denisova and N. Figurina showed that the infant is shape to the touch defines the bottle, pacifier, mother's breast. Visually, children begin to distinguish shape of objects from 5 months. In this case, the indicator of discrimination is the movements of the arms and body towards the experimental object and grasping it (with food reinforcement).

Other studies have found that if objects differ in color, then a 3-year-old child singles them out form only if, If item familiar to the child from practical experience (experience of manipulations, actions).

This is also proven by the fact that the child recognizes upright and inverted images equally (he can look at and understand familiar pictures while holding a book "upside down", items, painted in unusual colors (a black apple, but a square turned at an angle, i.e. in the form of a rhombus, is not recognized, since the direct similarity disappears object shapes, which is not in experience.

2. Peculiarities of children's perception preschool age shapes of objects and geometric figures

One of the leading cognitive processes preschool children is perception. Perception helps to distinguish one item from another, highlight some items or phenomena from others similar to it.

Primary acquisition shape of the object Item Shape, as such, not subject precede practical actions. Actions of children with objects on different stages are different.

Research by psychologist S. N. Shabalin shows that geometric figure is perceived preschoolers in a peculiar way. If an adult perceives bucket or glass items, having a cylindrical form, then in his perception includes knowledge geometric shapes . In preschoolers, the opposite occurs.

At 3-4 years old children objectify geometric shapes since they are in their experience presented inseparably with objects, are not abstracted. A geometric figure is perceived by children as a picture. like some item: a square is a handkerchief, a pocket; triangle - roof, circle - wheel, ball, two circles next to each other - glasses, several circles next to each other - beads, etc.

At 4 years old objectification of a geometric figure occurs only when a child encounters an unfamiliar figure: a cylinder is a bucket, a glass.

At 4-5 years old, the child begins to compare geometric figure with an object: talking about a square “It’s like a handkerchief”.

As a result of organized learning, children begin to distinguish in those around them objects a familiar geometric figure, compare object with a figure(the glass is like a cylinder, the roof is like a triangle, learns to give the correct name geometric figure and shape of an object, words appear in their speech "square", "circle", "square", "round" and so on.

The problem of introducing children to geometric shapesand their properties should be considered in two aspects:

In terms of sensory perception of geometric shapes and using them as standards in knowledge shapes of surrounding objects;

In the sense of knowledge features of their structure, properties, basic connections and patterns in their construction, i.e. actually geometric material.

Circuit the subject is the general beginning, which is the source for both visual and tactile perception. However, the question of the role of the circuit in perception of form and formation a holistic image requires further development.

Primary acquisition shape of the object carried out in actions with it. Item Shape, as such, not perceived separately from the subject, it is its integral feature. Specific visual responses of contour following subject appear at the end of the second year of life and begin precede practical actions.

Actions of children with objects different at different stages. Babies strive, first of all, to grab item hands and start manipulating it. Children 2.5 years old, before acting, become familiar with the objects. The importance of practical actions remains paramount. From this follows the conclusion about the need to guide the development of perceptual actions of two-year-old children. Depending on the pedagogical guidance, the nature of children’s perceptual actions gradually reaches the cognitive level. The child begins to be interested in various signs subject, including form. However, for a long time he cannot identify and generalize this or that feature, including the shape of different objects.

Touch perception of the shape of an object should be aimed not only at see, learn forms, along with its other signs, but be able to, abstracting shape from the thing, see her in other things too. Such perception of the shape of objects and its generalization is facilitated by children’s knowledge of standards - geometric figures. Therefore the task sensory development is formation the child's ability to recognize in accordance with the standard (one or another geometric figure) the shape of different objects.

Experimental data by L. A. Wenger showed that the ability to distinguish geometric figures children 3-4 months old have. Focusing on something new figure- evidence of this.

Already in the second year of life, children freely choose figuremodeled after such pairs: square and semicircle, rectangle and triangle. But children can distinguish between a rectangle and a square, a square and a triangle only after 2.5 years. Selection according to sample more figures complex shape available around the age of 4-5 years, and reproduction of a complex figure carried out by children of the fifth and sixth year of life.

Under the teaching influence of adults perception of geometric shapes is gradually being rebuilt. Geometric figures begin to be perceived by children as standards, with the help of which cognition of structure subject, his forms and size is carried out not only in the process perception of one form or another by vision, but also through active touch, feeling it under the control of vision and denoting it with a word.

Collaboration of all analyzers promotes a more accurate perception of the shape of objects. To know better item, children strive to touch it with their hand, pick it up, turn it; Moreover, viewing and feeling are different depending on forms and the construction of the cognizable object. Therefore, the main role in perception of an object and determination of its shape has an examination, carried out simultaneously by the visual and motor-tactile analyzers, followed by a word designation. However, preschoolers have a very low level of screening shapes of objects; most often they are limited to fluent visual perception and therefore do not distinguish between similar ones figures(oval and circle, rectangle and square, different triangles).

In the perceptual activity of children, tactile-motor and visual techniques gradually become the main ones. way of recognizing form. Survey figures not only provides their integrity perception, but also allows you to feel them peculiarities(character, directions of lines and their combinations, formed angles and vertices, the child learns to sensually highlight in any figure the image as a whole and its parts. This makes it possible to further focus the child’s attention on meaningful analysis. figures, consciously highlighting in it structural elements (sides, corners, vertices). Children are already consciously beginning to understand such properties as stability, instability, etc., to understand how vertices, angles, etc. are formed. Comparing volumetric and flat figures, children already find commonality between them ( "The cube has squares", “The beam has rectangles, the cylinder has circles” etc.).

Comparison figures with the shape of an object helps children understand that geometric shapes you can compare different objects or parts thereof. Yes, gradually geometric figure becomes a standard determining the shape of objects.

3. Peculiarities examinations and examination training stages children preschool age shapes of objects and geometric figures

It is known that the basis of cognition is always sensory examination, mediated by thinking and speech. In the studies of L. Wenger with children 2-3 years visual discrimination indicator the shapes of objects served as the child’s objective actions.

According to research by S. Yakobson, V. Zinchenko, A. Ruzskaya, children 2-4 years old recognized better objects by shape, When it was suggested to first feel the object, and then find the same one. Lower results were observed when the object was perceived visually.

Research by T. Ginevskaya reveals peculiarities hand movements during examination items by shape. The children were blindfolded and offered to get acquainted with the subject by touch.

At 3-4 years – executive movements (roll, knock, carry). There are few movements inside figures, Sometimes (one time) along the center line, many erroneous answers, mixing of different figures. At 4-5 years - installation movements (held in hand). The number of movements doubles; judging by the trajectory, they are oriented towards size and area; large, sweeping, groups of closely spaced fixations are found, which are among the most characteristic features figures; give better results. At 5-6 years old – exploration movements (contour tracing, elasticity testing). Movements appear that trace the contour, but they cover the most characteristic part of the contour, other parts are unexamined; movements within the circuit, the same quantity, good results; As in previous period, there is a mixing of loved ones figures. At 6-7 years old - movement along the contour, crossing the field figures, and movements are concentrated on the most informative signs, excellent results are observed not only in recognition, but also in playback.

Thus, in order for the child to highlight the essential features geometric shapes, their visual and motor examination is necessary. Hand movements organize eye movements and children need to be taught this.

Stages of examination training

The task of the first stage of education for children 3-4 years old is sensory perception of the shape of objects and geometric figures.

The second stage of teaching children 5-6 years old should be devoted to formation of systematic knowledge about geometric shapes and their development initial techniques And ways« geometric thinking» .

« Geometric thinking» it is quite possible to develop further in preschool age. In development « geometric knowledge» Children exhibit several different levels.

The first level is characterized by the fact that the figure is perceived by children as a whole, the child does not yet know how to identify individual elements in it, does not notice the similarities and differences between figures, each of them perceives separately.

At the second level, the child already identifies elements in figure and establishes relationships both between them and between individual figures, however, is not yet aware of the commonality between figures.

At the third level, the child is able to establish connections between properties and structure figures, connections between the properties themselves. The transition from one level to another is not spontaneous, running in parallel biological development person and depending on age. It occurs under the influence targeted training, which helps accelerate the transition to more high level. Lack of training hinders development. Training should therefore be organized in such a way that, in connection with the acquisition of knowledge about geometric shapes children also developed elementary geometric thinking.

Cognition geometric shapes, their properties and relationships broadens the horizons of children, allows them to more accurately and diversified perceive the shape of surrounding objects, which has a positive impact on their productive activity (for example, drawing, modeling).

Great importance in development geometric thinking and spatial submissions have transformation actions figures(make a square from two triangles or make two triangles from five sticks).

All these types of exercises develop spatial ideas and beginnings of children's geometric thinking, form they have the ability to observe, analyze, generalize, highlight the main, essential and at the same time educate such personality traits as focus and perseverance.

So, in preschool age, mastery of perceptual and intellectual systematization occurs geometric shapes. Perceptual activity in cognition figures advances the development of intellectual systematization.

Bibliography

1. Beloshistaya A.V. Acquaintance with geometric concepts/ A. White-haired // Preschool upbringing. - 2008. - No. 9. - p. 41- 51

2. Wenger L. A. Upbringing sensory culture of the child / L. A. Venger E. G. Pilyugina, N. B. Wenger. - M. : Education, 1988.- 144 p.

3. Upbringingand teaching children of the fifth year of life: book for kindergarten teacher /(A. N. Davidchuk, T. I. Osokina, L. A. Paramonova, etc.); edited by V.V. Kholmovskoy. - M. : Education, 1986. - 144 p.

4. Gabova M. A. Introducing children to geometric shapes / M. A. Gabova // Preschool upbringing. - 2002. - No. 9. - p. 2-17.

5. Didactic games and sensory exercises education of preschool children: (teacher's manual kindergarten / ed. L.A. Venger). - M. : Education, 1978. - 203 p.

6. Kerbs E. V. Mathematical leisure / E. V. Kerbs // Child in kindergarten. - 2008. - No. 3. - p. 21-23.

7.Mathematics in kindergarten: (manual for kindergarten teachers. garden / compiled by G. M. Lyamina). - M. : Education, 1977. - P. 224 - 228.

8. Metlina L. S. Mathematics in kindergarten: (manual for kindergarten teachers. garden)/ L. S. Metlina. - M. : Education, 1994. - 256 p.

Geometric figures are a complex of points, lines, solids or surfaces. These elements can be located both on the plane and in space, forming a finite number of straight lines.

The term “figure” implies several sets of points. They must be located on one or more planes and at the same time limited to a specific number of completed lines.

The main geometric figures are the point and the straight line. They are located on a plane. In addition to them, among simple figures there is a ray, a broken line and a segment.

Dot

Straight

This figure is completely placed in one plane. A straight line does not have a specific mathematical definition, since it consists of a huge number of points located on one endless line, which has no limit or boundaries.

There is also a segment. This is also a straight line, but it starts and ends from a point, which means it has geometric restrictions.

Several segments that are sequentially connected to each other by ends at a common point and are not located on the same straight line are usually called a broken line.

Corner

Geometric figures, the names of which we discussed above, are considered key elements used in the construction of more complex models.

An angle is a structure consisting of a vertex and two rays that extend from it. That is, the sides of this figure connect at one point.

Plane

Any smooth bounded surface can be considered a plane. This could be an ironing board, a piece of paper, or even a door.

Quadrilaterals

A parallelogram is a geometric figure whose opposite sides are parallel to each other in pairs. Among the particular types of this design are diamond, rectangle and square.

A rectangle is a parallelogram in which all sides touch at right angles.

A square is a quadrilateral with equal sides and angles.

Trapezoid

Geometric shapes can be completely different and bizarre. Each of them has a unique shape and properties.

A trapezoid is a figure that is somewhat similar to a quadrilateral. It has two parallel opposite sides and is considered curved.

Circle

This geometric figure implies the location on one plane of points equidistant from its center. In this case, a given non-zero segment is usually called a radius.

Triangle

This is a simple geometric figure that is very often encountered and studied.

A triangle is considered a subtype of a polygon, located on one plane and limited by three edges and three points of contact. These elements are connected in pairs.

Polygon

The vertices of polygons are the points connecting the segments. And the latter, in turn, are considered to be parties.

Volumetric geometric shapes

prism;
sphere;
cone;
cylinder;
pyramid;

These bodies have something in common. All of them are limited to a closed surface, inside of which there are many points.

Volumetric bodies are studied not only in geometry, but also in crystallography.

Curious facts

Surely you will be interested in reading the information provided below.

Geometry was formed as a science back in ancient times. This phenomenon is usually associated with the development of art and various crafts. And the names of geometric figures indicate the use of the principles of determining similarity and similarity.
Translated from ancient Greek, the term “trapezoid” means a table for a meal.
If you take different shapes whose perimeter is the same, then the circle is guaranteed to have the largest area.
Translated from Greek, the term “cone” means a pine cone.
There is a famous painting by Kazemir Malevich, which, since the last century, has attracted the views of many painters. The work “Black Square” has always been mystical and mysterious. The geometric figure on the white canvas delights and amazes at the same time.

There are a large number of geometric shapes. They all differ in parameters, and sometimes even surprise in shape.

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 figures. 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 figure 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 identical opposite sides. Just like a square, a rectangle's angles are all 90 degrees.

You can find many objects shaped like a rectangle: cabinets, household 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, a human face, galaxies, etc. have an oval shape.

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 couple of spicy ones.

You can study a rhombus with the help of visual aids - a drawn picture or a three-dimensional object.

Memorization techniques

Geometric shapes are easy to remember by name. 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 figures and their analogies from the surrounding world.

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.

Geometric volumetric figures are solids, which occupy a non-zero volume in Euclidean (three-dimensional) space. These figures are studied by a branch of mathematics called “spatial geometry”. Knowledge about the properties of three-dimensional figures is used in engineering and the natural sciences. In the article we will consider the question of geometric three-dimensional figures and their names.

Geometric solids

Since these bodies have a finite dimension in three spatial directions, a system of three is used to describe them in geometry coordinate axes. These axes have the following properties:

They are orthogonal to each other, that is, perpendicular.
These axes are normalized, meaning the basis vectors of each axis are the same length.
Any of the coordinate axes is the result vector product two others.

Speaking about geometric volumetric figures and their names, it should be noted that they all belong to one of 2 large classes:

Class of polyhedra. These figures, based on the name of the class, have straight edges and flat faces. A face is a plane that limits a shape. The point where two faces join is called an edge, and the point where three faces join is called a vertex. Polyhedra include the geometric figure of a cube, tetrahedrons, prisms, and pyramids. For these figures, Euler's theorem is valid, which establishes a connection between the number of sides (C), edges (P) and vertices (B) for each polyhedron. Mathematically, this theorem is written as follows: C + B = P + 2.
Class of round bodies or bodies of revolution. These figures have at least one surface forming them that is curved. For example, a ball, a cone, a cylinder, a torus.

As for the properties of volumetric figures, the two most important of them should be highlighted:

The presence of a certain volume that a figure occupies in space.
The presence of a surface area for each volumetric figure.

Both properties for each figure are described by specific mathematical formulas.

Let us consider below the simplest geometric volumetric figures and their names: cube, pyramid, prism, tetrahedron and ball.

Cube figure: description

The geometric figure cube is a three-dimensional body formed by 6 square planes or surfaces. This figure is also called a regular hexahedron, since it has 6 sides, or a rectangular parallelepiped, since it consists of 3 pairs of parallel sides that are mutually perpendicular to each other. They call it a cube whose base is a square and whose height is equal to the side of the base.

Since a cube is a polyhedron or polyhedron, Euler's theorem can be applied to it to determine the number of its edges. Knowing that the number of sides is 6, and the cube has 8 vertices, the number of edges is: P = C + B - 2 = 6 + 8 - 2 = 12.

If we denote the length of the side of a cube with the letter “a”, then the formulas for its volume and surface area will look like: V = a 3 and S = 6*a 2, respectively.

Pyramid figure

A pyramid is a polyhedron that consists of a simple polyhedron (the base of the pyramid) and triangles that connect to the base and have one common vertex (the top of the pyramid). The triangles are called the lateral faces of the pyramid.

The geometric characteristics of a pyramid depend on which polygon lies at its base, as well as on whether the pyramid is straight or oblique. A straight pyramid is understood to be a pyramid for which a straight line perpendicular to the base, drawn through the top of the pyramid, intersects the base at its geometric center.

One of the simple pyramids is a quadrangular straight pyramid, at the base of which lies a square with side “a”, the height of this pyramid is “h”. For this pyramid figure, the volume and surface area will be equal: V = a 2 *h/3 and S = 2*a*√(h 2 +a 2 /4) + a 2, respectively. Applying Euler's theorem for it, taking into account that the number of faces is 5 and the number of vertices is 5, we obtain the number of edges: P = 5 + 5 - 2 = 8.

Tetrahedron figure: description

The geometric figure tetrahedron is understood as a three-dimensional body formed by 4 faces. Based on the properties of space, such faces can only represent triangles. Thus, a tetrahedron is a special case of a pyramid, which has a triangle at its base.

If all 4 triangles forming the faces of a tetrahedron are equilateral and equal to each other, then such a tetrahedron is called regular. This tetrahedron has 4 faces and 4 vertices, the number of edges is 4 + 4 - 2 = 6. Applying standard formulas from plane geometry for the figure in question, we obtain: V = a 3 * √2/12 and S = √3*a 2, where a is the length of the side of an equilateral triangle.

It is interesting to note that in nature some molecules have the form regular tetrahedron. For example, a methane molecule CH 4, in which the hydrogen atoms are located at the vertices of the tetrahedron and are connected to the carbon atom by covalent chemical bonds. The carbon atom is located at the geometric center of the tetrahedron.

The tetrahedron shape, which is easy to manufacture, is also used in engineering. For example, the tetrahedral shape is used in the manufacture of anchors for ships. Note that NASA's Mars Pathfinder space probe, which landed on the surface of Mars on July 4, 1997, also had the shape of a tetrahedron.

Prism figure

This geometric figure can be obtained by taking two polyhedra, placing them parallel to each other in different planes of space, and connecting their vertices accordingly. The result will be a prism, two polyhedra are called its bases, and the surfaces connecting these polyhedra will have the shape of parallelograms. A prism is called straight if its sides (parallelograms) are rectangles.

A prism is a polyhedron, so it is true for it. For example, if the base of the prism is a hexagon, then the number of sides of the prism is 8, and the number of vertices is 12. The number of edges will be equal to: P = 8 + 12 - 2 = 18. For a straight line a prism of height h, at the base of which lies a regular hexagon with side a, the volume is equal to: V = a 2 *h*√3/4, the surface area is equal to: S = 3*a*(a*√3 + 2*h).

Speaking about simple geometric volumetric figures and their names, we should mention the ball. A volumetric body called a ball is understood as a body that is limited to a sphere. In turn, a sphere is a collection of points in space equidistant from one point, which is called the center of the sphere.

Since the ball belongs to the class of round bodies, there is no concept of sides, edges and vertices for it. the sphere bounding the ball is found by the formula: S = 4*pi*r 2, and the volume of the ball can be calculated by the formula: V = 4*pi*r 3 /3, where pi is the number pi (3.14), r - radius of the sphere (ball).