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Geometric puzzles theory. Columbovo Egg is an exciting puzzle for children and adults. Schemes and Figures Game Tangram

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Presentation on the topic

Geometric puzzles

Recreation games from geometric figures figurative and plot images.


  • Puzzles - toys for all times. Before the appearance of computer and rapid development board gamesOne of the main entertainment for most people was the game - Puzzle "Tangram". Nowadays, a lot of people are fond of puzzles. They are loved not only by children, but also adults. The game helps to develop logical thinking, geometric intuition. This is a way to distract from everyday problems and aims to develop various thought processes - comparison, generalization, sequence, determination of the relationship of "whole" - "part". All these skills are needed by future mathematicians.
  • Now the puzzles are sold in different versions - both wooden, and paper, and plastic.
  • On the plane it is necessary to lay out any shapes that you think or you can use the sample. At the same time it is impossible to impose parts so that they overlap each other. You must also use all the details.


Game "Tangram"

Tangram ( whale. 七巧板 , pinyin qī Qiǎo Bǎn, letters. "Seven skimmer skill") - puzzle consisting of seven flat figures , which are folded in a certain way to obtain another, more complex, shape (person depicting, animal, household goods, letter, or digit, etc.). The figure that needs to be obtained is usually set as silhouette or external contour. When solving a puzzle, two conditions are required: first - it is necessary to use all the seven Tangram figures, and the second - the figures should not be superimposed on each other.

How many big triangles?

How many little triangles?

How many medium triangles?

How many triangles and what size are they?

Two large two small and one medium


  •  In each collected figure should include all seven elements.
  •  When drawing up the shapes, items should not lean each other.
  •  Elements of figures must adjoin one to another.
  •  Start you need to find the place of the biggest triangle.
  • As a result of the game, a plane silhouette is obtained. It is conditional, schematically, but the image is easily guessed according to the basic characteristic features of the subject: its structure, proportional to the ratio of parts and form.

  • Tangram - very ancient game - Puzzle. She appeared in China more
  • 4000 years ago. There are a number of versions and hypotheses of the game "Tangram".
  • The legend is the first.

Broken tile.

More than 4,000 thousand years ago, a porcelain tile fell out of her hands and crashed into seven parts. Upset, he tried to fold it in a hurry, but every time he received all new interesting images. This lesson turned out to be so fascinating that later the square made from seven geometric shapes was called the wisdom board.


Shi-Chao-Su

  • Legend Second: Three wise men invented "Shi-Chao-Shea."

The appearance of this Chinese puzzle is associated with a beautiful legend.

Almost two and a half thousand years ago, the long-awaited emperor of China was born a long-awaited son and heir. Years passed. The boy grew up healthy and intelligent not in the years. One was disturbed by the old emperor: his son, the future lord of a huge country, did not want to learn. The boy delivered a greater pleasure all day to toys toys. The emperor called for three wise men, one of whom was known as a mathematician, the other became famous as an artist, and the third was a famous philosopher, and commanded them to come up with a game, to having fun, his son would have become the beginning of mathematics, learned to look at the world The artist's close eyes would be patient as a true philosopher, and would understand that often complex things consist of simple things. Three wise men invented "Shi-Chao-Shea" - a square cut into seven parts.

Seven books Tana

  • Legend Third: Seven Books Tana.

"In the notes of the deceased professor of the Chalalanah, who came to the author's hands," said Loyad, "there are information that seven books about Tangramama, each of which has exactly a thousand figures, were drawn up in China over 4,000 years ago. These books have now become such a big rarity that for the forty years that Professor Chelylandor spent in China, he only once managed to see the first edition of the first of seven volumes. "

According to the legend of the Loyad, Tang was the legendary Chinese sage, which his compatriots worshiped as a deity. Figures in their seven books, he placed in accordance with the seven stages in the evolution of the Earth. His tangramas begin with the symbolic images of chaos and the principle "Yin and Yang." Then the simplest forms of life are followed, as they move along the tree of evolution, figures of fish, birds, animals and humans appear. On the way in various places there are images of what is created by a person: tools of labor, furniture, clothing and architectural structures. Loyad often quotes the statements of Confucius, a philosopher named Shufuce, Lee commentator Lee Juanzhan and a fictional professor of Chalalenor. Lee Huangzhan is mentioned in connection with the fact that by legend he knew all the figures from the seven books of Tana before he learned to speak. It is found at the Loyad and links to "famous" Chinese proverbs like "Only a fool would take to write the eighth book of Tana."

  • The first image of Tangram (1780) was found on the xylography of the Japanese artist Tomaro, where two girls fold figures. The name "Tangram" appeared in Europe, most likely, from the word "Tan" (which means "Chinese") and the root of "gram" (translated from the Greek "letter") at first they used not for entertainment, but to teach geometry .

  • Tangram may lead to its origin from names the types of furniture that appeared during the time empire Sun. ., In the future, the word has turned into a set of wooden figures for the game.
  • Writer and Mathematics Lewis Carroll it is considered to be the enthusiast of Tangram. He stored a Chinese book with 323 tasks.
  • W. Napoleon during his expulsion on saint Helena Island there was a set for Tangram and a book containing tasks and solutions.
  • Book Sam. Loyada "The Eight Book Tang" ( english THE EIGHTH BOOK OF TAN ), published in 1903. , Contains the fictional history of Tangram, according to which this puzzle was invented 4 thousand years ago by the Divine named Tan. The book includes 700 tasks, some of which are insoluble.
  • What figure am made up?





  • "The charm of Tangram consists of simplicity of the material and in the apparent unsuitability to create figures with aesthetic attractiveness"

M. Gardner:



  • Columbovo Egg is a winged expression that denotes an unexpectedly simple way out of a predicament.
  • He lived in the 16th century Italian Girolamo Benzoni. He loved to travel. And one day at the dinner at Cardinal Mendos, he met Columbus. There was this story there. According to a legend, when Columbus, during dinner, Cardinal Mendoza told about how he opened America, the century Italian Jirolamo Benzoni said: "What can be easier than opening new earth? " In response to this, Columbus offered him a simple task: how to put an egg on the table vertically? When none of those present could do this, Columbus, taking an egg, broke it from one end and put on the table, showing that it was really simple. Seeing it, everyone protested, saying that they could and they could. What Columbus replied: "The difference is, gentlemen, that you could do it, and I did it in fact."

  • The name "Columbovo Egg" is very suitable for the proposed puzzle. It also has long to break his head over how to collect out of ten pieces of eggs, and the resulting image is usually very simple. This mysterious I. fascinating game refers to the class of geometric designers (tangrams). The game with geometric designers contributes to the development of intelligence, spatial imagination, constructive thinking, combinatorial abilities.

This oval out of 10 parts: among them 4 triangles (2 large and 2 small), 2 figures, similar to a quadrilateral, one side of which rounded shape, 4 figures (large and small), having a similarity with a triangle, but with a rounded one side .


  • . Best of the details of the Puzzle "Columbovo Egg" to form the silhouettes of birds (54 different forms of birds are known), you can also make up the silhouettes of objects, people, animals.
  • What figure am made up?





  • Geometric puzzles - a wonderful means for the development of mind, and also puzzles can be used to create an interior:
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  • http://www.youtube.com/watch?v\u003djclq8xiuk6m.

Kuba Gami ( Cubigami)

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Puzzle is a developing game for all ages aimed at strengthening spatial perception and imagination.



  • What was interesting in class?
  • What is especially remembered?
  • What composition would you prefer? Why?


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  • http: // www.youtube.com/watch?v\u003djclq8xiuk6m.
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  • http://festival.1september.ru/articles/626772. /
  • Animation:
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Games that make thinking will always be popular, no matter how technologically abstract is a century. Puzzles are developing and if they use a visual material, then also figurative. Games based on various shape and size help develop spatial imagination. Tangram, in particular "Columbovo Egg", forms such mental processes as a comparison of part and a whole, analysis of the situation and generalization.

What are the puzzles?

Any task, to solve which you will need to show reality, will relate to puzzles. It does not need special scientific knowledge to search for a response. Here, rather, intuition and creativity will be required.

No special classification puzzles. However, they can be divided into groups depending on what they operate.

  1. The basis of the game is the word. The assignment itself, the course of its solution and the result - everything can be performed only using oral or written speech. This puzzle does not require the attraction of items. Its example is a mystery or charade.
  2. Task using items. It can be folded from any things that will be found in the house: matches or toothpicks, coins or buttons, cards.
  3. Puzzle shown on paper. This includes all kinds of crossword puzzles and rebuses.
  4. Games with specially manufactured items. Popular examples: Puzzles, Rubik Cube, Snake, Columbovo Egg.

What is a geometric puzzle?

For this game, the main figure is divided into parts. Flat, correct and not very details are obtained. The initial figure can be almost any. In Tangram, for example, this is usually a square. And from the name of the puzzle "Columbovo egg" it is clear that there is a oval, which resembles an egg. There are games in which the main figure is a circle or heart.

From the resulting details you need to fold something another, some kind of complex figure. And this drawing should be recognizable. Such a folding can be both arbitrary and in the task. Schemes for drawing drawings can only contain silhouettes or depict the contours of the parts. It all depends on the level of player's training.

How to make a puzzle yourself?

Like any other toy, such designers can be purchased in the store. But it will be more interesting if you make a "Columbovo Egg" with your own hands.

Since the multiple use of the details of the designer is assumed, it is desirable that the material is dense. For example, a solid cardboard or a piece of smooth plastic.

In order to simplify the process of making the game, you can take the basis of oval, which is to lay the same as the egg. But you can spend a little more time and draw an egg.

First you need to draw a circle in which there are two perpendicular diameters. They will become the first lines for which the egg will be cut. Then at the extreme points of one of the segments to carry out two circles with a radius equal to this diameter. Then you need to read the lines connecting three points on the circle, which will give big triangles. Finish them needed on large circles. Draw the upper small circle and lower the same radius. The first will show the border of the egg, and the lower will give three points that will prompt where to draw small triangles.

As a result, it should be 5 pairs of figures that are formed:

  • from large and small triangles;
  • large and small figures resembling triangles, but with one rounded side;
  • details resembling a trapezium, one side of which is curved.

For clarity and easier understanding of how to lay out "Columbovo Egg", the scheme is presented below. The lines for which you need to split the puzzle on the parts are highlighted in red.

In some embodiments of this game to simplify the task, small triangles inside the egg are combined into one.

Rules game with a puzzle

The essence of the task is to fold the figures from the details of the Columbovo Egg designer. It can be people, animals or birds, transport and furniture, flowers, letters and numbers.

In the game there are only two rules that cannot be disrupted:

  • first - you need to use all the details;
  • second - parts should not intersect, they should be applied to each other.

When meeting a puzzle, you can simply consider the details and think about what they look like. It will simplify the game in the "Columbovo Egg". For preschoolers, this item is simply necessary. Because so it will be easier for them to understand how to make figures. In addition, this moment contributes to the development of imagination and the ability to analyze and break the whole part.

As the skills improve the skills with a puzzle, you need to move from simple to complex. First, the schemes must contain lines that show the boundaries of parts. Then they can no longer be.

Folding figures preferably on a white sheet of paper. Then you can circle and draw clarifying details and background. This will help develop imagination and diversify the game.

Possible puzzle schemes

As an example of a simplified version of the game, in which 9 parts, such schemes can be used at the initial stage.

For connoisseurs and lovers, break the heads without auxiliary lines.

No one will remain indifferent. The whole family will be involved in the search for a solution.

The geometric puzzle "Columbovo Egg" is a game-designer for children 3-8 years, which contributes to the development of logical thinking, memory, perfection, sensory and creative abilities. Games of this kind are very popular with the guys.

What are the puzzle games?

Puzzles call any tasks that require to show a mixture and intelligence. For such games, special scientific knowledge is not required. In first place here are logical thinking and creative fantasy.

Usually puzzles are divided into the following groups:

  • Wonderful (riddles, charaks). They do not require the attraction of foreign objects. The basis of the game is oral or written.
  • Subject. These are tasks with the involvement of objects (matches, buttons, toothpicks and others).
  • Puzzles with a picture on paper (rebuses, crosswords).
  • Design Sample Games (Rubik Cube, Snake, Puzzles, Tangles, "Vietnamese Game", "Columbovo Egg" and others).

All games are aimed at the development of logical thinking and the activation of the thought process of the child.

What is a geometric puzzle?

The word "geometry" itself implies the use of any shape in the game. For example, in Tangram, a square was taken as the basis. There are games where the main figure is heart, leaf and others. In the game "Columbovo Egg" the main figure - oval. The main figures in geometric puzzles are divided into a certain number of parts. The "Columbovo Egg" game has 10 parts in its composition:

  • four triangles (two large and two small);
  • two figures similar to a trapezium, with a rounded one side;
  • two large and two small figures, similar to a triangle, with a rounded side.

Rules of the game

Of these parts, the guys must be added to the silhouette of the bird, the animal or something else. But the drawing must be recognized. This may be arbitrary drawing up a new drawing or on the task of the teacher (parent). The game "Columbovo Egg" for preschoolers has the following rules:

  • the child must use all the details by laying out a new figure;
  • parts of the geometric puzzle should be applied to each other (do not apply one to another, they should not intersect).

You can offer children to lay out silhouettes on a white sheet of paper, and after simply circling them along the contour. Then you can add the drawing with the necessary parts and make the background. This will help to diversify the game and will contribute to the development of the creative imagination of the child.

Gradual complication of the game

At first, the child must become acquainted with such a game as "Columbovo Egg". It should be examined with it details, name the main parts, talk about their form, the amount, search similarity with other figures and so on. Let the child himself turn all the parts in his hands, try to fold various combinations of them.

The next stage is a conversation about what these figures can look like, which can be folded. For example, triangles with a rounded side resemble the wings of birds, small triangles - keyboy and so on. Thus, the child learns to relate and compare the puzzle parts with its surrounding items, allocate general, analyze and systematize.

Then the child can be asked to portray any figure of an animal or bird, showing it a scheme with painted parts. The kid must make a silhouette on this sample on the table. Next occurs gradual complication, and the child is already working with diagrams without painted parts.

How to make the game yourself?

This puzzle game is free to buy in the store, but you can make it yourself. There are many schemes and step-by-step instructionsthat will help make it from the girlfriend. You see one of the possible variations in the figure below.

When choosing a material, you should consider the fact that the details will be used repeatedly, so it should be durable. It can be a very dense cardboard or plastic. As a basis, you need to take an oval and lay it as an egg, then the details neatly cut. Everything can be processed to the game!

The game "Columbovo Egg" for children is designed for preschool age, but adults play it in her with pleasure. The designer game is perfect for the organization of family leisure.

Inna Mishavka

Games mathematical content help to form in children cognitive interest, the ability to research and creative search, desire and ability to learn, develop intellectual abilities and independence.

Games- puzzle, or games geometric design, known for a long time. It - "Tangram", "Magic Circle", "Vietnamese game", "Columbovo Egg", "Pythagoras", "Pintamo" etc.

Each game is a kit geometric figures. Such a kit is obtained as a result of dividing one geometric Figure(for example, square in the game "Tangram" or Circle B. "Magic Circle") To several parts. The essence of the game is to recreate on the plane from geometric figuresincluded in the set, silhouettes of items according to the sample, according to the scheme or intention. These games cause great interest in children, contribute to the development of planning activities.

Geometric puzzles Develop the fantasy of the child, spatial representation. During the game, the child learns to make new figures, first create figures according to the sample, then according to the interpretation in the future.

These puzzles are not difficult to make with your own hands. For this you need a dense cardboard or plastic (Take the old plastic folder) or dense felt (Figures from felt like small children). Distribute the sample, cut better by the stationery knife, the game is ready. Cut and play.

Tangarm Scheme

The basis is the square 10x10 cm (or other dimensions, it is divided into 7 figures, as on the sample.

Columbovo Egg

To make the game Columbovo egg we take the basis of oval (for example 15 cm, cut as in the figure. We get 10 parts.

I recommend to make a special envelope for each puzzle. To do this, print the schemes at half a sheet A4, on the other half print the name of the game. We fold in half, glue the edges - the envelope is ready.


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Tangram is the opinion that the history of Tangram has about 4,000 years. However, this is universal delusion. The myth of this created S.Lud. In 1903, having released the Book of the Eighth Book of Tana, in which for the first time published his beautiful version of the ancient origin of the game. The place where the game was invented is China. In China, the title of tangram is unknown, and the game has the name of Shi-Chao-Su (seven inching figures). The creation date can be defined approximately the XVII - XVIII century. The first famous ancient book in Tangram is the collection of figures from seven parts (China 1803). She was published on rice paper.


Each of the seven books about Tangramama, has exactly a thousand figures. These books now have become very rare. One of the books printed by gold on the parchment was found in Beijing by the English soldier, which to sell his find for 300 pounds of sterling to one collector of Chinese antiquity, which kindly provided some of the most exquisite figures for playing in this book.


According to the legend of the Loyad, Tang was the legendary Chinese sage, which his compatriots worshiped as a deity. Figures in their seven books, he placed in accordance with the seven stages in the evolution of the Earth. His tangramas begin with the symbolic images of Chaos and the principle of Yin and Yang. Then the simplest forms of life are followed, as they move along the tree of evolution, figures of fish, birds, animals and humans appear. On the way in various places there are images of what is created by a person: a tool of labor, furniture, clothing and architectural structures. Loaded links to famous Chinese proverbs.


Pentamino Pentamino (from other Domino) - Polyminico from five identical squares, that is, flat figures, each of which consists of five identical squares, connected by the parties ("Purchase"). By the same word Sometimes they call a puzzle in which such figures need to be laid into a rectangle or other forms. There is only one type of domino, two types of trimino and five types of tetramino. Pentamino, the number of different shapes increases to twelve. There are 35 different types of hexamino and 108 heptamo varieties.


Obviously, to cover the chessboard with a size of 8x8 cells alone only trimino is impossible (at least because the number 64 is not divided into 3). Is it possible to cover the same board twenty one direct trimino and one monomino? With the help of a cunning coloring of squares, of which the bones of trimino, in three different colors, the Golomb showed that this is possible only when monomico closes one of the shaded squares. On the other hand, the method of complete mathematical induction can be proved that twenty one trimino and one monomino can be fully covered with a chessboard, regardless of where the monomino is located.


It turns out that the board can be covered with sixteen identical tetramino of any type, except zigzag. Zigzag Tetramino cannot be laid even so as to close at least the strip at the edge of the board. If the board is coloring with multi-colored stripes, you can prove that 15 L-shaped tetramino and one square tetramino cannot form coatings. Collecting board with bands in the form of zigzags, we will prove that the square tetramino plus any combination of direct and zigzag tetramino can also not cover the entire board entirely. When looking at Pentamino, the question involuntarily arises: is it possible from these 12 figures and one square tetramino to fold the usual chessboard of 8x8 cells in size? For the first time, the solution of this task appeared in 1907. It belonged to Henry Djudeni. In the decision of the Dewden, the square tetramino adjoins the side of the board.


Principles of the game 1. Play so that there is always a place for an even number of "bones" (if you play together). 2. You find it difficult to analyze the created position, try to complicate it if possible, so that the enemy is in an even more difficult situation than you.




Stomakhion came up with it 2200 years ago an ancient Greek thinker and mathematician Archimedes (GG. BC), but decided only in 2003. American mathematician Bill Cutler. Resorting to a specially developed computer program, he learned everything possible solutions, without taking into account the rotation of the square and its mirror reflections, there are 536, and including all options


Archimeda tried to establish how many options for new square configurations could exist with its 14 components. This question solves the combinatorics, which turned into an independent discipline only in the XIX century. We do not know whether the Archhymedim managed to solve its own task. Netz came across at her by chance, copying the old Archimedean works from the parchment sheets of the twentieth century, which are considered the latest copies of the original records. But from Parchment, which is kept in Baltimor Walters Art Museum, the monks scraped the old letters and rewrote the document in a new way. When once in the morning, the nets rewrite the parchment, he was brought by a gift from the mail a children's game based on the Stomakhion model. The researcher immediately noticed the similarity of the contents of the package with a pattern on the parchment depicting the cutting of the square. He occurred to him that Archimeda created not a game for children, but the basis of the combinatorics. Eureka!



Conclusion: These games have a thousand-year history. The tendency to geometric mysteries is peculiar to people different epochs and nationalities. These puzzles are interesting to people of any age, but first of all they bring tremendous benefits to children, because they stimulate the figurative, spatial and creative thinking, develop memory, logic and imagination.