Tangram shapes printables

Puzzles with objects logic puzzles with common household items (matches, coins, card puzzles).

Printed puzzles printed or drawn "pictures" in which you have to draw some symbols according to certain rules (crossword puzzles, rebuses).

Mechanical puzzles items specially made as puzzles (Rubik's cube, Rubik's snake, puzzles, tangrams).

So what is Tangram?

Tangram (from the Chinese "seven boards of skill") - a puzzle consisting of seven tans (flat geometric figures) obtained by dividing a square into seven parts - 2 large, 2 small and 1 medium triangle, 1 small square and a parallelogram that is folded in a certain way to obtain another, more complex figure (depicting a person, an animal, a household item, a letter or number, etc.).

The figure to be obtained is usually given as a silhouette or outer contour. When solving the puzzle, two conditions must be met: first, all seven tangram figures must be used, and second, the figures must not overlap.

The basic element of the tangram is the tan. Tanya can be obtained by cutting the square initially into two large equal triangles, then according to the figure. The minimum number of basic pieces equal to seven leads to an ingenious simplicity of combinations. To make a tangram, you will need a puzzle template, colored cardboard, and scissors. You can also make a puzzle out of plastic boxes from CDs or plywood.

Origin of the name "Tangram" and distribution of the game.

It is impossible to establish the exact origin of this name. According to one version, it was given to the puzzle by people who lived on the banks of the Tanka River in China. They were famous merchants. Sailors from the West who visited Chinese ports probably learned how to play the tangram by communicating with the locals, and then brought the puzzle back to their homeland.

According to another version, this name comes from the old English word "tangram", meaning "puzzle". At 1903 Sam Loyd described in detail the origin of the tangram. The seven tangram figures were associated with the Moon, Mars, Mercury, Jupiter, Venus, Saturn and the Sun - with seven celestial bodies known from ancient times and giving the name to the days of the week. In his book, Sam Loyd presented 652 figures that can be folded from the details of a tangram. Some figures were borrowed from Chinese books, others he invented himself.

The earliest edition in which tangram figures were presented appeared in China in 1813, although only references to it have survived in later publications of 1815.

At that time, tangram as an exciting game was already very popular.

At the beginning of the 19th century, the game quickly spread throughout Europe and America as a result of trade relations with China. The market was flooded with publications and board games with tangram figures. In England, France, Italy, Germany, Holland, Denmark, Sweden, Switzerland and Austria, the puzzle became more and more popular. Such prominent personalities as Lewis Carroll and Edgar Allan Poe did not hide their predilection for her.

A bit of history

The first legend: the broken tile version.

More than 4000 thousand years ago, a porcelain tile fell out of the hands of one person and broke into seven pieces. Frustrated, he hurriedly tried to fold it, but each time he received more and more interesting images. This lesson turned out to be so fascinating that subsequently a square made up of seven geometric figures was called the Board of Wisdom.

The second legend: three wise men invented "Shi-Chao-Chu".

The appearance of this Chinese puzzle is associated with a beautiful legend. Almost two and a half thousand years ago, the long-awaited son and heir was born to the elderly emperor of China. Years passed. The boy grew up healthy and quick-witted beyond his years. One thing bothered the old emperor: his son, the future ruler of a vast country, did not want to study. It gave the boy more pleasure to play with toys all day long. The emperor called three wise men to himself, one of whom was known as a mathematician, the other became famous as an artist, and the third was a famous philosopher, and ordered them to come up with a game, having fun with which, his son would comprehend the beginnings of mathematics, learned to look at the world around him with the gaze of an artist , would become patient, like a true philosopher, and would understand that often complex things are made up of simple things. Three wise men came up with "Shi-Chao-Chu" - a square cut into seven parts.

The third legend: seven books of Tan.

More than 4000 years ago, seven books about tangrams were compiled in China, each of which has exactly a thousand figures.

According to Loyd's legend, Tang was a legendary Chinese sage who was worshiped as a deity by his countrymen.

He arranged the figures in his seven books according to the seven stages in the evolution of the earth. His tangrams begin with symbolic representations of chaos and the yin and yang principle. Then the simplest forms of life follow, as we move along the tree of evolution, figures of fish, birds, animals and humans appear. Along the way, in various places, images of what has been created by man come across: tools, furniture, clothing and architectural structures.

One of the "famous" Chinese proverbs: "Only a fool would undertake to write the eighth book of Tang. "

Rules of the game:

The classic tangram rules are very simple. The game consists in adding geometric shapes, letters, ciyr, silhouettes of animals, plants, people, objects from puzzle pieces - everything that fantasy tells.

• Each assembled figure must include all seven elements.

• When composing the figures, the elements must not overlap each other.

• Shape elements must touch each other.

• Start by finding the location of the largest triangle.

The result of the game is a planar silhouette image. It is conditional, schematic, but the image is easily guessed by the main characteristic features of the object: its structure, proportional ratio of parts and shape.

Tangram application.

The scope of "Tangram" is much wider than just a game. From the pieces of the puzzle, you can compose the studied geometric shapes (triangle, square, parallelogram, trapezoid, rectangle), calculate their areas, and compare these shapes using overlay.

In 1942, Chinese mathematicians showed that 13 convex figures can be added from the details of a tangram alone, which are presented below.

Also tangram is a universal tool with which you can explain the Pythagorean theorem. To do this, take a piece of paper and trace the outline of a small triangle on it. Then we draw squares in which one of the sides corresponds to one side of the triangle. Get the shape in the picture. The Pythagorean theorem states that the sum of the squares of the legs (b and c in the figure) of a right triangle is equal to the square of the hypotenuse (a). In this case, this is easily seen thanks to the details of the tangram.

=

The most important theorem of geometry is clearly and simply proved.

And there are a number of geometric relationships between the details of the tangram.

Area ratio:

• The area of ​​the large triangle is twice the area of ​​the middle triangle.

• Medium triangle, square and parallelogram have the same area.

• The area of ​​the middle triangle is twice the area of ​​the small triangle.

The ratio between sides and angles makes it possible to build various figures from tangram parts by attaching parts to each other. There are more than 7,000 different combinations in total.

The scope of "Tangram" is much wider than just a game: it can be found in fashion design, architecture and landscape design.

Conclusion.

Tangram is one of the amazing puzzles that almost anyone can get carried away with. For mathematicians, it serves as an inexhaustible source of geometric relations. Teachers use the tangram as a visual aid. Collectors value wood and ivory tangrams, as well as historical editions dedicated to rich collections of figures. It is possible to play with a tangram, the details of which are cut out from a sheet of paper, and for those who only recognize games with a keyboard and a screen, there are all kinds of computer programs for tangrams.

At the beginning of my work, I assumed that this ancient puzzle would help me in my studies. My hypothesis was confirmed, since indeed with the help of the Tangram I learned useful geometric information.

We also have an interesting board game at home. This elegant antique puzzle, surprising with the simplicity of the details and the variety of shapes that can be made from them, still fascinates connoisseurs, whatever their age.

It seems to me that games develop children, they teach them to find the right solution, to find a way out of a difficult game situation. Games not only occupy leisure, but also teach.

In general, puzzle games are a good relaxation from difficult daily problems and they are just interesting!

References.

1. I.F. Sharygin, L.N. Erganzhieva: "Visual geometry, grades 5-6".

2. G. K. Muravin, O. V. Muravina: "Mathematics, Grade 5".

3. L. Carroll: Alice in Wonderland.

4. Internet resources:

http//www.yandex.ru/

http//www.rambler.ru/

http://ru.wikipedia.org/wiki/Tangram

Project This wonderful tangram | Educational Social Network

MBOU "Likino - Dulevskaya Basic Educational School No. 4"

Project

Research work

in mathematics on the topic:

were performed by students of grade

Head: Mathematics teacher

Application of the tangram ________________________________ page 11

Other puzzles _________________________________ page 15

Conclusion _________________________________ page 19

References _____________________ page 20

Introduction.

At an extracurricular math activity, I heard about an ancient Chinese game called the tangram puzzle. I was very interested in this game. I wanted to learn as much as possible about the tangram. I decided to study in detail the history of this puzzle and explore the possibilities of this game, its application in the form of a game.

Therefore, the purpose of this work is:

To study the history of the emergence of the Tangram puzzle game and explore its application.

Puzzle toys for all time. Before the advent of computer and the rapid development of board games, one of the main entertainment for most people was the Tangram puzzle game. Nowadays, a lot of people are addicted to puzzles. They are loved not only by children, but also by adults. The game helps to develop logical thinking, geometric intuition. This is a way of distraction from everyday problems and is aimed at the development of various thought processes - comparison, generalization, sequencing, determining the relationship "whole" - "part".

What is a tangram?

A puzzle is a difficult task that usually requires quick wit rather than high-level special knowledge. There is no generally accepted classification of puzzles, they can only be conditionally divided into several groups:

➢ Oral puzzles - tasks, the full condition of which can be communicated orally and does not require any additional objects (riddles, charades) to solve.

➢ Puzzles with objects - logical tasks with ordinary household items (matches, coins, card puzzles).

➢ Printed puzzles - printed or drawn "pictures" in which you need to draw some symbols according to certain rules (crossword puzzles, rebuses).

➢ Mechanical puzzles - items specially made as puzzles (Rubik's cube, Rubik's snake, puzzles, tangrams).

Literally, the word tangram means "seven boards of mastery." Tangram is a puzzle consisting of seven thanes (flat geometric figures) obtained by dividing a square into seven parts - two large (1, 2), two small (3, 4) and one middle triangle (5), one square (6) and one parallelogram (7), which are folded in a certain way to obtain another, more complex, figure (depicting a person, animal, household item, letter or number, etc. ). The figure to be obtained is usually specified in the form of a silhouette or an external contour. When solving the puzzle, two conditions must be met: first, all seven tangram figures must be used, and second, the figures must not overlap.

The basic element of the tangram is the tan. Tanya can be obtained by cutting the square initially into two large equal triangles, then according to the figure. The minimum number of basic pieces equal to seven leads to an ingenious simplicity of combinations.

Tangram legends

Tangram is a very ancient puzzle game. It appeared in China over

4000 years ago. There are a number of versions and hypotheses about the emergence of the game "Tangram".

The first legend: the broken tile version.

More than 4000 thousand years ago, a porcelain tile fell out of the hands of a man and broke into seven pieces. Frustrated, he hurriedly tried to fold it, but each time he received more and more interesting images. This lesson turned out to be so fascinating that subsequently a square made up of seven geometric figures was called the Board of Wisdom.

The second legend: three wise men invented "Shi-Chao-Tyu".

The appearance of this Chinese puzzle is associated with a beautiful legend. Almost two and a half thousand years ago, the long-awaited son and heir was born to the elderly emperor of China. Years passed. The boy grew up healthy and quick-witted beyond his years. One thing bothered the old emperor: his son, the future ruler of a vast country, did not want to study. It gave the boy more pleasure to play with toys all day long. The emperor called three wise men to himself, one of whom was known as a mathematician, the other became famous as an artist, and the third was a famous philosopher, and ordered them to come up with a game, having fun with which, his son would comprehend the beginnings of mathematics, learned to look at the world around him with the gaze of an artist , would become patient, like a true philosopher, and would understand that often complex things are made up of simple things. Three wise men came up with "Shi-Chao-Chu" - a square cut into seven parts.

The third legend: seven books of Tan.

“In the notes of the late Professor Challenor, which fell into the hands of the author,” Loyd stated, “there is information that seven books on tangrams, each of which has exactly a thousand figures, were compiled in China more than 4000 years ago. These books have now become so rare that in the forty years that Professor Challenor spent in China, he only once managed to see the first edition of the first of seven volumes (preserved in full) and several scattered fragments of the second volume.

According to Loyd's legend, Tang was a legendary Chinese sage who was worshiped as a deity by his countrymen. He arranged the figures in his seven books according to the family stages in the evolution of the earth. His tangrams begin with symbolic representations of chaos and the yin and yang principle. Then the simplest forms of life follow, as we move along the tree of evolution, figures of fish, birds, animals and humans appear. Along the way, in various places, images of what was created by man come across: tools, furniture, clothing and architectural structures. Loyd frequently cites the sayings of Confucius, the philosopher Shufutse, the commentator Li Huangzhang, and the fictional Professor Challenor. Li Huangzhang is mentioned because, according to legend, he knew all the figures from the seven books of Tang before he could speak. There are also references in Loyd to "famous" Chinese proverbs such as "Only a fool would undertake to write the eighth book of Tang."

The first image of a tangram (1780) was found on a woodcut by the Japanese artist Utomaro, where two girls fold the figures. The name "tangram" originated in Europe, most likely from the word "tan" (which means "Chinese") and the root "gram" (translated from Greek "letter") At first, it was used not for entertainment, but for teaching geometry .

Tangram in literary works

Lewis Carroll

We all know the book “Alice in Wonderland” by L. Carroll (Charles Lutwidge Dodgson) well. However, this is not his only work. In The Fashionable Chinese Puzzle, he writes that the tangram was the favorite game of Napoleon Bonaparte, who, having lost his throne, spent long hours in exile on Saint Helena, "exercising his patience and resourcefulness."

Edgar A. Poe

One of the fans of the game was Edgar A. Poe. His tangram is made of ivory and is currently in the New York Public Library.

The well-known writer and diplomat Robert Van Gulik built the whole plot of the book around the tangram in his novel “Killing with Nails”. From the pieces of the puzzle, you can compose the studied geometric shapes (triangle, square, parallelogram, trapezoid, rectangle), calculate their areas, and compare these shapes using overlay.

We are interested in the Tangram puzzle as a game, because you can spend your time creatively. It is fascinating that more complex compositions can be made from simple geometric shapes.

The essence of the game consists in constructing various subject silhouettes on a plane, resembling animals, people, household items, vehicles, letters, numbers, flowers, etc. In total, there are more than 7,000 different combinations. The most common of them are the figures of animals, birds and humans.

Rules of the game:

➢ Each completed piece must include all seven elements.

➢ When composing figures, the elements must not overlap each other.

➢ The elements of the figures must be adjacent to each other.

➢ Start by finding the location of the largest triangle.

The result of the game is a planar silhouette image. It is conditional, schematic, but the image is easily guessed by the main characteristic features of the object: its structure, proportional ratio of parts and shape.

Types of tasks solved by tangram.

1. It is necessary to fold the figure according to the contour drawing.

2. You need to fold the figure according to the drawing with a solid fill, in which the borders of the elements are not visible.

Then you can practice on your own, creating your own - the simplest images. Thus, one's own imagination develops.

It is possible not to dwell only on the constructive part of the game. Passionate about transferring the resulting silhouettes to paper. You can make a painting, create and work out the background, come up with a plot. And successful compositions can be used to decorate the interior of a room or a play corner.

3. Making a more complex double or triple tangram (two or three sets of seven "tans" are used for this). As an illustration, we can offer the drawing "Playing billiards", given in the book by Ya.I. Perelman "Funny Problems"

Application of tangram

1. Tangram can be used in mathematics lessons to obtain basic information about geometry. Acquaintance with the simplest geometric shapes: square, triangle, rhombus, acquaintance with angles. Comparison of figures by shape, size, area.

Composition of several figures of a new geometric figure: from two triangles - a rhombus, a large triangle, a square, from three - a triangle,

a trapezoid, a parallelogram, etc.

While playing, we memorize the names of geometric shapes, their properties, distinguishing features, examine the forms visually and tactilely-motorly, freely move them in order to obtain a new figure. We develop the ability to analyze simple images, to identify geometric shapes in them and in surrounding objects, to practically modify shapes by cutting and compose them from parts.

2. Tangram can be used in speech therapy groups of kindergarten and elementary school, work is carried out on lexical and grammatical topics, within which children's knowledge of the world around them is clarified and consolidated. Playing with pictures, laying them out, children memorize a variety of speech material, as well as consolidate and automate the sounds set by the speech therapist.

For example, a fairy tale about a girl named Masha.

Once the girl Masha went for a walk in the forest. She rejoiced and ran along the narrow forest paths. Masha ran out into the clearing and saw three very beautiful and fluffy green Christmas trees, Masha admired the Christmas trees, stood near them and suddenly noticed two bunnies: one was sitting under the Christmas tree, saw the girl and got scared, and the other quickly ran away and hid in the bushes. So Masha walked, admiring the Christmas trees, playing with bunnies, listening to the birds singing, and suddenly realized that she was lost. She was not afraid, but found a beautiful magical flower, whispered her cherished desire to him: “I want to be near my house,” and found herself in her house.

3. Tangram in all its manifestations can be found, from fashion design to architecture and landscape design. The most successful use of tangram, perhaps, as furniture. There are also tangram tables and convertible upholstered furniture and the famous Lago wall shelves.

All tangram furniture is very comfortable and functional. Each time it can be modified depending on the mood and desire of the owner. How many different options and combinations can be made from these pretty shelves. The manufacturers themselves released, along with the assembly instructions, several pages with ideas for the library, living room, bedroom and nursery.

Paradoxes

As a variation of the previous type of problems - the solution of a paradox in tangrams of seven parts (an example - where did the little man's leg come from: a paradox discovered by G. Dudeni. As can be seen from the diagram, the first figure is slightly thicker than the second; the area of ​​​​the "leg" is accuracy is equal to the area of ​​the excess strip on the abdomen, indicated by the segment AB).

Other puzzles

Pythagorean puzzle

The Pythagorean puzzle is a square divided into seven parts - 2 squares, 4 triangles and a parallelogram. The visual possibilities of the game are quite large - you can create silhouettes of varying degrees of complexity and complex geometric shapes that resemble household items, animals, birds, etc.

Stomachion game

The ancient Greeks did not only measure land and distances to ships at sea. They loved geometric games. One of them was called "STOMACHION". In this game, it was necessary to add various figures from 14 parts of the square. Archimedes was considered its creator. In 1899, the Swiss historian Heinrich Suter discovered in the book depositories of Berlin and Cambridge an Arabic manuscript "The book of Archimedes on the division of the figure of the stomachion into 14 parts that are in rational relations. " The Danish historian of mathematics Geiberg later confirmed that Archimedes was the creator of the game.

A partition of the stomachion into 14 parts is obtained from a rectangle, one side of which is twice as large as the other.

Yes, the game "Stomachion" requires more patience. After all, it is much more complicated than the game "Tangram", not without reason the word "stomachion" is translated as "infuriating".

The game "Pentamino"

Pentomino (from the ancient Greek penta five, and domino - polyomino) - 12 pieces, each of which consists of five identical squares connected by the sides ("rook's move"). The same word is sometimes called a puzzle, in which such figures are required to be laid in a rectangle or other shapes.

Columbus Egg game

There was an Italian Girolamo Benzoni in the 16th century. He loved to travel. And once at a dinner with Cardinal Mendoza, he met Columbus. This is where the story took place. Christopher Columbus talked about his discovery of America. And suddenly he hears from one of the guests: “How simply new lands are opening up!” Then Columbus suggested "just put the egg upright on the table?" Nobody could do it. Then Columbus hits the egg on the table, flattening one end, and the egg stands upright. Everyone was indignant that they could do it. To which Columbus replied: "You could, but I did it." Since then, the expression "Columbian egg" has been used when talking about a simple and unexpected solution to a complex problem.

A Columbus egg is an egg cut into 10 pieces. Now this puzzle is sold in different versions - wooden, paper, and plastic. On the plane, you need to lay out any shapes that you can think of or you can use a sample. In this case, you can not overlap the parts so that they overlap each other. And it is also necessary to use all the details

Conclusion

Having studied the practical application of the Tangram, I came to the conclusion that by combining the elements of a square cut into pieces on a plane, you can create many new shapes, both geometric and genre - the outlines of animals , people, household items, etc.

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