Tangrams

This is the normal configuration of the Tangram parts.

The tangram is a very old Chinese game, which consists of forming silhouettes of figures with the seven given pieces without overlapping them. The 7 pieces, called "Tans", are the following:

• 5 triangles, two built with the main diagonal of the same size, the two small ones of the central strip are also of the same size and one of medium size located in a corner.
• 1 square
• 1 parallelogram or romboid

Normally the "Tans" they are stored forming a square.

There are several versions of the origin and popularity of the tangram, one of the most famous with the Latin word "grama" which means written or graphic. Another version says that the origin of the game goes back to the years 618 to 907 of our era, the time in which the Tang dynasty reigned in China, from which its name would derive.

History of tangrams

The Tangram is a puzzle that is made up of 7 pieces: a parallelogram (rhomboid), a square and 5 triangles. The objective of this game is to create figures using the 7 pieces. The pieces should touch but not overlap. According to Chinese historical records, this furniture originally consisted of a set of 6 rectangular tables. Later a triangular table was added and people could arrange the tables to make one big square table. There was another variation later, during the Ming dynasty, and it was made into a game a bit later.

There is a legend that a servant of a Chinese emperor was carrying a very expensive and fragile ceramic mosaic, and he tripped breaking it into pieces. Desperate, the servant tried to reshape the mosaic into a square shape but couldn't. However, he realized that he could make many other shapes out of the pieces.

It is not known with certainty who invented the game or when, since the first Chinese publications in which it appears are from the 18th century, and then the game was already well known in several countries. In China, the Tangram was very popular and was considered a game for women and children.

Starting in the 18th century, several translations of Chinese books were published in America and Europe explaining the Tangram rules, the game was called "the Chinese puzzle" and it became so popular that it was played by children and adults, ordinary people and personalities from the world of science and the arts; the tangram had become a universal diversion. Napoleon Bonaparte became a true Tangram specialist since his exile on the island of Saint Helena.

Paradoxes

A tangram paradox is an apparent fallacy in the composition of figures. For example, two figures composed of the same set of pieces, one of which appears to be a subset of the other. One of these famous paradoxes is that of the two monks, attributed to Dudeney, which consists of two similar shapes, one with foot and one without. The other was proposed by Sam Loyd in The Eighth Book Of Tan:

The seventh and eighth figures represent the mysterious square, built with seven pieces. There is a corner that is suppressed and yet the result still has seven pieces.

These seeming paradoxes are actually fallacies. For example, in the case of the two monks mentioned above, the foot of one of them is actually offset by a slightly larger body of the other.

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  The paradox of the two monks: two similar figures, but one with one foot less.

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  Magic cup paradox, Sam Loyd's book Eighth Book of Tan (1903). Each of these cups was composed using the same seven geometric shapes, but the first one is complete and the others have holes of different sizes.

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  The paradox of the square, of the book of Sam Loyd Eighth Book of Tan (1903).

Figures

One of the many figures that can be made.

As for the figures that can be made with the tangram, most of the European books copied the original Chinese figures, which numbered only a few hundred. By 1900 new figures and geometric forms had been invented and there were approximately more than 900 figures. The first books on the tangram gave more attention to the game itself and its seven components, so that the tangram was produced and sold as an object: cards with the silhouettes, ivory pieces and box-shaped wrappers, etc. A few hundred images appeared in the books, mostly figurative, such as animals, houses, and flowers, along with a sparse depiction of very strange shapes.

Current uses

Today, the Tangram is used for entertainment, in psychology, in physical education, in design, in philosophy and particularly in pedagogy. In the area of teaching mathematics, the Tangram is used to introduce concepts of plane geometry, and to promote the development of psychomotor and intellectual capacities of children, since it allows the playful linking of the concrete manipulation of materials with the formation of abstract ideas..