The novelty of this magnetic Tangram is that it works with a third dimension and includes a new element: the need to strike a balance between the 7 pieces. The attraction between the tans (tangram pieces) is what ultimately sustains the figures and makes their handling so rewarding. As a result the upright figures can be seen and enjoyed from any perspective.
Tangram is no ordinary puzzle. The placement of the ‘tans’ and the observation of the figures come together to confer an aura of enigma and magic to the game, giving the Tangram its own special place in the world of puzzles and riddles. The possibilities that it provides for our imagination are virtually infinite. Much like when we put together a collage, the individual pieces of a Tangram lose their identity and appear before our eyes, magically, as part of a new form.
The puzzle is made up of seven flat, geometric pieces resulting from the dissection of a square. Each one of these pieces is called a ‘tan’ (part, in Chinese). There are 2 large triangles, 1 medium-sized triangle, 2 small triangles, a square and a rhomboid. How is it that the partition of a square in 7 parts – these 7 in particular – can yield such a vast array of fascinating, evocative figures? We have yet to come up with an answer, despite our search in specialized publications and web sites; perhaps the question would best be put to a mathematician.
It may be that the seemingly unsolvable nature of this question is itself part of the fascination that the puzzle holds over us. Or could the answer have something to do with the Chinese legend of the dragon Yu and the God of Thunder? The geometric shape of the square was, after all, of considerable importance in Chinese Antiquity, and a well – known Chinese proverb states that “Infinity is a square with no angles”.
The puzzle, whose popularity spread quickly throughout the Western world in the second half of the 19th century, had an impact on modern drawing as well. The ‘cubist’ nature of the figures helped to expand people’s visual habits, while the preponderance of a new triangular and cube-based drawing led to a renewed methodology of graphic construction. (The Tangram was also one of the sources of the 7th gift of Froebel’s program, which dealt with operations involving surfaces and planes). Its role in novel graphic approaches and methods would subsequently make the Tangram an important precursor of Western artistic vanguards in the late 19th and early 20th centuries such as cubism, vorticism and rayonism.
The puzzle has been used widely, especially in games and exercises involving spatial intuition. Its applications range from infant education to the advanced mathematical treatment of figures, partitions, metric geometry (area and perimeter problems) and Pythagorean and Euclidian mathematics. Archimedes himself (287 – 212 B.C.) came up with his own partition of the square in 14 pieces, each of which had a rational, knowable relation to the whole. He called it ‘Stomachin’ and used it to solve a variety of problems involving mathematical dissection.
As a puzzle, the Tangram can be played with individually or practiced competitively; with two or more Tangram, players can challenge each other to make different figures or to see who can make them fastest.
The 7 ‘tans’ can be used freely to create figures from our imaginations or to reproduce the given models, but in either case there are three basic rules: all 7 of the ‘tans’ must be used in the figure, they have to be in the same plane (in other words, they cannot be mounted on top of each other), and they must all be contiguous, having at least one point of contact with the rest of the pieces.
The 1600 figures compiled include a great variety of human and animal figures as well as objects and geometric shapes. We also find certain ‘paradoxes’, such as the way that two figures can be made that are identical except for one extra element – or a missing one – in one of the figures. For example, two human forms that are identical except for one missing foot, or that differ only in that one is holding something in its hand; or two squares that are the same except that one has a space in the center.
ORIGINS OF THE GAME.
Beyond the fact that it comes from China, little is known about the precise origins of the Tangram. The first written mention appears in a Chinese book from the year 1813. However, there is evidence from the year 1742 of a Japanese puzzle called “ch’ich’ae pan”, (puzzle of of the 7 pieces), a word dating from from the Chu era, which extended from 740 – 300 B.C. This has led a number of investigators to situate the origins of the game in this remote epoch. While the word Tangram was coined a little over a century ago by a North American, in Chinese the game has always been known as ‘the board of wisdom’ or ‘the board of the 7 elements’.
As a result of the Chinese publication from 1813 describing the puzzle, the popularity of the Tangram spread rapidly throughout Europe and North America, making it the Rubic’s Cube of its time. Numerous books were published depicting the figures that could be created. These were initially limited to the several hundred shapes described in Chinese books and texts, but new shapes and forms expanded the number to around 900. In 1973 the Dutch designers Joost Elffers and Michael Schuyt created, with a new, rustic version of the Tangram that they had conceived, 750 new figures, bringing the total number to over 1,600.
A Chinese legend related to the game makes reference to a fight between the God of Thunder and the dragon Yu that caused the sky to fall to the earth in 7 pieces. The pieces were so black that they absorbed all of the world’s light, thereby obliterating the forms of all of the objects on the face of the earth. The dragon, saddened by such a tragic happening, took the 7 pieces and set about constructing the different forms and beings that had existed, starting with the plants, animals and humans.
The novelty of this Tangram is that it works with a third dimension and includes a new element: the need to strike a balance between the ‘tans’. The attraction between the ‘tans’ is what ultimately sustains the figures and makes their handling so rewarding. As a result the upright figures can be seen and enjoyed from any perspective.
Author: Javier Bermejo. Made by: PICO PAO
Mixed, Red, Green, Yellow, Blue, Pink, White, Black
The triangle is the polygon with the fewest number of sides that can be made with straight lines. It is also the most elementary polygon, the primary polygonal unit, the proto-cell with which we can cover an entire flat surface and form all other possible geometric figures.
The cube, an orthogonal parallelepipedic prism of six equal sides, is inextricably linked, from the time of the very first civilizations, to open, inhabitable spaces. For such a simple, sparse and symmetrical shape to achieve any sort of expressiveness there must be some irregularity involved or some relationship with its surroundings.
Objects that we are drawn to – personal adornments, ornaments in general, a feathered embroidery, a necklace, a capital, an eave… - are more often than not imitations of models found in nature: a flower’s petals, a plant’s leaves, a bird’s plumage…We’re struck not only by the beautiful colors of these objects but also by the arrangement of their different elements. When we take objects that are seemingly identical and try to create something new with them we have no choice but to subject ourselves to the laws of physics, letting them guide us in our effort to create something that will mirror the beauty and harmony that exist in nature.
What makes the Pentaminos fascinating is its initial simplicity, so different from the ennigmas and problems described below. Unlike a 1000-piece puzzle, which has a single solution, the Pentaminos, while consisting of only 12 pieces, has thousands of possible solutions.
Altogether there are twelve different Pentaminos, each designated by a different letter of the alphabet: (F, I, L, N, P, T, U, V, W, X, Y, Z). Pentaminos obtained by joining others at their axis or by rotation are not considered to be ‘different’ Pentaminos.