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.
This enigmatic figure has captured the imaginations of geometrists the world over, from the builders of the Egyptian pyramids, where astronomer Thales of Miletus (630 BC) began the study of geometry, to the most advanced investigators. The codes for the formulation of secret keys, the communication system by fax, the improved definition of a photographic reproduction, the transmission of X-ray images, or the storage of sounds on disc, are some of its applications in advanced geometry. We shouldn’t forget that since prehistoric times, and later in ancient history, geometry has been inspired by the same popular culture that has produced the Mudejar coffered ceilings, the prints of fabrics such as Zulu Ndebele, the mosaics of the gates of Babylon, the Greek and Roman pavement patterns, multitudes of musical styles or the creation of a great many modern sculptures and graphic works.
Mosaics makes the most of two of the isosceles triangles´ properties: that which dictates that two of these triangles of the same size are always “congruent”, and the one stating that two of them, placed on the same plane so that the ends of the hypotenuse touch, make a rectangle whose sides are formed by the legs of the triangles. Therefore, one orthogonal grid is formed by the legs and another one by the diagonal lines formed by the hypotenuse. In combination with the two colors, white and black (positive / negative), the mosaic can form four-way sequences based on mathematical, rhythmic or random patterns. Compositions can be made pixel by pixel or set by set, following the intuition of the players’ pathos or adhering strictly to their logos, finding abstract forms as well as figurative and optical illusions. Not coincidentally, the word mosaic is derived from museum, the temple of the Muses.
As noted by Juan Bordes in his book The Childhood of the Vanguard (Ed Chair), “These ideas were already demonstrated by Jean Sébastien Truchet (1657-1729), the French mathematician who applied his mathematical skills to typography, to graphic systematization and to engineering, before being developed by the Dominican monk Douat in publications that inspired the creation of geometric compositions based on this system.”
Simply put, Mosaics is a game of geometric thinking. It is free of rules, allowing you to explore your mind, accompanied by the Muses, while you enjoy exhilarating the moments of inspiration or relive exciting experiences that you can share with those who, so long ago in history, were seduced by this same geometry.
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.
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.
CÍRCULO is a game that involves a very simple mechanical force, pressure, but the results, always surprising, seem haphazard.
The circular ring is placed on a table, and different pieces will be put inside without any order or position. Then, the combination is pressed turning the screw. The pieces are moved by the pressure until they fit and the screw stops. When lifting the ring, it may happen that some parts fall down; those which remain inside will form figures that will surprise us.
How do you play Tangram?
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.