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.
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.
Could these trunks have once belonged to a cherry tree, with its shimmering red leaves? Or to an elegant birch tree, nestled close to a mountain stream? In either case, happy little creatures would have been found skittering about under their branches, which would have undoubtedly provided shade for more than one weary, long-forgotten traveler.
The game of the arches could also be called the game of strokes. Each piece is a line that can make drawings in the air, i.e. three-dimensional drawings. Drawing lines in the air and marveling at the forms that are created, pushing the boundaries of balance, interpreting the unexpected abstract and figurative forms that emerge... this is what the game consists of.
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.