this column I am happy to transcribe the Colombian newspaper El Espectador speaks about the artist Maurits Escher and his particular way of integrating art and mathematics in a work full of meaning but at the same time defined for simplicity:
The Art of M. Escher
By: Klaus Ziegler
A conspicuous aspect of the relationship between arts and mathematics: how the arts viewed the concept of symmetry.
For mathematics the symmetry of a design means that it remains unchanged after running certain types of transformations. Rotate a square 90 degrees around its center, or to reflect along the diagonal, are examples of symmetries of this figure.
In 1891, the crystallographer E. Fedorov showed the existence of 17 types of possible symmetries for the lattice planes, although for several centuries Islamic artists intuitively knew in the majestic possibilities offered by these changes, and made use of them for covering the two-dimensional space with complex and exquisite tiling.
These motifs inspired to Maurits Cornelis Escher, Dutch graphic artist rather peculiar. Born in 1898, did not work in the style that characterized it until 1941, when he began to experiment with inventive imagery that is now universally known. His method for making patterns based on the gradual complication Details about initial motive.
In a strict sense of order, Escher manages to create images that are true metaphors of mathematical concepts. Used, for example, the progressive reduction of the figures that serve as a template to create the illusion that the repetition is infinite uses Counter changes as a way of expressing the duality in mathematics, in such a way that the gaps appear to repeat on an image are themselves new figures.
Thus, figure and background become ambivalent, and the correspondence between positive and negative ways becomes a great power of seduction.
The concept of relativity did not leave indifferent. Amused him confused with changes in size, relative sizes and the contrasts and positions.
He loved to show the ambiguities and contradictions in our reading of images, creating spaces that are modified, that move and transform before our eyes. One observer judged to be below what happens there, but a sudden shift in point of view it is above! Understanding the logic of change. What seemed to be rising suddenly, is declining.
Towards the end of his life he wrote: "For Above all I am happy with the contact and friendship of mathematicians. I often have good ideas and has sometimes even a significant interaction existed between us. "
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