Escher. The language of an artist between art and mathematics

Abstract

In looking at works of Escher is natural to ask whether there is a geometrical principle underlying its elaboration, which tend to confuse us and deceiving us through the clever use of illusory tricks. It seems that several worlds coexist in the same pictorial space, the orientation of which varies according to the relative position between the eye and flat.
And is it possible to trace stable elements, officers of the points in its system of representation?
This work which attempts to provide an answer to this question was developed on the two prints, "Relativity" and "Tower of Babel," apparently made ??a second oblique perspective. It was investigated whether the apparently irreconcilable worlds of living space had been obtained through projective strict rules or by the artist's creative sensibility. We have tried some sort of confirmation of the artist's words when remarked that "Even though I had no education or knowledge of the exact sciences, I often feel closer to the mathematicians to my fellow artists." The research has its roots in the field of return perspective, which reconstructs the reference (where ever it exists) of the representation and to obtain orthogonal projections of the objects by a rollover. This operation has also enabled us to discover what are the devices put in place to make possible the coexistence of these worlds. With this investigation we were able to go into construction in the activity of the artist, tracing back the steps of his work.