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The Mathematical Art Of M. C. Escher

1597 words - 6 pages

Maurits Cornelis Escher, who was born in Leeuwarden, Holland in 1898, created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas.While he was still in school his family planned for him to follow his father's career of architecture, but poor grades and an aptitude for drawing and design eventually led him to a career in the graphic arts. Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles. This was the more remarkable in that Escher had no formal mathematics training beyond secondary school.Escher used logic of space, by the "logic" of space I mean those spatial relations among physical objects which are necessary, and which when violated result in visual paradoxes, sometimes called optical illusions. All artists are concerned with the logic of space, and many have explored its rules quite deliberately, Picasso for instance.Escher understood that the geometry of space determines its logic, and likewise the logic of space often determines its geometry. One of the features of the logic of space which he often applied is the play of light and shadow on inwardly and outwardly objects. In the picture Cube with Ribbons, the bumps on the bands are our visual clue to how they are intertwined with the cube. However, if we are to believe our eyes, then we cannot believe the ribbons.Another of Escher's chief concerns was with perspective. In any perspective drawing, vanishing points are chosen which represent for the eye the point(s) at infinity. It was the study of perspective and "points at infinity" by Alberti, Desargues, and others during the renaissance that led directly to the modern field of projective geometry.By introducing unusual vanishing points and forcing elements of a composition to obey them, Escher was able to render scenes in which the "up/down" and "left/right" orientations of its elements shift, depending on how the viewer's eye takes it in. In his perspective study for High and Low, the artist has placed five vanishing points: top left and right, bottom left and right, and centre. The result is that in the bottom half of the composition the viewer is looking up, but in the top half he or she is looking down. To emphasize what he has accomplished, Escher has made the top and bottom halves depictions of the same composition.A third type of "impossible drawing" relies on the brain's insistence upon using visual clues to construct a three-dimensional object from a two-dimensional representation, and Escher created many works which address this type of anomaly.One of the most intriguing is based on an idea of the mathematician Roger Penrose's the impossible triangle. In this picture, Waterfall, two Penrose triangles have been combined into one impossible figure. I can see immediately one of the reasons the logic of space must preclude such a construction: the waterfall is a closed system, yet it turns the mill wheel...

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