Biography (3/3)

Escher's Relationship to Mathematics Artists and designers who have experimented with tessellations have probably unwittingly performed some mathematical research! M. C. Escher stands out as an example of such an artist and designer. Although Escher did not have a strong background in mathematics, his careful explorations of tilings of the plane were extensive and representative of mathematical research. In fact, Escher once said, "Although I am absolute innocent of training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists" (The Graphic Work of M. C. Escher, New York, 1967, p.9). One of the sources of inspiration for Escher's designs is the Alhambra in Granada, Spain whose ceilings and walls are covered with beautiful ornamentation. During his lifetime M. C. Escher designed over a hundred tessellated patterns, many of which were transformed into the famous works of art that we recognize. Unlike the Islamic designs he saw, almost all of Escher's tilings were designed to resemble recognizable objects, usually living ones. In the Preface to Visions of Symmetry he writes, "without recognizability no meaning and without shade contrast no visibility." Escher means that he values both resemblance to actual objects and careful shading in order to draw attention to the specific shapes used. Escher's work with tilings of the plane embodies many ideas that scientists and mathematicians discovered only after Escher did. For example, the research regarding polychromatic symmetry (symmetry of multiple colors) published in 1951 by Russian crystallographers had been, in a large part, already anticipated by Escher. In 1963 Heinrich Heesch and Otto Kienzle published critical research dealing with something known as the fundamental region, the smallest region that would allow an entire tessellation to be created through a set of isometries. As in the example described earlier, Escher had already developed the necessary ideas regarding fundamental regions years earlier. Nevertheless, in spite of his lack of formal training in mathematics, Escher was influenced by developments in science and mathematics. Many, if not most, of his works of art that involve topology, optical illusions, hyperbolic tessellations, and other advanced mathematical topics were the direct result of collaboration with various mathematicians such as Roger Penrose, J. F. Schouten, H S. M. Coxeter, and J. W. Wagenaar. Web Links Crystallography 101 X-RAY Crystallography Because Escher's artworks have a close affinity to mathematical topics, they have been used not only for visual enjoyment but also for instructional purposes. An example can be cited from an event during the Fifth International Congress of the International Union of Crystallography held in Cambridge, United Kingdom, in 1960. During this gathering, x-ray crystallographers used some of M. C. Escher's works of art to explain the concepts of symmetry and transformations, very important in the field of x-ray crystallography. Another example occurred in a presentation given by the Nobel Prize winner Chen Ning Yang who used "Horseman," one of Escher's famous tessellated works, to explain the symmetry principle of quantum mechanics, a scientific field that deals with particles smaller than even atoms.)   Conclusion Escher truly loved his work and we, as his audience, can understand the beauty of his designs. You may even find a profound enjoyment in creating your own tessellations of irregular shapes as Escher had: "While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures which I am conjuring up. It is as if they themselves decide on the shape in which they choose to appear" ó M. C. Escher (Symmetry Aspects of M. C. Escher's Periodic Drawings, New York, 1976, p.8).   top of the page