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From the second half of the twentieth century onward there has been a groundswell of interest in the relationship between mathematics and art, particularly since 1992 when artists and mathematicians from around the world began holding joint annual conferences to explore old and new ideas about the connections between their disciplines. The popularity in the West of this interdisciplinary study is in no small part due to the unusual drawings and prints made by Maurits Cornelis Escher (1898–1972), a Dutch graphic artist—or “craftsman,†as he wished to be known. Escher was deeply interested in tessellations and “impossible†objects that are not constructible in three dimensions but that can nevertheless be portrayed in two dimensions. While his oeuvre is not thought of as an integral part of twentieth century art, he is greatly appreciated by mathematicians and also by the general public. Among his best-known works are pictures based on Penrose triangles and on the Möbius strip.
He was inspired by knowing and learning from mathematicians including Georg Pólya (1887–1985), Roger Penrose (1931–), and Harold Scott MacDonald “Donald†Coxeter (1907–2003). Escher was introduced to the international mathematics community in 1954 when the organizing committee for the Amsterdam meeting of the International Congress of Mathematicians inaugurated an exhibition of his work at the Stedelijk Museum. After Penrose viewed Escher’s 1953 print Relativity at this exhibition, he and his father, geneticist Lionel Penrose (1898–1972), were inspired to create impossible figures: the Penrose tribar and the Penrose staircase published in the British Journal of Psychology in 1958—the Penroses sent Escher an offprint of the article. Escher subsequently used these in two well-known lithographs: Waterfall (1961), in which water runs in perpetual motion from the base of a waterfall to the top of the waterfall; and Ascending and Descending (1960), which features a building with an impossible staircase which constantly rises or falls (depending on the direction you go around it) but returns to the same level. Coxeter’s field was symmetry in the Euclidean and hyperbolic planes, but he also took pleasure in analyzing the works of artists from a mathematical point of view. Escher began a correspondence with him shortly after the congress, at which they met, and it lasted until his death in 1972. In 1957 Coxeter requested the use of two of Escher’s drawings to illustrate planar symmetry in “Crystal Symmetry and Its Generalizations,†his presidential address to the Royal Society of Canada—in this way Escher’s work spread among the mathematical community. In 1958, Coxeter sent Escher a letter containing a reprint of his address. The response was a request: “Could [you] give me a simple explanation how to construct the following circles, whose centers approach gradually from the outside till they reach the limit?†Coxeter’s reply, meant to be helpful, gave Escher one small piece of useful information; the rest of the lengthy letter was unintelligible to the artist. But from the pictures and his own keen geometric intuition, Escher was able to construct the circles he required, and by 1958 he was the first graphic artist to have used the three main geometries in his works: Euclidean, spherical, and hyperbolic. Coxeter was astounded that an artist, untrained in mathematics, could produce such accurate “equidistant curves†as he did in his 1958 woodcut Circle Limit III. Escher always claimed that he knew little mathematics, but many of his prints are a direct result of using mathematics. Mathematician Doris Schattschneider has said that Escher was really a “secret mathematician,†since much of his work depended on his pursuit of mathematical questions that arose from his interests and his interaction with mathematicians, which he referred to as “Coxetering.†He did, however, write that he preferred to find solutions and understanding by himself.
As well as his artistic and mathematical legacy, Escher had an important influence on crystallographers, who have used his symmetry drawings for analysis. Crystallographer Caroline MacGillavry has pointed out that Escher began a deep study of color symmetry and created a classification system in 1941–42, which was some time before crystallographers became interested in this field of study, which has become very active. The International Union of Crystallography subsequently commissioned Escher to illustrate MacGillavry’s Symmetry Aspects of M. C. Escher’s Periodic Drawings, first published in 1965. Its purpose was to interest “students in the laws which underlie repeating designs and their colorings.â€

And round our way no role model either as in a lot of single parent families.