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After Escher left Italy and stopped focusing on Italian landscapes in 1936, Escher visited the Mediterranean where he became interested in the order and symmetry of Moorish mosaics. The Moorish mosaics consisted primarily of tessellation's. In an effort to improve upon the Moorish tessellation's which only consisted of shapes Escher started to distort the tessellation's into animals such as birds and lions. This would shape Eschers work for the rest of his life.
In 1937 Escher printed Metamorphosis which tells a story via pictures. This was one of the first well known examples of Escher incorporating mathematics into art through his use of transforming convex polygons into regular patterns in a plane to form a human motif.
After becoming fascinated with the Geometry of art he spent the next year studying plane symmetry groups. This study and his earlier influences lead him to develop a mathematical approach to expressions of symmetry in his prints displayed through a serious of woodcuts.
Escher went on to write his first paper on mathematics in art in 1941, Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. In his paper Escher studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties. By studying these areas, he explored an area that later mathematicians labeled crystallography.
During this time many of Eschers prints started to reflect his growing interest in mathematics and geometric shapes. As he grew more and more knowledgeable of geometric patterns he began to grow interested in representing impossible objects. In 1956 he began to explore representing infinity in two dimensions, which lead to his work with hyperbolic planes. Escher’s works Circle Limit I–IV demonstrate this concept.
In 1958 he further cemented his place in mathematical history through his paper, Regular Division of the Plane, where he described the systematic buildup of mathematical designs in his artworks.
Escher also studied the mathematical concepts of topology and the Möbius strip which can be seen in his works Waterfall and Up and Down.
His mathematical interests led to over 150 woodcuts, lithographs, mezzotints and more created using the concepts of regular division of a plane, topology superposition of a hyperbolic plane, as well as the use of three dimensional objects. These themes can easily be spotted in much of his life's work all the way up to his last work Ringsnakes which represented a culmination of his mathematical concepts, particularly the concept of representing infinity on a two dimensional plane. |