**M.C. Escher**

Maurits Cornelis Escher (Leeuwarden, June 17, 1898 – March 27, 1972 in Laren) was a Dutch mathematical artist known for his woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, and tessellations.

Youth

Maurits Cornelis, or Mauk as he was to be nicknamed, was born in Leeuwarden (Friesland), the Netherlands. He was the youngest son of civil engineer George Arnold Escher and his second wife, Sarah Gleichman. In 1903, the family moved to Arnhem where he took carpentry and piano lessons until the age of thirteen.

From 1912 until 1918 he attended secondary school. Though he excelled at drawing, his grades were generally poor, and he was required to repeat the second form. In 1919 Escher attended the Haarlem School of Architecture and Decorative Arts. He briefly studied architecture, but switched to decorative arts and studied under Samuel Jesserun de Mesquita, an artist with whom he would remain friends for years. In 1922 Escher left the school, having gained experience in drawing and particularly woodcutting. Sadly, de Mesquita, his wife and son were murdered by the Nazis in early 1944.

Marriage and later life

Escher travelled to Italy regularly in the following years. It was in Italy that he first met Jetta Umiker, the woman whom he married in 1924. The young couple settled down in Rome and stayed there until 1935, when the political climate under Mussolini became unbearable. The family next moved to Château-d'Oex, Switzerland where they remained for two years.

Escher, who had been very fond of and inspired by the landscape in Italy, was decidedly unhappy in Switzerland, so in 1937, the family moved again, to Ukkel, a small town near Brussels, Belgium. World War II forced them to move for the last time in January 1941, this time to Baarn, the Netherlands, where Escher lived until 1970.

Most of Escher's better-known pictures date from this period. The sometimes cloudy, cold, wet weather of the Netherlands allowed him to focus intently on his works, and only during 1962, when he endured surgery, was there a time when no new images were created.

Escher moved to the Rosa-Spier house in Laren in the northern Netherlands in 1970, a retirement home for artists where he could have a studio of his own. He died at the home on the 27th of March 1972, he was 73 years of age. Escher and Umiker had three sons.

Works

Well known examples of his work include Drawing Hands, a work in which two hands are shown drawing each other, Sky and Water, in which light plays on shadow to morph fish in water into birds in the sky, and Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.

Escher's work has a strong mathematical component, and many of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle. Many of Escher's works employed repeated tilings called Tessellations. Escher's artwork is especially well-liked by mathematicians and scientists who enjoy his use of polyhedra and geometric distortions. For example, in Gravity, multi-colored turtles poke their heads out of a stellated dodecahedron.

One of his most notable works is the piece Metamorphosis III, which is wide enough to cover all the walls in a room, and then loop back onto itself.

He used lithographs and woodcuts as media. In his graphic art, he portrayed mathematical relationships among shapes and figures to space. Additionally, he explored interlocking figures using black and white to enhance different dimensions. Integrated into his prints were mirror images of cones, spheres, cubes, rings, and spirals. This results in circular waterfalls and endless staircases. (Escher, M. C. 357)

In addition to sketching landscape and nature in his early years, he also sketched insects, which frequently appeared in his later work. His first artistic work was completed in 1922, which featured eight human heads divided in different planes. Later in about 1924, he lost interest in “regular division” of planes, and turned to sketching landscapes in Italy with irregular perspectives that are impossible in natural form.

Mathematical influence in his work emerged in about 1936, when he was journeying the Mediterranean with the Adria Shipping Company. Specifically, he became interested with order and symmetry. Escher described his journey through the Mediterranean as “the richest source of inspiration I have ever tapped.”

After the journey, at the Alhambra Palace, Escher tried to improve upon the art works of Moors and used his sketches as basic geometric grid, which then he built on with additional designs, mainly animals such as birds and lions.

His first study of mathematics, which would later lead to its incorporation into his art works, began with George Pólya’s academic paper on plane symmetry groups sent to him by his brother Berend. This paper inspired him to learn the concept of the 17 plane symmetry groups. Utilizing this mathematical concept, Escher created periodic tiling with 43 colored drawings of different types of symmetry. From this point on he developed a mathematical approach to expressions of symmetry in his art works. For the years following 1937 he created woodcuts using the concept of the 17 plane symmetry groups.

In 1941 Escher wrote his first notebook, now publicly recognized, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. His intention in writing this was to aid himself in progressing the integration of mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this notebook. In this notebook, he 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, an area of mathematics.

Around 1956 Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher’s interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher’s work Circle Limit I demonstrates this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, "[Escher] got it absolutely right to the millimetre."

Escher later completed Circle Limit II, III and IV. These works continued to demonstrate his ability to create perfectly consistent mathematical designs. His works gained him fame: He was awarded the Knighthood of the Oranje Nassau award in 1955. Subsequently he regularly designed art for dignitaries around the world.

In 1958 he published a paper called Regular Division of the Plane, in which he described the systematic buildup of mathematical designs in his artworks. He emphasized, "[Mathematicians] have opened the gate leading to an extensive domain."

Overall, his early love of Roman and Italian landscapes and of nature led to his interest in regular division of a plane. He used the media woodcuts, lithographs, and mezzotints. In his lifetime he created over 150 colored works utilizing the concept of regular division of a plane. Other mathematical principals evidenced in his works include hyperbolic plane on a fixed 2-dimensional plane, and application three-dimensional objects such as spheres, columns, and cubes into his works. For example, in a print called "Reptiles," he combined two and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality to him and described himself as "irritated" by flat shapes: "I make them come out of the plane."

Topology is another mathematical concept he studied in his life. Topology is the study of properties that are left unchanged by continuous deformation. Topology is the founding concept for its branches general (point-set) topology, algebraic topology, and differential topology. Escher learned additional concepts in mathematics from British mathematician Roger Penrose. From the new knowledge he created Waterfall and Up and Down, featuring irregular perspectives similar to the concept of the Möbius strip; Möbius being a mathematician who studied topology.

Escher printed Metamorphosis I in 1933, which was a beginning part of a series of designs that told a story through the use of pictures. These works demonstrated a columniation of Escher’s skills to incorporate mathematics into art. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. This effect symbolizes his life change of interest from landscape and nature to regular division of a plane.

After 1953 Escher was a lecturer to many organizations. A planned series of lectures in North America in 1964 was cancelled due to illness, but the illustrations and text for the lectures, written out in full by Escher, was later published as part of the book Escher on Escher. In July of 1969, he finished his last work before his death, a woodcut called Snakes. It features etchings of patterns that fade to infinity both to the center and the edge of a circle. Snakes transverse the circle and the patterns in it, with their heads sticking out of the circle.

During his life time he painted the self-portraits Reflection in a Glass Ball and Rind, which combined a self-portrait integrated with irregular perspectives. (O'Connor )