M. C. Escher

Maurits Cornelis Escher (June 18, 1898 – March 27, 1972) was a Dutch graphic artist known for his often mathematically inspired woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, architecture, and tessellations.

Maurits Cornelis, or Mauk as he came 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, Sara Gleichman. In 1903, the family moved to Arnhem where he took carpentry and piano lessons until he was thirteen years old.

From 1903 until 1918 he attended primary and secondary school. Though he excelled at drawing, his grades were generally poor, and he was required to repeat the course twice. 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 Jessurun de Mesquita, a Jew with Portuguese ancestors with whom he would remain friends for years. In 1922 Escher left the school, having gained experience in drawing and making woodcuts.

In 1922, a crucial year in his life, Escher traveled through Italy (Florence, San Gimignano, Volterra, Siena) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada. He came back 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'Œx, 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.

On April 30, 1955, Escher was awarded a Knighthood of the Order of Orange-Nassau.

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 1970, a retirement home for artists where he could have a studio of his own. He died at the home on 27 March 1972, at 73 years of age.

Escher's first print of an impossible reality was Still Life and Street, 1937. His artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. Well known examples of his work also include Drawing Hands, a work in which two hands are shown, each drawing the other; Sky and Water, in which light plays on shadow to morph fish in water into birds in the sky; 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.

He worked primarily in the media of lithographs and woodcuts, though the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and 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.

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.

Although Escher did not have a mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's work has a strong mathematical component, and more than a few 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.

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

After his journey to the Alhambra, Escher tried to improve upon the art works of the Moors using geometric grids as the basis for his sketches, which he then overlaid 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 wallpaper groups (plane symmetry groups). Utilizing this mathematical concept, Escher created periodic tilings 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. Starting in 1937, he created woodcuts using the concept of the 17 plane symmetry groups.

In 1941, Escher wrote his first paper, 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 integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper. In it, 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 millimeter."

Escher later completed Circle Limit II, III and IV. These works continued to demonstrate his ability to create perfectly consistent mathematical designs. His works brought him fame: he was awarded the Knighthood of the Order of Orange Nassau 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 worked in the media of woodcuts, lithographs, and mezzotints. In his lifetime he created over 150 colored works utilizing the concept of regular division of a plane. Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of 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 and described himself as "irritated" by flat shapes: "I make them come out of the plane."

Escher also studied the mathematical concepts of 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 himself being a mathematician who studied topology.

Escher printed Metamorphosis I in 1937, which was a beginning part of a series of designs that told a story through the use of pictures. These works demonstrated a culmination 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 change of interest from landscape and nature to regular division of a plane.

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.

After 1953, Escher became a lecturer to many organizations. A planned series of lectures in North America in 1962 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.

Many well known museums include original works by Escher in their collections. Some leading public collections include the following: The National Gallery of Art in Washington, D.C., The National Gallery of Canada in Ottawa, The Israel Museum in Jerusalem, The Escher Museum at The Hague, The Netherlands, and the Fine Arts Museums of San Francisco. Escher's work appears in many of the finest private collections including the Schwartz Collection of Boston, the Walker Collection of San Diego, the Vess Collection of Detroit, the Roosevelt Collection of Palm Beach, the Price Collection of Connecticut, and the Elder Collection of San Francisco.

Selected list of works:

* 1920 Trees, ink
* 1920 St. Bavo's, Haarlem, ink
* 1921 Flor de Pascua (The Easter Flower), woodcut/book illustrations
* 1922 Eight Heads, woodcut
* 1923 Dolphins (Dolphins in Phosphorescent Sea), woodcut
* 1928 Tower of Babel, ink and chalk
* 1930 Street in Scanno, Abruzzi, lithograph
* 1930 Castrovalva, lithograph
* 1930 The Bridge, lithograph
* 1930 Palizzi, Calabria, woodcut
* 1930 Pentedattilo, Calabria, lithograph
* 1931 Atrani, Coast of Amalfi, lithograph
* 1931 Ravello and the Coast of Amalfi, lithograph
* 1931 Covered Alley in Atrani, Coast of Amalfi, wood engraving
* 1933 Phosphorescent Sea, lithograph
* 1934 Still Life with Spherical Mirror, lithograph
* 1935 Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), lithograph
* 1935 Inside St. Peter's, wood engraving
* 1935 Portrait of G.A. Escher, lithograph
* 1935 “Hell”, lithograph, (copied from a painting by Hieronymus Bosch)
* 1936 Regular Division of the Plane, series of drawings that continued until the 1960’s
* 1937 Still Life and Street, woodcut
* 1937 Metamorphosis I, woodcut
* 1938 Day and Night, woodcut
* 1938 Cycle, lithograph
* 1938 Sky and Water, woodcut
* 1939-40 Metamorphosis II, woodcut
* 1942 Verbum (Earth, Sky and Water), lithograph
* 1943 Reptiles, lithograph
* 1943 Ant, lithograph
* 1944 Encounter, lithograph
* 1945 Doric Columns, wood engraving
* 1945 Three Spheres I, wood engraving
* 1946 Magic Mirror, lithograph
* 1946 Three Spheres II, lithograph
* 1946 Another World Mezzotint (Other World Gallery), mezzotint
* 1947 Another World (Other World), wood engraving and woodcut
* 1947 Crystal, mezzotint
* 1947 Up and Down aka High and Low, lithograph
* 1948 Drawing Hands, lithograph
* 1948 Dewdrop, mezzotint
* 1948 Stars, wood engraving
* 1949 Double Planetoid, wood engraving
* 1950 Order and Chaos (Contrast), [[Lithography|lithograph]
* 1950 Rippled Surface, woodcut and linoleum cut
* 1951 Curl-up, lithograph
* 1951 House of Stairs, lithograph
* 1951 House of Stairs II, lithograph
* 1952 Puddle, woodcut
* 1952 Gravitation, lithograph and watercolor
* 1952 Cubic Space Division, lithograph
* 1953 Relativity, lithograph
* 1954 Tetrahedral Planetoid, woodcut
* 1955 Compass Rose (Order and Chaos II), lithograph
* 1955 Convex and Concave, lithograph
* 1955 Three Worlds, lithograph
* 1956 Print Gallery, lithograph
* 1957 Mosaic II, lithograph
* 1958 Belvedere, lithograph
* 1958 Sphere Spirals, woodcut
* 1960 Ascending and Descending, lithograph
* 1961 Waterfall, lithograph
* 1963 Möbius Strip II (Red Ants) woodcut
* 1966 Knot, pencil and crayon
* 1967-8 Metamorphosis III, woodcut


* M.C. Escher, The Graphic Work of M.C. Escher, Ballantine, 1971. Includes Escher's own commentary.
* M.C. Escher, The Fantastic World of M.C. Escher, Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.
* Locher, J.L. (2000). The Magic of M. C. Escher. Harry N. Abrams, Inc. ISBN 0-8109-6720-0.
* Ernst, Bruno; Escher, M.C. (1995). The Magic Mirror of M.C. Escher (Taschen Series). TASCHEN America Llc. ISBN 1-886155-00-3 Escher's art with commentary by Ernst on Escher's life and art, including several pages on his use of polyhedra.
* Abrams (1995). The M.C. Escher Sticker Book. Harry N. Abrams. ISBN 0-8109-2638-5 .
* "Escher, M. C.." The World Book Encyclopedia. 10th ed. 2001.
* O'Connor, J. J. "Escher." Escher. 01 2000. University of St Andrews, Scotland. 17 June 2005. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Escher.html.
* Schattschneider, Doris and Walker, Wallace. M. C. Escher Kaleidocycles, Pomegranate Communications; Petaluma, CA, 1987. ISBN 0-906212-28-6.
* Schattschneider, Doris. M.C. Escher : visions of symmetry, New York, N.Y. : Harry N. Abrams, 2004. ISBN 0-8109-4308-5.
* M.C. Escher's legacy: a centennial celebration; collection of articles coming from the M.C. Escher Centennial Conference, Rome, 1998 / Doris Schattschneider, Michele Emmer (editors). Berlin; London: Springer-Verlag, 2003. ISBN 3-540-42458-X (alk. paper), ISBN 3-540-42458-X (hbk).
* M.C. Escher: His Life and Complete Graphic Work; By J. L. Locher, Amsterdam 1981.Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back-Cover Texts.
Virtual Magic is a human knowledge database blog. Text Based On Information From Wikipedia, Under The GNU Free Documentation License. Copyright (c) 2007 Virtual Magic. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

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