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.

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.

Related Topics:
Drawing Hands - Morph - Infinite loop - Quirks of perception - Perspective

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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.

Related Topics:
Impossible objects - Necker cube - Penrose triangle - Tessellation - Mathematicians - Scientists - Polyhedra - Geometric - Gravity - Stellated - Dodecahedron

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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.

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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)

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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.

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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.?

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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.

Related Topics:
Alhambra - Moors

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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 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.

Related Topics:
George Pólya - Symmetry group - Wallpaper group

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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.

Related Topics:
1941 - Crystallography

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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, " got it absolutely right to the millimetre."

Related Topics:
Canadian - H.S.M. Coxeter - Hyperbolic plane

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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 order of Oranje Nassau in 1955. Subsequently he regularly designed art for dignitaries around the world.

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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, " have opened the gate leading to an extensive domain."

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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."

Related Topics:
Roman - Mezzotint

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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.

Related Topics:
Topology - Algebraic topology - Differential topology - Roger Penrose - Möbius strip - Möbius

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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.

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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.

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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 )

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Selected list of works

• Trees, ink, (1920)
• St. Bavo's, Haarlem, ink, (1920)
• Flor de Pascua (The Easter Flower), woodcut/book illustrations, (1921)
• Eight Heads, woodcut, (1922)
• Dolphins (Dolphins in Phosphorescent Sea), woodcut, (1923)
• Tower of Babel, woodcut, (1928)
• Landscape at Abruzzi, scratch drawing, ink and chalk, (1929)
• Street in Scanno, Abruzzi, lithograph, (1930)
• Castrovalva, lithograph, (1930)
• The Bridge, lithograph, (1930)
• Palizzi, Calabria, woodcut, (1930)
• Pentedattilo, Calabria, lithograph, (1930)
• Atrani, Coast of Amalfi, lithograph, (1931)
• Ravello and the Coast of Amalfi, lithograph, (1931)
• Covered Alley in Atrani, Coast of Amalfi, wood engraving, (1931)
• Still Life with Spherical Mirror, lithograph, (1934)
• 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, (1935) (copied from a painting by Hieronymus Bosch)
• Regular Division of the Plane, series of drawings, (1936-196?)
• Still Life and Street, woodcut, (1937)
• Metamorphosis I, woodcut, (1937)
• Day and Night, woodcut, (1938)
• Cycle, lithograph, (1938)
• Sky and Water I, woodcut, (1938)
• Metamorphosis II, woodcut, (1939-1940)
• Verbum (Earth, Sky and Water), lithograph, (1942)
• Reptiles, lithograph, (1943)
• Ant, lithograph, (1943)
• Encounter, lithograph, (1944)
• Doric Columns, wood engraving, (1945)
• Three Spheres I, wood engraving, (1945)
• Magic Mirror, lithograph, (1946)
• Three Spheres II, lithograph, (1946)
• Another World Mezzotint (Other World Gallery), mezzotint, (1946)
• Another World (Other World), wood engraving and woodcut, (1947)
• Crystal, mezzotint, (1947)
• Up and Down, lithograph, (1947)
• Drawing Hands, lithograph, (1948)
• Dewdrop, mezzotint, (1948)
• Stars, wood engraving, (1948)
• Double Planetoid, wood engraving, (1949)
• Order and Chaos (Contrast), lithograph, (1950)
• Rippled Surface, woodcut and linoleum cut, (1950)
• Curl-up, lithograph, (1951)
• House of Stairs, lithograph, (1951)
• House of Stairs II, lithograph, (1951)
• Puddle, woodcut, (1952)
• Gravitation, lithograph and watercolor, (1952)
• Cubic Space Division, lithograph, (1952)
• Relativity, lithograph, (1953)
• Tetrahedral Planetoid, woodcut, (1954)
• Compass Rose (Order and Chaos II), lithograph, (1955)
• Convex and Concave, lithograph, (1955)
• Three Worlds, lithograph, (1955)
• Print Gallery, lithograph, (1956)
• Belvedere, lithograph, (1958)
• Sphere Spirals, woodcut, (1958)
• Ascending and Descending, lithograph, (1960)
• Waterfall, lithograph, (1961)
• Möbius Strip II (Red Ants) woodcut, (1963)
• Knot, pencil and crayon, (1966)
• Metamorphosis III, woodcut, (1967-1968)
• Snakes, woodcut, (1969)