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| Escher worked primarily in the media of ] and ], though the few ]s he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.<ref>{{cite web|url=http://www.mcescher.com/Biography/biography.htm |title=The Official M.C. Escher Website – Biography |accessdate=7 December 2013}}</ref> | Escher worked primarily in the media of ] and ], though the few ]s he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.<ref>{{cite web|url=http://www.mcescher.com/Biography/biography.htm |title=The Official M.C. Escher Website – Biography |accessdate=7 December 2013}}</ref> | ||
| Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's ], and several of the worlds which he drew were built around ] such as the ] and the ], named for the British mathematician ].<ref>{{cite journal |last1=Penrose |first1=L.S. |last2=Penrose |first2=R. |title=Impossible objects: A special type of visual illusion |journal=] |year=1958 |volume=49 |pages=31–33 |doi=10.1111/j.2044-8295.1958.tb00634.x | pmid=13536303}}</ref><ref>{{cite journal | last1=Kirousis | first1=Lefteris M. | last2=Papadimitriou | first2=Christos H. | author2-link=Christos Papadimitriou | title=The complexity of recognizing polyhedral scenes | doi=10.1109/sfcs.1985.59 | pages=175–185 | work=] (FOCS 1985) | year=1985}}</ref><ref>{{cite book | last=Cooper | first=Martin | contribution=Tractability of Drawing Interpretation | doi=10.1007/978-1-84800-229-6_9 | isbn=978-1-84800-229-6 | pages=217–230 | publisher=Springer-Verlag | title=Line Drawing Interpretation | year=2008}}</ref> From this knowledge he created works such as '']'' (1961), which makes use of two Penrose triangles. |
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's ], and several of the worlds which he drew were built around ] such as the ] and the ], named for the British mathematician ].<ref>{{cite journal |last1=Penrose |first1=L.S. |last2=Penrose |first2=R. |title=Impossible objects: A special type of visual illusion |journal=] |year=1958 |volume=49 |pages=31–33 |doi=10.1111/j.2044-8295.1958.tb00634.x | pmid=13536303}}</ref><ref>{{cite journal | last1=Kirousis | first1=Lefteris M. | last2=Papadimitriou | first2=Christos H. | author2-link=Christos Papadimitriou | title=The complexity of recognizing polyhedral scenes | doi=10.1109/sfcs.1985.59 | pages=175–185 | work=] (FOCS 1985) | year=1985}}</ref><ref>{{cite book | last=Cooper | first=Martin | contribution=Tractability of Drawing Interpretation | doi=10.1007/978-1-84800-229-6_9 | isbn=978-1-84800-229-6 | pages=217–230 | publisher=Springer-Verlag | title=Line Drawing Interpretation | year=2008}}</ref> From this knowledge he created works such as '']'' (1961), which makes use of two Penrose triangles.<ref name=Seckel2004>{{cite book |last=Seckel |first=Al |title=Masters of Deception: Escher, Dalí & the Artists of Optical Illusion |url=http://books.google.com/books?id=t5IgWas4rJwC&pg=PA262 |year=2004 |publisher=Sterling |isbn=978-1-4027-0577-9 |page=262}}</ref> | ||
| Escher was also fascinated by mathematical objects like the ], which has only one surface. His wood engraving ''Möbius Strip II'' (1963) depicts a chain of ]s marching for ever around over what at any one place are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. | Escher was also fascinated by mathematical objects like the ], which has only one surface. His wood engraving ''Möbius Strip II'' (1963) depicts a chain of ]s marching for ever around over what at any one place are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. | ||
| ⚫ | The mathematical influence in his work emerged around 1936, when he journeyed to the ] with the Adria Shipping Company and became interested in order and ]. Escher described his journey through the Mediterranean as "the richest source of inspiration I have ever tapped." | ||
| ⚫ | ] as in Escher's 1952 work '']''. ]]] | ||
| ⚫ | |||
| ===Platonic and other solids=== | ===Platonic and other solids=== | ||
| ⚫ | ] as in Escher's 1952 work '']''. ]]] | ||
| ⚫ | Escher often incorporated three-dimensional objects such as the ]s such as spheres, tetrahedons and cubes into his works, as well as mathematical objects like ]s and ]. In the print ], 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's artwork is especially well liked by mathematicians and scientists, who enjoy his use of ] and ] distortions. For example, in '']'', multicolored turtles poke their heads out of a ] ]. | ||
| The two towers of ''Waterfall''<nowiki></nowiki>'s impossible building are topped with compound polyhedra, one a ], the other a stellated ] known as ]. Escher had used this solid in his 1948 woodcut '']'', which also contains all five of the ] and various stellated solids, representing stars; the central solid is animated by ]s climbing through the frame as it whirls in space. Escher possessed a 6 cm ] and was a keen enough amateur ] to have recorded observations of ]s.<ref>Locher, 1974. p. 104</ref><ref name=Beech>{{cite journal |title=Escher's ''Stars'' |last=Beech |first=Martin |journal=Journal of the Royal Astronomical Society of Canada |volume=86 |pages=169–177}}</ref><ref name=CoxeterReview>{{cite journal |last=Coxeter |first=H. S. M. |authorlink=Harold Scott MacDonald Coxeter |doi=10.1007/BF03023010 |issue=1 | journal=The Mathematical Intelligencer |pages=59–69 |title=A special book review: M. C. Escher: His life and complete graphic work |volume=7 |year=1985}}</ref> | |||
| ⚫ | Escher often incorporated three-dimensional objects such as the ]s such as spheres, tetrahedons and cubes into his works, as well as mathematical objects like ]s and ]. |
||
| ===Levels of reality=== | ===Levels of reality=== | ||
Revision as of 08:58, 2 November 2015
| M. C. Escher | |
|---|---|
| File:EscherSelf1929.jpgA 1929 self-portrait | |
| Born | Maurits Cornelis Escher (1898-06-17)17 June 1898 Leeuwarden, Netherlands |
| Died | 27 March 1972(1972-03-27) (aged 73) Laren, Netherlands |
| Nationality | Dutch |
| Education | Haarlem School of Architecture and Decorative Arts |
| Known for | Drawing, printmaking |
| Notable work | Relativity, Waterfall, Hand with Reflecting Sphere |
| Awards | Knighthood of the Order of Orange-Nassau |
Maurits Cornelis Escher (/ˈɛʃər/, Template:IPA-nl; 17 June 1898 – 27 March 1972) was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, reflection, symmetry, perspective, and tessellations.
Early life
Maurits Cornelis was born in Leeuwarden, Friesland, in a house that forms part of the Princessehof Ceramics Museum today. 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 attended primary school and secondary school until 1918 when he went to the technical college in Delft.
Known to his friends and family as "Mauk", he was a sickly child, and was placed in a special school at the age of seven and failed the second grade. Although he excelled at drawing, his grades were generally poor. He also took carpentry and piano lessons until he was thirteen years old. From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts. He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched to decorative arts. He studied under Samuel Jessurun de Mesquita, with whom he remained friends for years.
Later life
In 1922, an important year of his life, Escher traveled through Italy (Florence, San Gimignano, Volterra, Siena, Ravello) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada. The intricate decorative designs at Alhambra, which were based on geometrical symmetries featuring interlocking repetitive patterns sculpted into the stone walls and ceilings, were a powerful influence on Escher's works. He returned to Italy regularly in the following years.
In Italy, Escher met Jetta Umiker, whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons: Arthur and Jan.
In 1935, the political climate in Italy (under Mussolini) became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear a Ballila uniform in school, the family left Italy and moved to Château-d'Œx, Switzerland, where they remained for two years.
Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland. In 1937, the family moved again, to Uccle, a suburb of Brussels, Belgium. World War II forced them to move in January 1941, this time to Baarn, Netherlands, where Escher lived until 1970. Most of Escher's better-known works date from this period. The sometimes cloudy, cold and wet weather of the Netherlands allowed him to focus intently on his work. For a time after undergoing surgery in 1962, Escher did not work on new pieces.
Escher moved to the Rosa Spier Huis in Laren in 1970, an artists' retirement home in which he had his own studio. He died at the home on 27 March 1972, aged 73.
Mathematically-inspired work
Further information: Mathematics and artTessellation
In his early years, Escher sketched landscapes and nature. He also sketched insects such as ants, bees, grasshoppers and mantises, which appeared frequently in his later work. His early love of Roman and Italian landscapes and of nature created an interest in tessellation, which he called Regular Division of the Plane; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations 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." He applied the concept of regular division of a plane to over 150 artworks. His woodcut Eight Heads, completed in 1922, features eight human heads divided in different planes.
After his journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the architecture and the tessellated mosaic decorations, 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, fish, and reptiles.
His first study of mathematics, which later led 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). Using this mathematical concept, Escher created periodic tilings with 43 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. His Metamorphosis I (1937) began a series of designs that told a story through the use of pictures. These works demonstrate Escher's skill in incorporating 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. He extended the approach in his piece Metamorphosis III, which is four metres long.
In 1941, Escher summarized his findings in a sketchbook, which he labeled Regelmatige vlakverdeling in asymmetrische congruente veelhoeken ("Regular division of the plane with asymmetric congruent polygons"). His intention in writing this was to aid himself in integrating mathematics into art.
Geometries
Further information: perspective (geometry)
After 1924, he turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. Escher's first print of an impossible reality was Still Life and Street, 1937. In Sky and Water, light plays on shadow to morph the water background behind fish figures into bird figures on a sky background. In Relativity and Ascending and Descending, 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 was interested enough in Hieronymus Bosch's 1500 triptych The Garden of Earthly Delights to recreate part of its right-hand panel, Hell, as a lithograph in 1935. He reused the figure of a Mediaeval woman in a two-pointed headdress and a long gown in his lithograph Belvedere in 1958; the image is, like many of his other "extraordinary invented places", peopled with "jesters, knaves and contemplators". Escher was thus not only interested in possible or impossible geometry, but was in his own words a "reality enthusiast"; he combined "formal astonishment with a vivid and idiosyncratic vision."
Escher 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. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's art had a strong mathematical component, and several of the worlds which he drew were built around impossible objects such as the Penrose triangle and the Penrose stairs, named for the British mathematician Roger Penrose. From this knowledge he created works such as Waterfall (1961), which makes use of two Penrose triangles.
Escher was also fascinated by mathematical objects like the Möbius strip, which has only one surface. His wood engraving Möbius Strip II (1963) depicts a chain of ants marching for ever around over what at any one place are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface.
The mathematical influence in his work emerged around 1936, when he journeyed to the Mediterranean with the Adria Shipping Company and became interested in order and symmetry. Escher described his journey through the Mediterranean as "the richest source of inspiration I have ever tapped."
Platonic and other solids
Escher often incorporated three-dimensional objects such as the Platonic solids such as spheres, tetrahedons and cubes into his works, as well as mathematical objects like cylinders and stellated polyhedra. In the print 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's artwork is especially well liked by mathematicians and scientists, who enjoy his use of polyhedra and geometric distortions. For example, in Gravitation, multicolored turtles poke their heads out of a stellated dodecahedron.
The two towers of Waterfall's impossible building are topped with compound polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron known as Escher's solid. Escher had used this solid in his 1948 woodcut Stars, which also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space. Escher possessed a 6 cm refracting telescope and was a keen enough amateur astronomer to have recorded observations of binary stars.
Levels of reality
Escher's artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. Examples of his interest in the multiple levels of reality in art include Drawing Hands, a work in which two hands are shown, each drawing the other.
Infinity and hyperbolic geometry
Around 1956, Escher started to explore the representation of infinity on a two-dimensional plane. Discussions with the Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's wood engravings Circle Limit I–IV demonstrate this concept. In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter."
Honours and distinctions
After 1953, Escher became a lecturer at many organizations. A planned series of lectures in North America in 1962 was cancelled due to an illness, but the illustrations and text for the lectures, written out in full by Escher, were later published as part of the book Escher on Escher. In July 1969 he finished his last work, a woodcut called Snakes, in which snakes wind through a pattern of linked rings which shrink to infinity toward both the center and the edge of a circle.
Escher was awarded the Knighthood of the Order of Orange Nassau in 1955. Subsequently he regularly designed art for dignitaries around the world.
Legacy
Escher's special way of thinking and rich graphics have had a continuous influence in science and art, as well as in popular culture.
Ownership of the Escher intellectual property and of his art works have been separated from each other. In 1969, Escher's business advisor, Jan W. Vermeulen, author of a biography on the artist, established the M.C. Escher Foundation, and transferred into this entity virtually all of Escher's unique work as well as hundreds of his original prints. These works were lent by the Foundation to the Hague Museum. Upon Escher's death, his three sons dissolved the Foundation, and they became partners in the ownership of the art works. In 1980, this holding was sold to an American art dealer and the Hague Museum. The Museum obtained all of the documentation and the smaller portion of the art works. The copyrights remained the possession of Escher's three sons – who later sold them to Cordon Art, a Dutch company. Control was subsequently transferred to The M.C. Escher Company B.V. of Baarn, Netherlands, which licenses use of the copyrights on all of Escher's art and on his spoken and written text. A related entity, the M.C. Escher Foundation of Baarn, promotes Escher's work by organizing exhibitions, publishing books and producing films about his life and work.
The primary institutional collections of original works by M.C. Escher are the Escher Museum, a subsidiary of the Haags Gemeentemuseum in The Hague; the National Gallery of Art (Washington, DC); the National Gallery of Canada (Ottawa); the Israel Museum (Jerusalem); Huis ten Bosch (Nagasaki, Japan); and the Boston Public Library. Despite wide international interest, his works have rarely been exhibited outside these collections; the first major exhibition in Britain, organized by the Scottish National Gallery of Modern Art, ran in Edinburgh from June to September 2015, and opened in October 2015 in the Dulwich Picture Gallery, London. The poster for the exhibition is based on Hand with Reflecting Sphere, 1935, which shows Escher in his house reflected in a handheld sphere, thus illustrating the artist, his interest in levels of reality in art (e.g., is the hand in the foreground more real than the reflected one?), perspective, and spherical geometry.
Gödel, Escher, Bach by Douglas Hofstadter, published in 1979, discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher's art and the music of J. S. Bach.
The asteroid 4444 Escher was named in Escher's honor in 1985.
Selected 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 also known as Dolphins in Phosphorescent Sea, woodcut (1923)
- Tower of Babel, woodcut (1928)
- 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)
- Phosphorescent Sea, lithograph (1933)
- Still Life with Spherical Mirror, lithograph (1934)
- Hand with Reflecting Sphere also known as 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) (1935)
- Regular Division of the Plane, series of drawings that continued until the 1960s (1936)
- Still Life and Street (his first impossible reality), woodcut (1937)
- Metamorphosis I, woodcut (1937)
- Day and Night, woodcut (1938)
- Cycle, lithograph (1938)
- Sky and Water I, woodcut (1938)
- Sky and Water II, lithograph (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)
- Balcony, lithograph (1945)
- Three Spheres I, wood engraving (1945)
- Magic Mirror, lithograph (1946)
- Three Spheres II, lithograph (1946)
- Another World Mezzotint also known as Other World Gallery, mezzotint (1946)
- Eye, mezzotint (1946)
- Another World also known as Other World, wood engraving and woodcut (1947)
- Crystal, mezzotint (1947)
- Up and Down also known as High and Low, 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, (1952)
- Dragon, woodcut 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)
- Mosaic II, lithograph (1957)
- Cube with Magic Ribbons, lithograph (1957)
- Belvedere, lithograph (1958)
- Sphere Spirals, woodcut (1958)
- Circle Limit III, woodcut (1959)
- 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)
Notes
- "We named him Maurits Cornelis after S.'s beloved uncle Van Hall, and called him 'Mauk' for short ....", Diary of Escher's father, quoted in M. C. Escher: His Life and Complete Graphic Work, Abradale Press, 1981, p. 9.
References
- Duden Aussprachewörterbuch (6 ed.). Mannheim: Bibliographisches Institut & F.A. Brockhaus AG. 2005. ISBN 3-411-04066-1.
- ^ "Chronology". World of Escher. Retrieved 1 November 2015.
- ^ Barbara E, PhD. Bryden. Sundial: Theoretical Relationships Between Psychological Type, Talent, And Disease. Gainesville, Fla: Center for Applications of Psychological Type. ISBN 0-935652-46-9.
- Roza, Greg (2005). An Optical Artist: Exploring Patterns and Symmetry. Rosen Classroom. p. 20. ISBN 978-1-4042-5117-5.
- "Escher". Geom.uiuc.edu. Retrieved 7 December 2013.
- Ernst, Bruno, The Magic Mirror of M.C. Escher, Taschen, 1978; p. 15
- Locher, 1974. p. 17
- Locher, 1974. pp. 62–63
- Locher, 1974. pp. 17, 70–71
- Locher, 1974. pp. 79–85
- Locher, 1974. p. 84
- Barry Cipra (1998). Paul Zorn (ed.). What's Happening in the Mathematical Sciences, Volume 4. American Mathematical Society. p. 103. ISBN 0-8218-0766-8.
- ^ Poole, Steven (20 June 2015). "The impossible world of MC Escher". The Guardian. Retrieved 2 November 2015.
- "The Official M.C. Escher Website – Biography". Retrieved 7 December 2013.
- Penrose, L.S.; Penrose, R. (1958). "Impossible objects: A special type of visual illusion". British Journal of Psychology. 49: 31–33. doi:10.1111/j.2044-8295.1958.tb00634.x. PMID 13536303.
- Kirousis, Lefteris M.; Papadimitriou, Christos H. (1985). "The complexity of recognizing polyhedral scenes". 26th Annual Symposium on Foundations of Computer Science (FOCS 1985): 175–185. doi:10.1109/sfcs.1985.59.
- Cooper, Martin (2008). "Tractability of Drawing Interpretation". Line Drawing Interpretation. Springer-Verlag. pp. 217–230. doi:10.1007/978-1-84800-229-6_9. ISBN 978-1-84800-229-6.
- Seckel, Al (2004). Masters of Deception: Escher, Dalí & the Artists of Optical Illusion. Sterling. p. 262. ISBN 978-1-4027-0577-9.
- Locher, 1974. p. 104
- Beech, Martin. "Escher's Stars". Journal of the Royal Astronomical Society of Canada. 86: 169–177.
- Coxeter, H. S. M. (1985). "A special book review: M. C. Escher: His life and complete graphic work". The Mathematical Intelligencer. 7 (1): 59–69. doi:10.1007/BF03023010.
- Malkevitch, Joseph. "Mathematics and Art. 4. Mathematical artists and artist mathematicians". American Mathematical Society. Retrieved 1 September 2015.
- Locher, 1974. p. 151
- "The Amazing World of M.C. Escher". National Galleries Scotland. Retrieved 1 November 2015.
- "The Amazing World of M.C. Escher". Dulwich Picture Gallery. Retrieved 1 November 2015.
- "Hand with Reflecting Sphere, 1935". The Collection, National Gallery of Art. National Gallery of Art, Washington. Retrieved 1 November 2015.
- "M.C. Escher — Life and Work". The Collection, National Gallery of Art. National Gallery of Art, Washington. Retrieved 1 November 2015.
Escher and the interior of his studio in Rome are reflected in the mirrored sphere that he holds in his hand. Escher's preoccupation with mirrored reflections and visual illusion belongs to a tradition of northern European art established in the fifteenth century.
- Hofstadter, Douglas R. (1999) , Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, ISBN 0-465-02656-7
Further reading
Books
- Ernst, Bruno; Escher, M. C. (1995). The Magic Mirror of M. C. Escher. Taschen America. 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.
- Escher, M. C. (1971) The Graphic Work of M. C. Escher, Ballantine. Includes Escher's own commentary.
- Locher, J. L. (1974). The World of M. C. Escher. Abrams. ISBN 0-451-799671-5.
- Locher, J. L., ed. (1981) M. C. Escher: His Life and Complete Graphic Work, Amsterdam.
- O'Connor, J. J. (17 June 2005) Escher. University of St Andrews.
- Schattschneider, Doris & Walker, Wallace. (1987) M. C. Escher Kaleidocycles, Petaluma, California, Pomegranate Communications ISBN 0-906212-28-6.
- Schattschneider, Doris (2004). M. C. Escher : Visions of Symmetry, New York: Harry N. Abrams, 2004. ISBN 0-8109-4308-5.
- Schattschneider, Doris & Emmer, Michele, eds (2003). M. C. Escher's Legacy: a Centennial Celebration; collection of articles from the M. C. Escher Centennial Conference, Rome, 1998 / Berlin; London: Springer-Verlag. ISBN 3-540-42458-X.
- "Escher, M. C." in: The World Book Encyclopedia; 10th ed. 2001.
Media
- Escher, M. C. The Fantastic World of M. C. Escher, Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.
External links
- "M.C. Escher official website".
- "Math and the Art of M.C. Escher". USA: SLU.
- Artful Mathematics: The Heritage of M. C. Escher (PDF). USA: AMS.
- Escherization problem and its solution. CA: University of Waterloo.
- "Escher for Real". IL: Technion. — physical replicas of some of Escher's "impossible" designs
- "M.C. Escher: Life and Work". USA: NGA.
- "US Copyright Protection for UK Artists". UK. Copyright issue regarding Escher from the Artquest Artlaw archive.
- Schattschneider, Doris (June–July 2010). "The Mathematical Side of M. C. Escher" (PDF). Notices of the American Mathematical Society. 57 (6). USA: 706–18. Retrieved 9 July 2010.
- Gallery of tessellations by M.C. Escher
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