The Art of Maurits Cornelis Escher
- há 7 anos
Maurits Cornelis Escher (17 June 1898 – 27 March 1972), or commonly M. C. Escher, was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints.
His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation.
Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure.
After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations, Escher began to explore the properties and possibilities of tessellation using geometric grids as the basis for his sketches. He then extended these to form complex interlocking designs, for example with animals such as birds, fish, and reptiles. One of his first attempts at a tessellation was his pencil, India ink and watercolour Study of Regular Division of the Plane with Reptiles (1939), constructed on a hexagonal grid. The heads of the red, green and white reptiles meet at a vertex; the tails, legs and sides of the animals exactly interlock. It was used as the basis for his 1943 lithograph Reptiles.
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds which he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was Still Life and Street (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as Relativity (1953). House of Stairs (1951) attracted the interest of the mathematician Roger Penrose and his father the biologist Lionel Penrose. In 1956 they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' continuously rising flights of steps, and enclosed a print of Ascending and Descending (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, Waterfall (1961).
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.
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.
Escher's special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture.
Source: Wikipedia - https://en.wikipedia.org/wiki/M._C._Escher
Music: Música: Infinite Perspective de Kevin MacLeod licensed by a Creative Commons Attribution license. - https://creativecommons.org/licenses/by/4.0/
Music source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1500024
Artist: Kevin MacLeod - http://incompetech.com/
His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation.
Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure.
After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations, Escher began to explore the properties and possibilities of tessellation using geometric grids as the basis for his sketches. He then extended these to form complex interlocking designs, for example with animals such as birds, fish, and reptiles. One of his first attempts at a tessellation was his pencil, India ink and watercolour Study of Regular Division of the Plane with Reptiles (1939), constructed on a hexagonal grid. The heads of the red, green and white reptiles meet at a vertex; the tails, legs and sides of the animals exactly interlock. It was used as the basis for his 1943 lithograph Reptiles.
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds which he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was Still Life and Street (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as Relativity (1953). House of Stairs (1951) attracted the interest of the mathematician Roger Penrose and his father the biologist Lionel Penrose. In 1956 they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' continuously rising flights of steps, and enclosed a print of Ascending and Descending (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, Waterfall (1961).
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.
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.
Escher's special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture.
Source: Wikipedia - https://en.wikipedia.org/wiki/M._C._Escher
Music: Música: Infinite Perspective de Kevin MacLeod licensed by a Creative Commons Attribution license. - https://creativecommons.org/licenses/by/4.0/
Music source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1500024
Artist: Kevin MacLeod - http://incompetech.com/