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Impossible Objects
An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline. Notable examples Notable impossible objects include: * Borromean rings — although conventionally drawn as three linked circles in three-dimensional space, any realization must be non-circular * Impossible cube — invented by M.C. Escher for '' Belvedere'', a lithograph in which a boy seated at the foot of the building holds an impossible cube. * Penrose stairs – created by Oscar Reutersvärd and later independently devised and popularised by Lionel Penrose and his mathematician son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impossible Cube Illusion Angle
Impossible, Imposible or Impossibles may refer to: Music * ''ImPossible'' (album), a 2016 album by Divinity Roxx * ''The Impossible'' (album) Groups * The Impossibles (American band), a 1990s indie-ska group from Austin, Texas * The Impossibles (Australian band), an Australian band * The Impossibles (Thai band), a 1970s Thai rock band Songs * "Impossible" (Captain Hollywood Project song) (1993) * "The Impossible" (song), a country music song by Joe Nichols (2002) * "Impossible" (Edyta song) (2003) * "Impossible" (Kanye West song) (2006) * "Impossible" (Daniel Merriweather song) (2009) * "Impossible" (Måns Zelmerlöw song) (2009) * "Impossible" (Anberlin song) (2010) * "Impossible" (Shontelle song) (2010) * "Impossible", from Rodgers and Hammerstein's 1957 musical ''Cinderella'' * "Impossible", a song written by Steve Allen and recorded by Nat King Cole for his 1958 album ''The Very Thought of You'' * "Impossible", from the 1994 album ''The Screaming Jets'' by The Screa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Research
Wolfram Research, Inc. ( ) is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include WolframAlpha, Wolfram SystemModeler, Wolfram Workbench, gridMathematica, Wolfram Finance Platform, webMathematica, the Wolfram Cloud, and the Wolfram Programming Lab. Wolfram Research founder Stephen Wolfram is the CEO. The company is headquartered in Champaign, Illinois, United States. History The company launched Wolfram Alpha, an answer engine on May 16, 2009. It brings a new approach to knowledge generation and acquisition that involves large amounts of curated computable data in addition to semantic indexing of text. Wolfram Research acquired MathCore Engineering AB on March 30, 2011. On July 21, 2011, Wolfram Research launched the Computable Document Format (CDF). CDF is an electronic document format designed to allow easy authorin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Journal Of Psychology
The ''British Journal of Psychology'' is a quarterly peer-reviewed psychology journal. It was established in 1904 and is published by Wiley-Blackwell on behalf of the British Psychological Society. The editor-in-chief is Stefan R. Schweinberger (University of Jena). According to the ''Journal Citation Reports'', the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 3.308, ranking it 20th out of 137 journals in the category "Psychology, Multidisciplinary". References External links * Psychology journals British Psychological Society academic journals Publications established in 1904 Quarterly journals English-language journals Wiley-Blackwell academic journals {{Psychology-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sweden
Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, Finland to the east, and is connected to Denmark in the southwest by a bridgetunnel across the Öresund. At , Sweden is the largest Nordic country, the third-largest country in the European Union, and the fifth-largest country in Europe. The capital and largest city is Stockholm. Sweden has a total population of 10.5 million, and a low population density of , with around 87% of Swedes residing in urban areas in the central and southern half of the country. Sweden has a nature dominated by forests and a large amount of lakes, including some of the largest in Europe. Many long rivers run from the Scandes range through the landscape, primarily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel Duchamp
Henri-Robert-Marcel Duchamp (, , ; 28 July 1887 – 2 October 1968) was a French painter, sculptor, chess player, and writer whose work is associated with Cubism, Dada, and conceptual art. Duchamp is commonly regarded, along with Pablo Picasso and Henri Matisse, as one of the three artists who helped to define the revolutionary developments in the plastic arts in the opening decades of the 20th century, responsible for significant developments in painting and sculpture. Duchamp has had an immense impact on twentieth-century and twenty first-century art, and he had a seminal influence on the development of conceptual art. By the time of World War I he had rejected the work of many of his fellow artists (such as Henri Matisse) as "retinal" art, intended only to please the eye. Instead, Duchamp wanted to use art to serve the mind. Early life and education Marcel Duchamp was born at Blainville-Crevon in Normandy, France, to Eugène Duchamp and Lucie Duchamp (formerly Lucie Nicolle) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apolinère Enameled
''Apolinère Enameled'' was painted in 1916–17 by Marcel Duchamp, as a heavily altered version of an advertisement for paint ("Sapolin Enamel"). The picture depicts a girl painting a bed-frame with white enamelled paint. The depiction of the frame deliberately includes conflicting perspective lines, to produce an impossible object. To emphasise the ''deliberate'' impossibility of the shape, a piece of the frame is missing. The piece is sometimes referred to as Duchamp's "impossible bed" painting. ''Apolinère'' is a play-on-words referencing the poet, writer and art critic Guillaume Apollinaire, a close associate of Duchamp during the Cubist adventure. Apollinaire wrote about Duchamp (and others) in his book ''The Cubist Painters, Aesthetic Meditations'' of 1913. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory. From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century. From the initial idea of homology as a method of constructing algebraic invariants of topological spaces, the range of applications of homology and cohomology theories has spread throughout geometry and algebra. The terminology tends to hide the fact that cohomology, a contravariant theory, is more natural than homology in many applications. At a basic level, this has to do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares. Orthogonal projections The ''cube'' has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A2 and B2 Coxeter planes. Spherical tiling The cube can also be represented as a spherical tiling, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necker Cube
The Necker cube is an optical illusion that was first published as a Rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side. Ambiguity The Necker cube is an ambiguous drawing. Each part of the picture is ambiguous by itself, yet the human visual system picks an interpretation of each part that makes the whole consistent. The Necker cube is sometimes used to test computer models of the human visual system to see whether they can arrive at consistent interpretations of the image the same way humans do. Humans do not usually see an inconsistent interpretation of the cube. A cube whose edges cross in an inconsistent way is an example of an impossible object, specifically an impossible cube (compare Penrose triangle). With the cube on the left, most people see the lower ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
