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Moebius
Moebius, Mœbius, Möbius or Mobius may refer to: People * August Ferdinand Möbius (1790–1868), German mathematician and astronomer * Friedrich Möbius (art historian) (1928–2024), German art historian and architectural historian * Theodor Möbius (1821–1890), German philologist, son of August Ferdinand * Karl Möbius (1825–1908), German zoologist and ecologist * Paul Julius Möbius (1853–1907), German neurologist, grandson of August Ferdinand * Dieter Moebius (1944–2015), Swiss-born German musician * Mark Mobius (born 1936), emerging markets investments pioneer * Jean Giraud (1938–2012), French comics artist who used the pseudonym Mœbius Fictional characters * Mobius M. Mobius, a character in Marvel Comics * Anti-Monitor, Mobius, also known as the Anti-Monitor, a supervillain in DC Comics * Johann Wilhelm Möbius, a character in the play ''The Physicists'' * Moebius, the main antagonistic faction in the video game ''Xenoblade Chronicles 3'' * Mobius, or Dr. Ignati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Giraud
Jean Henri Gaston Giraud (; 8 May 1938 – 10 March 2012) was a French artist, cartoonist, and writer who worked in the Franco-Belgian comics, Franco-Belgian ''bandes dessinées'' (BD) tradition. Giraud garnered worldwide acclaim predominantly under the pseudonym Mœbius (; ) for his fantasy/science-fiction work, and to a slightly lesser extent as Gir (), which he used for the ''Blueberry (comics), Blueberry'' series and his other Western (genre), Western-themed work. Esteemed by Federico Fellini, Stan Lee, and Hayao Miyazaki, among others,Screech, Matthew. 2005. "Moebius/Jean Giraud: ''Nouveau Réalisme'' and Science fiction". In Libbie McQuillan (ed.) ''The Francophone bande dessinée''. Rodopi. p. 1 he has been described as the most influential ''bande dessinée'' artist after Hergé. His most famous body of work as Gir concerns the ''Blueberry'' series, created with writer Jean-Michel Charlier, featuring one of the first antiheroes in Western comics, and which is parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Ladder
In graph theory, the Möbius ladder , for even numbers , is formed from an by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of (the utility graph ), has exactly four-cycles which link together by their shared edges to form a topological Möbius strip. Möbius ladders were named and first studied by . Properties For every even , the Möbius ladder is a nonplanar apex graph, meaning that it cannot be drawn without crossings in the plane but removing one vertex allows the remaining graph to be drawn without crossings. These graphs have crossing number one, and can be embedded without crossings on a torus or projective plane. Thus, they are examples of toroidal graphs. explores embeddings of these graphs onto higher genus surfaces. Möbius ladders are vertex-transitive – they have symmetries taking any vertex to any other vertex – but (with the exceptions of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodor Möbius
Theodor Möbius (June 22, 1821 Leipzig - April 25, 1890) was a German philologist who specialized in Germanic studies. Biography He was a son of German mathematician August Ferdinand Möbius. He studied at the Universities of Leipzig (1840–42) and Berlin (1842-43), receiving his doctorate in 1844 at Leipzig. From 1845 to 1861, he was an assistant, then later curator, at the university library. He earned his habilitation at Leipzig in 1852 with the thesis ''Über die ältere isländische Saga'', and in 1859 became a professor of Scandinavian languages and literature there. In 1865, he accepted a similar position at Kiel. He edited many old Norse works. Selected works * ''Catalogus librorum islandicorum et norvegicorum ætatis mediæ editorum versorum illustratorum : Skáldatal sive Poetarum recensus Eddæ upsaliensis'', Lipsiæ : Apud W. Engelmannum, 1856. * ''Altnordisches Glossar : wörterbuch zu einer Auswahl alt-isländischer und alt-norwegischer Prosatexte'', Leipzig : B. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Evil Within
''The Evil Within'' is a 2014 survival horror, survival horror game developed by Tango Gameworks and published by Bethesda Softworks. It was directed by ''Resident Evil'' series creator Shinji Mikami. The game centers on protagonist Sebastian Castellanos as he is pulled through a distorted world full of nightmarish locations and horrid creatures. Played in a third-person (video games), third-person perspective, players battle disfigured nightmare-like enemies, including boss (video games), bosses, using guns and melee weapons, and progress through the levels, avoiding traps, using stealth game, stealth, and finding collectables. ''The Evil Within'' was released for PlayStation 3, PlayStation 4, Windows, Xbox 360, and Xbox One in October 2014. Upon release, the game received generally positive reviews from critics, who praised the game's horror elements, gameplay and atmosphere, while criticism was directed at the game's story, characters, and technical issues. A sequel, ''The Evi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Plane
In mathematics, the classical Möbius plane (named after August Ferdinand Möbius) is the Euclidean plane supplemented by a single point at infinity. It is also called the inversive plane because it is closed under inversion with respect to any generalized circle, and thus a natural setting for planar inversive geometry. An inversion of the Möbius plane with respect to any circle is an involution (mathematics), involution which fixes the points on the circle and exchanges the points in the interior and exterior, the center of the circle exchanged with the point at infinity. In inversive geometry a straight line is considered to be a generalized circle containing the point at infinity; inversion of the plane with respect to a line is a Euclidean reflection (mathematics), reflection. More generally, a Möbius plane is an incidence structure with the same incidence relationships as the classical Möbius plane. It is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius–Kantor Graph
In the mathematics, mathematical field of graph theory, the Möbius–Kantor graph is a symmetric graph, symmetric bipartite graph, bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph ''G''(8,3): that is, it is formed by the vertices of an octagon, connected to the vertices of an eight-point star in which each point of the star is connected to the points three steps away from it (an octagram). Möbius–Kantor configuration asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For ''p'' = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges bel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius–Kantor Configuration
In geometry, the Möbius–Kantor configuration is a configuration consisting of eight points and eight lines, with three points on each line and three lines through each point. It is not possible to draw points and lines having this pattern of incidences in the Euclidean plane, but it is possible in the complex projective plane. Coordinates asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For p = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges belong to the complex projective plane. That is, in Kantor's solution, the coordinates of the polygon vertices are complex numbers. Kantor's solution for p = 4, a pair of mutually-inscribed quadrilateral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Configuration
In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ... or projective space, consisting of two tetrahedron, tetrahedra that are mutually Inscribed figure, inscribed: each Vertex (geometry), vertex of one tetrahedron lies on a Face (geometry), face plane of the other tetrahedron and vice versa. Thus, for the resulting system of eight points and eight planes, each point lies on four planes (the three planes defining it as a vertex of a tetrahedron and the fourth plane from the other tetrahedron that it lies on), and each plane contains four points (the three tetrahedron vertices of its face, and the vertex from the other tetrahedron that lies on it). Möbius's theorem The configuration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z) = \frac of one complex number, complex variable ; here the coefficients , , , are complex numbers satisfying . Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic projection from the plane to the unit sphere, moving and rotating the sphere to a new location and orientation in space, and then applying a stereographic projection to map from the sphere back to the plane. These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle. The Möbius transformations are the projective transformations of the complex projective line. They form a group (mathematics), group called the Möbius group, which is the projective linear group . Together with its subgroups, it has numerous applications in mathematics and physics. Möbius geometry, Möbius geometries and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Inversion Formula
In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius. A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra. Statement of the formula The classic version states that if and are arithmetic functions satisfying : g(n)=\sum_f(d)\quad\textn\ge 1 then :f(n)=\sum_\mu(d)\,g\!\left(\frac\right)\quad\textn\ge 1 where is the Möbius function and the sums extend over all positive divisors of (indicated by d \mid n in the above formulae). In effect, the original can be determined given by using the inversion formula. The two sequences are said to be Möbius transforms of each other. The formula is also correct if and are f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Transform
Moebius, Mœbius, Möbius or Mobius may refer to: People * August Ferdinand Möbius (1790–1868), German mathematician and astronomer * Friedrich Möbius (art historian) (1928–2024), German art historian and architectural historian * Theodor Möbius (1821–1890), German philologist, son of August Ferdinand * Karl Möbius (1825–1908), German zoologist and ecologist * Paul Julius Möbius (1853–1907), German neurologist, grandson of August Ferdinand * Dieter Moebius (1944–2015), Swiss-born German musician * Mark Mobius (born 1936), emerging markets investments pioneer * Jean Giraud (1938–2012), French comics artist who used the pseudonym Mœbius Fictional characters * Mobius M. Mobius, a character in Marvel Comics * Mobius, also known as the Anti-Monitor, a supervillain in DC Comics * Johann Wilhelm Möbius, a character in the play '' The Physicists'' * Moebius, the main antagonistic faction in the video game ''Xenoblade Chronicles 3'' * Mobius, or Dr. Ignatio Mobius, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Function
The Möbius function \mu(n) is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated ''Moebius'') in 1832. It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula. Following work of Gian-Carlo Rota in the 1960s, generalizations of the Möbius function were introduced into combinatorics, and are similarly denoted \mu(x). Definition The Möbius function is defined by :\mu(n) = \begin 1 & \text n = 1 \\ (-1)^k & \text n \text k \text \\ 0 & \text n \text > 1 \end The Möbius function can alternatively be represented as : \mu(n) = \delta_ \lambda(n), where \delta_ is the Kronecker delta, \lambda(n) is the Liouville function, Prime omega function, \omega(n) is the number of distinct prime divisors of n, and Prime omega function, \Omega(n) is the number of prime factors of n, counted with multiplicity. Another characterization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
