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Möbius Loop Roller Coaster
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] |
August Ferdinand Möbius
August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer. Life and education Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer Karl Mollweide. In 1813, he began to study astronomy under mathematician Carl Friedrich Gauss at the University of Göttingen, while Gauss was the director of the Göttingen Observatory. From there, he went to study with Carl Gauss's instructor, Johann Pfaff, at the University of Halle, where he completed his doctoral thesis ''The occultation of fixed stars'' in 1815. In 1816, he was appointed as Extraordinary Professor to the "chair of astronomy and hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Vegas
''Fallout: New Vegas'' is a 2010 action role-playing game that was developed by Obsidian Entertainment and published by Bethesda Softworks. The game, which was released for Microsoft Windows, PlayStation 3, and Xbox 360, is set in the Mojave Desert 204 years after a devastating nuclear war. The player controls a courier who survives an assassination attempt, and becomes embroiled in a conflict between different governing factions that are vying for control of the region. ''Fallout: New Vegas'' features a freely explorable open world, and the player can engage in combat with a variety of weapons. The player can also initiate conversations with non-player characters in the form of dialogue trees, and their responses determine their reputation among the different factions. After the release of ''Fallout 3'' in 2008, Bethesda contracted Obsidian to develop a spin-off game in the ''Fallout'' series. The developers chose Las Vegas, Nevada, and the surrounding Mojave Desert as the set ... [...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] |
Möbius Strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a Surface (topology), surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Ancient Rome, Roman mosaics from the third century Common Era, CE. The Möbius strip is a orientability, non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a Knot (mathematics), knotted centerline. Any two embeddings with the same knot for the centerline and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Energy
In mathematics, the Möbius energy of a knot is a particular knot energy, i.e., a functional on the space of knots. It was discovered by Jun O'Hara, who demonstrated that the energy blows up as the knot's strands get close to one another. This is a useful property because it prevents self-intersection and ensures the result under gradient descent is of the same knot type. Invariance of Möbius energy under Möbius transformations was demonstrated by Michael Freedman, Zheng-Xu He, and Zhenghan Wang (1994) who used it to show the existence of a C^ energy minimizer in each isotopy class of a prime knot. They also showed the minimum energy of any knot conformation is achieved by a round circle. Conjecturally, there is no energy minimizer for composite knots. Robert B. Kusner and John M. Sullivan have done computer experiments with a discretized version of the Möbius energy and concluded that there should be no energy minimizer for the knot sum of two trefoils (although this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
