|
Danzer's Configuration
In mathematics, Danzer's configuration is a self-dual configuration (geometry), configuration of 35 lines and 35 points, having 4 points on each line and 4 lines through each point. It is named after the German geometer Ludwig Danzer and was popularised by Branko Grünbaum. The Levi graph of the configuration is the bipartite double cover, Kronecker cover of the odd graph O4, and is isomorphic to the middle layer graph of the seven-dimensional hypercube graph Q7. The middle layer graph of an odd-dimensional hypercube graph Q2n+1(n,n+1) is a subgraph whose vertex set consists of all binary strings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding binary strings differ in exactly one bit. Every middle layer graph is Hamiltonian. Danzer's configuration DCD(4) is the fourth term of an infinite series of (\tbinom _n) configurations DCD(n), where DCD(1) is the trivial configuration (11), DCD(2) is the tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danzer Graph
Danzer or Dänzer is a surname. Notable people with the name include: *Emmerich Danzer (born 1944), Austrian figure skater *Frieda Dänzer (1930–2015), Swiss alpine skier *Georg Danzer (1946–2007), Austrian singer-songwriter *George Danzer (born 1983), German poker player *Gerald Danzer (born 1938), American historian *Ludwig Danzer (1927–2011), German geometer See also * Denzer (other) {{Surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Configuration
Clifford may refer to: People *Clifford (name), an English given name and surname, includes a list of people with that name *William Kingdon Clifford * Baron Clifford *Baron Clifford of Chudleigh * Baron de Clifford *Clifford baronets * Clifford family (bankers) * Jaryd Clifford * Justice Clifford (other) * Lord Clifford (other) Arts, entertainment, and media *'' Clifford the Big Red Dog'', a series of children's books **Clifford (character), the central character of ''Clifford the Big Red Dog'' ** ''Clifford the Big Red Dog'' (2000 TV series), 2000 animated TV series **'' Clifford's Puppy Days'', 2003 animated TV series **''Clifford's Really Big Movie'', 2004 animated movie ** ''Clifford the Big Red Dog'' (2019 TV series), 2019 animated TV series ** ''Clifford the Big Red Dog'' (film), 2021 live-action movie * ''Clifford'' (film), a 1994 film directed by Paul Flaherty * Clifford (Muppet) Mathematics *Clifford algebra, a type of associative algebra, named after W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Journal Of Combinatorics
European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe and other Western countries * ''European'', an adjective referring to something of, from, or related to the European Union ** Citizenship of the European Union ** Demographics of the European Union In publishing * ''The European'' (1953 magazine), a far-right cultural and political magazine published 1953–1959 * ''The European'' (newspaper), a British weekly newspaper published 1990–1998 * ''The European'' (2009 magazine), a German magazine first published in September 2009 *''The European Magazine'', a magazine published in London 1782–1826 *''The New European'', a British weekly pop-up newspaper first published in July 2016 Other uses * * Europeans (band), a British post-punk group, from Bristol See also * * * Europe (disam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Geometry
'' Advances in Geometry'' is a peer-reviewed mathematics journal published quarterly by Walter de Gruyter. Founded in 2001, the journal publishes articles on geometry. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2016 MCQ was 0.45, and its 2021 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 ... was 0.763. References External links * Mathematics journals Academic journals established in 2001 English-language journals De Gruyter academic journals Quarterly journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reye Configuration
In geometry, the Reye configuration, introduced by , is a configuration of 12 points and 16 lines Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts .... Each point of the configuration belongs to four lines, and each line contains three points. Therefore, in the notation of configurations, the Reye configuration is written as . Realization The Reye configuration can be realized in three-dimensional projective space by taking the lines to be the 12 edges and four long diagonals of a cube, and the points as the eight vertices of the cube, its center, and the three points where groups of four parallel cube edges meet the plane at infinity. Two regular tetrahedron, tetrahedra may be inscribed within a cube, forming a stella octangula; these two tetrahedra are perspective figures to each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miquel Configuration
In geometry, the Miquel configuration is a configuration of eight points and six circles in the Euclidean plane, with four points per circle and three circles through each point.. Its Levi graph is the Rhombic dodecahedral graph, the skeleton of both Rhombic dodecahedron and Bilinski dodecahedron. The configuration is related to Miquel's theorem Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles .... References Configurations (geometry) {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hasse Diagram Of Powerset Of 3
Hasse is both a surname and a given name. Notable people with the name include: Surname: * Clara H. Hasse (1880–1926), American botanist * Helmut Hasse (1898–1979), German mathematician * Henry Hasse (1913–1977), US writer of science fiction * Johann Adolph Hasse Johann Adolph Hasse (baptised 25 March 1699 – 16 December 1783) was an 18th-century German composer, singer and teacher of music. Immensely popular in his time, Hasse was best known for his prolific operatic output, though he also composed a co ... (1699–1783), German composer * Maria Hasse (1921–2014), German mathematician * Peter Hasse (c. 1585–1640), German organist and composer Given name or nickname: * Hans Alfredson (born 1931), Swedish actor, film director, writer and comedian * Hans Backe (born 1952), Swedish football manager * Hasse Borg (born 1953), Swedish footballer * Hasse Börjes (born 1948), Swedish speed skater * Hasse Ekman (1915-2004), Swedish film director and actor * Hans Wind (1919†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford's Circle Theorems
In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating to intersections of circles. Statement The first theorem considers any four circles passing through a common point ''M'' and otherwise in general position, meaning that there are six additional points where exactly two of the circles cross and that no three of these crossing points are collinear. Every set of three of these four circles has among them three crossing points, and (by the assumption of non-collinearity) there exists a circle passing through these three crossing points. The conclusion is that, like the first set of four circles, the second set of four circles defined in this way all pass through a single point ''P'' (in general not the same point as ''M''). The second theorem considers five circles in general position passing through a single point ''M''. Each subset of four circles defines a new point ''P'' according to the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues Configuration
In geometry, the Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues. The Desargues configuration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in three dimensions from five planes in general position, or in four dimensions from the 5-cell, the four-dimensional regular simplex. It has a large group of symmetries, taking any point to any other point and any line to any other line. It is also self-dual, meaning that if the points are replaced by lines and vice versa using projective duality, the same configuration results. Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph of non-incident lines). The Desargues configuration is one of ten different configurations with ten points and lines, three points per line, and three lines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points. Although certain specific configurations had been studied earlier (for instance by Thomas Kirkman in 1849), the formal study of configurations was first introduced by Theodor Reye in 1876, in the second edition of his book ''Geometrie der Lage'', in the context of a discussion of Desargues' theorem. Ernst Steinitz wrote his dissertation on the subject in 1894, and they were popularized by Hilbert and Cohn-Vossen's 1932 book ''Anschauliche Geometrie'', reprinted in English as . Configurations may be studied either as concrete sets of points and lines in a specific geometry, such as the Euclidean or projective planes (these are said to be ''realizable'' in that geometry), or as a type of abstract incidence geometry. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercube Graph
In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube. For instance, the cube graph is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. has vertices, edges, and is a regular graph with edges touching each vertex. The hypercube graph may also be constructed by creating a vertex for each subset of an -element set, with two vertices adjacent when their subsets differ in a single element, or by creating a vertex for each -digit binary number, with two vertices adjacent when their binary representations differ in a single digit. It is the -fold Cartesian product of the two-vertex complete graph, and may be decomposed into two copies of connected to each other by a perfect matching. Hypercube graphs should not be confused with cubic graphs, which are graphs that have exactly three edges touching each vertex. The only hypercube graph that is a cubic graph is the cubical graph . Constru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Layer Graph
Middle or The Middle may refer to: * Centre (geometry), the point equally distant from the outer limits. Places * Middle (sheading), a subdivision of the Isle of Man * Middle Bay (other) * Middle Brook (other) * Middle Creek (other) * Middle Island (other) * Middle Lake (other) * Middle Mountain, California * Middle Peninsula, Chesapeake Bay, Virginia * Middle Range, a former name of the Xueshan Range on Taiwan Island * Middle River (other) * Middle Rocks, two rocks at the eastern opening of the Straits of Singapore * Middle Sound, a bay in North Carolina * Middle Township (other) * Middle East Music * "Middle" (song), 2015 * "The Middle" (Jimmy Eat World song), 2001 * "The Middle" (Zedd, Maren Morris and Grey song), 2018 *"Middle", a song by Rocket from the Crypt from their 1995 album '' Scream, Dracula, Scream!'' *"The Middle", a song by Demi Lovato from their debut album '' Don't Forget'' *"The Middle", a song ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
