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Walther Von Dyck
Walther Franz Anton von Dyck (6 December 1856 – 5 November 1934), born Dyck () and later ennobled, was a German mathematician. He is credited with being the first to define a mathematical group, in the modern sense in . He laid the foundations of combinatorial group theory, being the first to systematically study a group by generators and relations. Biography Von Dyck was a student of Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ... and served as chairman of the commission publishing Klein's encyclopedia. Von Dyck was also the editor of Kepler's works. He promoted technological education as rector of the Technische Hochschule of Munich. He was a Plenary Speaker of the ICM in 1908 at Rome. Von Dyck is the son of the Bavarian painter Hermann Dyck. Legacy T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rector (academia)
A rector (Latin language, Latin for 'ruler') is a senior official in an educational institution, and can refer to an official in either a university or a secondary school. Outside the English-speaking world, the rector is often the most senior official in a university, while in the United States, the equivalent is often referred to as the President (education), president, and in the United Kingdom and Commonwealth of Nations, the equivalent is the Vice-chancellor (education), vice-chancellor. The term and office of a rector can be referred to as a rectorate. The title is used widely in universities in EuropeEuropean nations where the word ''rector'' or a cognate thereof (''rektor'', ''recteur'', etc.) is used in referring to university administrators include Albania, Austria, Benelux, the Benelux, Bosnia and Herzegovina, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Germany, Greece, Hungary, Iceland, Italy, Latvia, Malta, Moldova, North Macedonia, Poland, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Dyck
Hermann Dyck (4 October 1812 – 25 March 1874), a Bavarian painter, born at Würzburg in the Grand Duchy of Würzburg in 1812, studied architectural and genre painting at Munich. His works are original and of great humour, and are neatly and carefully executed. The satirical designs for the ''Fliegende Blätter,'' in reference to the rage for monuments, are incomparable. He was director of the Academy of Fine Arts, Munich, Art Schools at Munich, where he died in 1874. See also * Walther von Dyck * List of German painters References * External links Works by Hermann Dyck at HeidICON 1812 births 1874 deaths Painters from Würzburg People from the Grand Duchy of Würzburg 19th-century German painters 19th-century German male artists German male painters Artists from the Kingdom of Bavaria {{Germany-painter-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th century began on 1 January 1801 (represented by the Roman numerals MDCCCI), and ended on 31 December 1900 (MCM). It was the 9th century of the 2nd millennium. It was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanded beyond its British homeland for the first time during the 19th century, particularly remaking the economies and societies of the Low Countries, France, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Catholic Church, in response to the growing influence and power of modernism, secularism and materialism, formed the First Vatican Council in the late 19th century to deal with such problems and confirm ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Munich
A scientist is a person who researches to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales ( 624–545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. History The roles of "scientists", and their predecessors before the emergence of modern scientific disciplines, have evolved considerably over time. Scientists of different eras (and before them, natural philosophers, mathematicians, natur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1934 Deaths
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 1934 Nepal–Bihar earthquake, Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity scale, Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * February 6 – 6 February 1934 crisis, French political crisis: The French far-right leagues rally in front of the Palais Bourbon, in an attempted coup d'état against the French Third Republic, Third Republic. * February 9 ** Gaston Doumergue forms a new government in France. ** Second Hellenic Republic, Greece, Kingdom of Romania, Romania, Turkey and Kingdom of Yugoslavia, Yugoslavia form the Balkan Pact. * February 12–February 15, 15 – Austrian Civil War: The Fatherland Front (Austria), Fatherland Front consolidates its power in a series of clashes across the country. * February 16 – The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1856 Births
Events January–March * January 8 – Borax deposits are discovered in large quantities by John Veatch in California. * January 23 – The American sidewheel steamer SS ''Pacific'' leaves Liverpool (England) for a transatlantic voyage on which she will be lost with all 186 on board. * January 24 – U.S. President Franklin Pierce declares the new Free-State Topeka government in " Bleeding Kansas" to be in rebellion. * January 26 – First Battle of Seattle: Marines from the suppress an indigenous uprising, in response to Governor Stevens' declaration of a "war of extermination" on Native communities. * January 29 ** The 223-mile North Carolina Railroad is completed from Goldsboro through Raleigh and Salisbury to Charlotte. ** Queen Victoria institutes the Victoria Cross as a British military decoration. * February ** The Tintic War breaks out in Utah. ** The National Dress Reform Association is founded in the United States to promote "r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, Nigel Hitchin, and Thomas Schick. Currently, the managing editor of Mathematische Annalen is Yoshikazu Giga (University of Tokyo). Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947, the journal briefly ceased publication. References External links''Mathematische Annalen''homepage a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyck Graph
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian with 120 distinct Hamiltonian cycles. It has chromatic number 2, chromatic index 3, radius 5, diameter 5 and girth 6. It is also a 3- vertex-connected and a 3- edge-connected graph. It has book thickness 3 and queue number 2. Algebraic properties The automorphism group of the Dyck graph is a group of order 192. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore, the Dyck graph is a symmetric graph. It has automorphisms that take any vertex to any other vertex and any edge to any other edge. According to the ''Foster census'', the Dyck graph, referenced as F32A, is the only cubic symmetric graph on 32 vertices. The characteristic polynomial of the Dyck graph is equal to (x-3) (x-1)^9 (x+1)^9 (x+3) (x^2-5)^6. Toroidal graph The Dyck graph is a toroidal graph, contained in the skeleto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyck Path
The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu. The -th Catalan number can be expressed directly in terms of the central binomial coefficients by :C_n = \frac = \frac \qquad\textn\ge 0. The first Catalan numbers for are : . Properties An alternative expression for is :C_n = - for n\ge 0\,, which is equivalent to the expression given above because \tbinom=\tfrac\tbinomn. This expression shows that is an integer, which is not immediately obvious from the first formula given. This expression forms the basis for a proof of the correctness of the formula. Another alternative expression is :C_n = \frac \,, which can be directly interpreted in terms of the cycle lemma; see below. The Catalan numbers satisfy the recurrence relations :C_0 = 1 \quad \text \quad C_=\sum_^C_C_\qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyck Tessellation
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian with 120 distinct Hamiltonian cycles. It has chromatic number 2, chromatic index 3, radius 5, diameter 5 and girth 6. It is also a 3- vertex-connected and a 3- edge-connected graph. It has book thickness 3 and queue number 2. Algebraic properties The automorphism group of the Dyck graph is a group of order 192. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore, the Dyck graph is a symmetric graph. It has automorphisms that take any vertex to any other vertex and any edge to any other edge. According to the ''Foster census'', the Dyck graph, referenced as F32A, is the only cubic symmetric graph on 32 vertices. The characteristic polynomial of the Dyck graph is equal to (x-3) (x-1)^9 (x+1)^9 (x+3) (x^2-5)^6. Toroidal graph The Dyck graph is a toroidal graph, contained in the skeleto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Dyck Group
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere, or the hyperbolic plane by congruent triangles called Möbius triangles, each one a fundamental domain for the action. Definition Let ''l'', ''m'', ''n'' be integers greater than or equal to 2. A triangle group Δ(''l'',''m'',''n'') is a group of motions of the Euclidean plane, the two-dimensional sphere, the real projective plane, or the hyperbolic plane generated by the reflections in the sides of a triangle with angles π/''l'', π/''m'' and π/''n'' (measured in radians). The product of the reflections in two adjacent sides is a rotation by the angle which is twice the angle between those sides, 2π/''l'', 2π/''m'' and 2π/''n''. Therefore, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface (mathematics)
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space. The exact definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface may move in two directions (it has two degrees of freedom). In other words, around almost every point, there is a '' coordinate patch'' on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
