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Julius Petersen
Julius Peter Christian Petersen (16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) was a Danish mathematician. His contributions to the field of mathematics led to the birth of graph theory. Biography Petersen's interests in mathematics were manifold, including: geometry, complex analysis, number theory, mathematical physics, mathematical economics, cryptography and graph theory. His famous paper ''Die Theorie der regulären graphs'' was a fundamental contribution to modern graph theory as we know it today. In 1898, he presented a counterexample to Tait's claimed theorem about 1-factorability of 3-regular graphs, which is nowadays known as the "Petersen graph". In cryptography and mathematical economics he made contributions which today are seen as pioneering. He published a systematic treatment of geometrical constructions (with straightedge and compass) in 1880. A French translation was reprinted in 1990. A special issue of Discrete Mathematics has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petersen Julius
Petersen is a common Danish patronymic surname, meaning ''"son of Peter"''. There are other spellings. Petersen may refer to: People In arts and entertainment * Adolf Dahm-Petersen, Norwegian voice specialist * Anja Petersen, German operatic soprano and university lecturer * Anker Eli Petersen, Faroese writer and artist * Ann Petersen, Belgian actress * Chris Petersen (born 1963), American child actor * Devon Petersen (born 1986), South African darts player * Elmer Petersen, American artist * Gustaf Munch-Petersen, Danish writer and painter * Joel Petersen, bass guitarist * John Hahn-Petersen, Danish actor * Josef Petersen, Danish novelist * Patrick Petersen, American actor * Paul Petersen, American movie actor, singer, novelist, and activist * Robert E. Petersen, publisher, auto museum founder * Robert Storm Petersen, Danish cartoonist, writer, animator, illustrator, painter and humorist * Sandy Petersen, American game designer * Uwe Fahrenkrog-Petersen, German musicia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Straightedge And Compass
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an Idealization (science philosophy), idealized ruler and a pair of Compass (drawing tool), compasses. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory, 1736–1936
''Graph Theory, 1736–1936'' is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig. ''Graph Theory, 1736–1936'' was edited by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson, and published in 1976 by the Clarendon Press. The Oxford University Press published a paperback second edition in 1986, with a corrected reprint in 1998. Topics ''Graph Theory, 1736–1936'' contains copies, extracts, and translations of 37 original sources in graph theory, grouped into ten chapters and punctuated by commentary on their meaning and context. It begins with Euler's 1736 paper "Solutio problematis ad geometriam situs pertinentis" on the seven bridges of Königsberg (both in the original Latin and in English translation) and ending with Dénes Kőnig's book ''Theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petersen–Morley Theorem
In geometry, the Petersen–Morley theorem states that, if , , are three general skew lines in space, if , , are the lines of shortest distance respectively for the pairs , and , and if , and are the lines of shortest distance respectively for the pairs , and , then there is a single line meeting at right angles all of , , and . The theorem is named after Johannes Hjelmslev (who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley Frank Morley (September 9, 1860 – October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry. Among his mathematical accomplishments was the discovery and proof of the celebr .... References * * * {{DEFAULTSORT:Petersen-Morley theorem Mathematical theorems Theorems in geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vestre Cemetery
Vestre Cemetery ( da, Vestre Kirkegård, meaning "Western Cemetery") is located in a large park setting in the Kongens Enghave district of Copenhagen, Denmark. With its 54 hectares it is the largest cemetery in Denmark. The cemetery is landscaped and serves as an important open space, in which people take a stroll, and look at the old graves and monuments. It is located southwest of the city center, between the Enghave, Sydhavn, Sjælør and Valby train stations on Copenhagen's S-train system, and right next to the historic Carlsberg neighbourhood. The cemetery is one of five run by Copenhagen municipality. The other cemeteries are Assistens Cemetery, Brønshøj Cemetery, Sundby Cemetery, and Bispebjerg Cemetery. The cemetery has a Catholic section, and next to that is a Jewish cemetery (the Jewish Western Cemetery). History Vestre Kirkegård was opened on 2 November 1870 to accommodate an urgent need for adequate burial places for the growing population of Copenh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gösta Mittag-Leffler
Magnus Gustaf "Gösta" Mittag-Leffler (16 March 1846 – 7 July 1927) was a Swedish mathematician. His mathematical contributions are connected chiefly with the theory of functions, which today is called complex analysis. Biography Mittag-Leffler was born in Stockholm, son of the school principal John Olof Leffler and Gustava Wilhelmina Mittag; he later added his mother's maiden name to his paternal surname. His sister was the writer Anne Charlotte Leffler. He matriculated at Uppsala University in 1865, completed his PhD in 1872 and became docent at the university the same year. He was also curator (chairman) of the Stockholms nation (1872–1873). He next traveled to Paris, Göttingen and Berlin, studying under Weierstrass in the latter place. During this period he edited a weekly newspaper, ''Ny Illustrerad Tidning'', which was based in Stockholm. He then took up a position as professor of mathematics (as successor to Lorenz Lindelöf) at the University of Helsinki from 1877 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Danish Academy Of Science And Letters
{{Infobox organization , name = The Royal Danish Academy of Sciences and Letters , full_name = , native_name = Det Kongelige Danske Videnskabernes Selskab , native_name_lang = , logo = Royal Danish Academy of Sciences and Letters seal.svg , logo_size = 150 , logo_alt = , logo_caption = , image = Carlsbergfondet.JPG , image_size = , alt = , caption = The building on H.C. Andersens Boulevard. , map = , map_size = , map_alt = , map_caption = , map2 = , map2_size = , map2_alt = , map2_caption = , abbreviation = , nickname = , pronounce = , pronounce ref = , pronounce comment = , pronounce 2 = , named_after = , motto = , predecessor = , merged ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape. Construction There are several kinds of planimeters, but all operate in a similar way. The precise way in which they are constructed varies, with the main types of mechanical planimeter being polar, linear and Prytz or "hatchet" planimeters. The Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, the concept having been pioneered by Johann Martin Hermann in 1814. Many developments followed Amsler's famous planimeter, including electronic versions. The Amsler (polar) type consists of a two-bar linkage. At the end of one link is a pointer, used to trace around the boundary of the shape to be measured. The other end of the linkage pivots freely on a weight that keeps it from moving. Near the junction of the two links is a measuring wheel of calibrated diameter, with a scale to show fine rotation, and worm gearing for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petersen's Theorem
In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching.. In other words, if a graph has exactly three edges at each vertex, and every edge belongs to a cycle, then it has a set of edges that touches every vertex exactly once. Proof We show that for every cubic, bridgeless graph we have that for every set the number of connected components in the graph induced by with an odd number of vertices is at most the cardinality of . Then by Tutte theorem contains a perfect matching. Let be a component with an odd number of vertices in the graph induced by the vertex set . Let denote the vertices of and let denote the number of edges of with one vertex in and one vertex in . By a simple double counting argument we have that :\sum\nolimits_ \deg_G(v) = 2, E_i, + m_i , where is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-factor Theorem
In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: : 2-factor theorem. Let ''G'' be a regular graph whose degree is an even number, 2''k''. Then the edges of ''G'' can be partitioned into ''k'' edge-disjoint 2-factors. Here, a 2-factor is a subgraph of ''G'' in which all vertices have degree two; that is, it is a collection of cycles that together touch each vertex exactly once. Proof In order to prove this generalized form of the theorem, Petersen first proved that a 4-regular graph can be factorized into two 2-factors by taking alternate edges in a Eulerian trail. He noted that the same technique used for the 4-regular graph yields a factorization of a 2''k''-regular graph into two ''k''-factors. To prove this theorem, it is sufficient to consider connected graphs. A connected graph with even degree has an Eulerian trail. Traversing this Eulerian trai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Denmark
The Technical University of Denmark ( da, Danmarks Tekniske Universitet), often simply referred to as DTU, is a polytechnic university and school of engineering. It was founded in 1829 at the initiative of Hans Christian Ørsted as Denmark's first polytechnic, and it is today ranked among Europe's leading engineering institutions. It is located in the town Kongens Lyngby, north of central Copenhagen, Denmark. Along with École Polytechnique in Paris, École Polytechnique Fédérale de Lausanne, Eindhoven University of Technology, Technical University of Munich and Technion – Israel Institute of Technology, DTU is a member of EuroTech Universities Alliance. History DTU was founded in 1829 as the "College of Advanced Technology" (Danish: Den Polytekniske Læreanstalt). The Physicist Hans Christian Ørsted, at that time a professor at the University of Copenhagen, was one of the driving forces behind this initiative. He was inspired by the École Polytechnique in Paris, Fran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
