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Morwen Thistlethwaite
Morwen Bernard Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory and Rubik's Cube group theory. Biography Morwen Thistlethwaite received his BA from the University of Cambridge in 1967, his MSc from the University of London in 1968, and his PhD from the University of Manchester in 1972 where his advisor was Michael Barratt. He studied piano with Tanya Polunin, James Gibb and Balint Vazsonyi, giving concerts in London before deciding to pursue a career in mathematics in 1975. He taught at the North London Polytechnic from 1975 to 1978 and the Polytechnic of the South Bank, London from 1978 to 1987. He served as a visiting professor at the University of California, Santa Barbara for a year before going to the University of Tennessee, where he currently is a professor. His wife, Stella Thistlethwaite, also teaches at the University of Tennessee-Knoxville. Thistl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tait Conjectures
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture. Background Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram is called "reduced" if all the "isthmi", or "nugatory crossings" have been removed. Crossing number of alternating knots Tait conjectured that in certain circumstances, crossing number was a knot invariant, specifically: Any reduced diagram of an alterna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dowker Notation
Dowker is a surname. Notable people with the surname include: * Clifford Hugh Dowker (1912–1982), Canadian mathematician * Fay Dowker (born 1965), British physicist *Felicity Dowker, Australian fantasy writer * Hasted Dowker (1900–1986), Canadian Anglican priest *Ray Dowker (1919–2004), New Zealand cricketer * Yael Dowker (1919–2016), Israeli-English mathematician See also *Dowker Island, is an uninhabited island in Lake Saint Louis, a widening of the Saint Lawrence River south of Montreal Island, Quebec * Dowker notation, is mathematical notation *Dowker space In the mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact. They are named after Clifford Hugh Dowker. The non-trivial task of providing an example of a Dowker space (and therefor ..., is mathematical field of general topology * The Haunting of Hewie Dowker, is an Australian film {{Surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Hugh Dowker
Clifford Hugh Dowker (; March 2, 1912 – October 14, 1982) was a topologist known for his work in point-set topology and also for his contributions in category theory, sheaf theory and knot theory. Biography Clifford Hugh Dowker grew up on a small farm in Western Ontario, Canada. He excelled in mathematics and was paid to teach his math teacher math at his secondary school. He was awarded a scholarship at Western Ontario University, where he got his B.S. in 1933. He wanted to pursue a career as a teacher, but he was persuaded to continue with his education because of his extraordinary mathematical talent. He earned his M.A. from the University of Toronto in 1936 and his Ph.D. from Princeton University in 1938. His dissertation ''Mapping theorems in non-compact spaces'' was written under the supervision of Solomon Lefschetz and was published (with additions) in 1947 in the ''American Journal of Mathematics''. After earning his doctorate, Dowker became an instructor at the Weste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a set and an operation that combines any two elements of the set to produce a third element of the set, in such a way that the operation is associative, an identity element exists and every element has an inverse. These three axioms hold for number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Company, Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 Spiel des Jahres, German Game of the Year special award for Best Puzzle. , 350 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014. On the original classic Rubik's Cube, each of the six faces was covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. Some later versions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Menasco
William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory. Biography Menasco received his B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the University of California, Berkeley in 1981, where his advisor was Robion Kirby. He served as assistant professor at Rutgers University from 1981 to 1984. He then taught as a visiting professor at the University at Buffalo where he became an assistant professor in 1985, an associate professor in 1991. In 1994 he became a professor at the University at Buffalo where he currently serves. Work Menasco proved that a link with an alternating diagram, such as an alternating link, will be non-split if and only if the diagram is connected. Menasco, along with Morwen Thistlethwaite Morwen Bernard Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kunio Murasugi
Kunio (written: 邦夫, 邦男, 邦雄, 邦生, 國男, 國士, 国男, 国夫, 州男 or 久仁生) is a masculine Japanese given name. Notable people with the name include: *, Japanese businessman *, Japanese businessman *, Japanese judge *, Japanese politician *, Japanese mayor *, Japanese Go player *, Japanese field hockey player *, Japanese animator *, Japanese dramatist and writer *Kunio Kitamura (born 1968), Japanese footballer *Kunio Kobayashi (karateka), Kunio Kobayashi (born 1967), Japanese karateka *Kunio Lemari (1942–2008), Marshallese politician and President of the Marshall Islands *, Japanese architect *, Japanese photographer *, Japanese actor and voice actor (not to be confused with the manga character of the same name) *, Japanese politician *, Japanese general *, Japanese businessman *, Japanese footballer *, Japanese writer *, Japanese mechanical designer *, Japanese cross-country skier *Kunio Shimizu (born 1934), Japanese playwright *, Japanese writer *Kunio Y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Kauffman
Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, topologist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago. He is known for the introduction and development of the bracket polynomial and the Kauffman polynomial. Biography Kauffman was valedictorian of his graduating class at Norwood Norfolk Central High School in 1962. He received his B.S. at the Massachusetts Institute of Technology in 1966 and his Ph.D. in mathematics from Princeton University in 1972 (with William Browder as thesis advisor). Kauffman has worked at many places as a visiting professor and researcher, including the University of Zaragoza in Spain, the University of Iowa in Iowa City, the Institut des Hautes Études Scientifiques in Bures Sur Yevette, France, the Institut Henri Poincaré in Paris, France, the University of Bologna, Italy, the Federal University of Pernambuco in Recife, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tait Flyping Conjecture
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture. Background Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram is called "reduced" if all the "isthmi", or "nugatory crossings" have been removed. Crossing number of alternating knots Tait conjectured that in certain circumstances, crossing number was a knot invariant, specifically: Any reduced diagram of an alterna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flype
In the mathematical theory of knots, a flype is a kind of manipulation of knot and link diagrams used in the Tait flyping conjecture. It consists of twisting a part of a knot, a tangle T, by 180 degrees. Flype comes from a Scots word meaning ''to fold'' or ''to turn back'' ("as with a sock").. Tait used the term to mean, "a change of infinite complementary region"). Two reduced alternating diagrams of an alternating link can be transformed to each other using flypes. This is the Tait flyping conjecture, proven in 1991 by Morwen Thistlethwaite and William Menasco. See also * Reidemeister move Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Göttinge ...s are another commonly studied kind of manipulation to knot diagrams. References Knot operations {{knottheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amount of "coiling" of a mathematical knot (or any closed simple curve) in three-dimensional space and assumes real numbers as values. In both cases, writhe is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its writhe. Writhe of link diagrams In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. For each crossing one comes across while traveling in this direction, if the strand underneath goes from ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
