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Dichromatic Symmetry
Dichromatic symmetry,Loeb, A.L. (1971). ''Color and Symmetry'', Wiley, New York, also referred to as antisymmetry,Shubnikov, A.V. (1951). ''Symmetry and antisymmetry of finite figures'', Izv. Akad. Nauk SSSR, Moscow black-and-white symmetry, magnetic symmetry, counterchange symmetry or dichroic symmetry, is a symmetry operation which reverses an object to its opposite. A more precise definition is "operations of antisymmetry transform objects possessing two possible values of a given property from one value to the other."Mackay, A.L. (1957). Extensions of space-group theory', Acta Crystallogr. 10, 543-548, Dichromatic symmetry refers specifically to two-coloured symmetry; this can be extended to three or more colours in which case it is termed polychromatic symmetry. A general term for dichromatic and polychromatic symmetry is simply colour symmetry. Dichromatic symmetry is used to describe Magnetic space group, magnetic crystals and in other areas of physics,Padmanabhan, H., Munr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichromatic Triangle
Dichromatic may refer to: * Dichromacy, a form of color-blindness in which only two light wavelengths are distinguished rather than the usual three * Dichromatic, describing an optical device which splits light into two parts according to its wavelength: a form of dichroism * A form of polymorphism (biology), typical in sexual dimorphism, in which two phenotypes have different colouration or ornamentation. * Dichromatic reflectance model * Dichromatism: the property of a substance that changes hue due to change in its concentration or the thickness of a layer. See also * Chromatic * * {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Landau
Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and made seminal contributions to all branches of physics. He is credited with laying the foundations of twentieth century condensed matter physics, and is also considered arguably the greatest Soviet theoretical physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, invention of order parameter technique, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visions Of Symmetry
Vision, Visions, or The Vision may refer to: Perception Optical perception * Visual perception, the sense of sight * Visual system, the physical mechanism of eyesight * Computer vision, a field dealing with how computers can be made to gain understanding from digital images or videos * Machine vision, technology for imaging-based automatic inspection Perception of the future * Foresight (psychology), in business, the ability to envisage future market trends and plan accordingly * Goal, a desired result ** Vision statement, a declaration of objectives to guide decision-making Other perceptions * Vision (spirituality), a supernatural experience that conveys a revelation * Hallucination, a perception of something that does not exist Arts and media Events * Vision Festival, a New York City art festival * Visions (convention), a science fiction event Film and television Film * ''Vision'' (2009 film), German film * ''Vision'' (2018 film), Japanese-French film * ''The Vision'' (f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Aspects Of M
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art, and music. The opposite of symmetry is asymmetry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tilings And Patterns
''Tilings and patterns'' is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed. Structure and topics The book is concerned with Tessellation, tilings—a partition of the plane into regions (the tiles)—and patterns—repetitions of a motif in the plane in a regular manner. The book is divided into two parts. The first seven chapters define concepts and terminology, establish the general theory of tilings, survey tilings by regular polygons, review the theory of patterns, and discuss tilings in which all the tiles, or all the edges, or all the vertices, play the same role. The last five chapters survey a variety of advanced topics in tiling theory: Dichromatic symmetry, colored patterns and tilings, Euclidean tilings by convex regular polygons, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoffrey Colin Shephard
Geoffrey Colin Shephard (16 August 1927 - 3 August 2016) was a British mathematician who worked on convex geometry and reflection groups. He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups. Shephard earned his Ph.D. in 1954 from Queens' College, Cambridge, under the supervision of J. A. Todd. He was a professor of mathematics at the University of East Anglia The University of East Anglia (UEA) is a Public university, public research university in Norwich, England. Established in 1963 on a campus university, campus west of the city centre, the university has four faculties and twenty-six schools of ... until his retirement. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branko Grünbaum
Branko Grünbaum (; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descentBranko Grünbaum Hrvatska enciklopedija LZMK. and a professor at the in . He received his Ph.D. in 1957 from Hebrew University of Jerusalem. Life< ...
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Rolph Ludwig Edward Schwarzenberger
Rolph Ludwig Edward Schwarzenberger (7 February 1936 – 29 February 1992) was a British mathematician at the University of Warwick who worked on vector bundles (where he introduced jumping lines), crystallography, and mathematics education. He was President of the Mathematical Association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ... in 1983–1984. Publications * Schwarzenberger translated this book into English and added a long appendix on later developments. * * * References * * * 1936 births 1992 deaths 20th-century British mathematicians {{mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Alexandrovich Koptsik
Vladimir Alexandrovich Koptsik (; 26February 1924 – 2April 2005) was a Soviet crystallographer and physicist. In 1966 Koptsik was the first to publish the complete atlas of all 1651 antisymmetry space groups.Koptsik, V.A. (1966). ''Shubnikov groups: handbook on the symmetry and physical properties of crystal structures'' (in Russian), Moscow: Moscow University In 1972 he published ''Symmetry in science and art'' with extensive coverage of dichromatic and polychromatic symmetry. Life Career Koptsik was born on 26 February 1924 in Ivanovo. In 1941-1944 he worked as a turner in a defence plant in Moscow. Koptsik graduated from Moscow State University in 1949. He then began post-graduate work under the supervision of A.V. Shubnikov and submitted his candidate's dissertation in 1953.The Editors (2005), ''Vladimir Aleksandrovich Koptsik (February 26, 1924 – April 2, 2005)'', Crystallog. Reports, 50(5), 890-891 In 1953 Koptsik was hired as an assistant to Shubnikov in the new de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Lindsay Mackay
Alan Lindsay Mackay FRS (6 September 1926 – 24 February 2025) was a British crystallographer. Life and career Mackay was born in Wolverhampton on 6 September 1926. He was educated at Wolverhampton Grammar School, Oundle School, Trinity College, Cambridge, and the University of London, where he received his doctorate. He spent his scientific career at Birkbeck College, founded by George Birkbeck, one of the Colleges of the University of London, where he was immersed in a liberal scientific atmosphere under the leadership of John Desmond Bernal. Mackay made important scientific contributions related to the structure of materials: In 1962 he published a manuscript that showed how to pack atoms in an icosahedral fashion; a first step towards five-fold symmetry in materials science. These arrangements are now called Mackay icosahedra. He is a pioneer in the introduction of five-fold symmetry in materials and in 1981 predicted quasicrystals in a paper (in Russian) entitled "De N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolay Belov (geochemist)
Nikolay Vasilyevich Belov (; December 14, 1891 – March 6, 1982) was a Soviet and Russian crystallographer, geochemist, academician (1953), and Hero of Socialist Labour (1969). Belov worked primarily in the fields of mineralogy (particularly silicates), determination of crystal structures using X-ray crystallography, and the theory of symmetry, specifically dichromatic, and polychromatic symmetry, a field which Belov founded. Career Belov’s career has been summarised in a number of jubilees and obituaries.The editors (1981). ''Nikolai Vasil'evich Belov: ninetieth birthday'', Sov. Phys. Cryst., 26(6), 647-650 * 1921: graduated from the Polytechnic Institute of St. Petersburg with a degree in electrochemistry * 1924: worked as a chemist/analyst at industrial laboratories in St. Petersburg * 1928: directed the chemical laboratory of the Institute of Northern Studies in St. Petersburg * 1933: researcher at the Lomonosov Institute of the Russian Academy of Sciences under Ale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Moment
In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied, objects with larger magnetic moments experience larger torques. The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. Its direction points from the south pole to the north pole of the magnet (i.e., inside the magnet). The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
