|
Polychromatic Symmetry
Polychromatic symmetry is a colour symmetry which interchanges three or more colours in a symmetrical pattern. It is a natural extension of dichromatic symmetry. The coloured symmetry groups are derived by adding to the position coordinates (''x'' and ''y'' in two dimensions, ''x'','' y'' and ''z'' in three dimensions) an extra coordinate, ''k'', which takes three or more possible values (colours). An example of an application of polychromatic symmetry is crystals of substances containing molecules or ions in triplet states, that is with an electronic spin of magnitude 1, should sometimes have structures in which the spins of these groups have projections of + 1, 0 and -1 onto local magnetic fields. If these three cases are present with equal frequency in an orderly array, then the magnetic space group of such a crystal should be three-coloured. Example The group ''Wallpaper group#Group p3, '' has three different rotation centres of order three (120°), but no reflections or gl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bartel Leendert Van Der Waerden
Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced by Emmy Noether at Göttingen, Germany. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry, supervised by Hendrick de Vries. Göttingen awarded him the habilitation in 1928. In that year, at the age of 25, he accepted a professorship at the University of Groningen. In his 27th year, Van der Waerden published his '' Moderne Algebra'', an influential two-volume treatise on abstract algebra, still cited, and perhaps the first treatise to treat the subject as a comprehensive whole. This work systematized an ample body of research by Emmy Noether, David Hilbert, Richard Dedekind, and Emil Artin. In the following year, 1931, he was appointed pro ... [...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 * Visions (convention), a science fiction event * Vision Festival, a New York City art festival Film and television * "The Vision", episode of '' Alcoa Presents: One Step Beyond'' * ''The Vision'' (film), 1998 British televisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Aspects Of M
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" 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; a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoffrey Colin Shephard
Geoffrey Colin Shephard is a mathematician who works 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 Queens' College is a constituent college of the University of Cambridge. Queens' is one of the oldest colleges of the university, founded in 1448 by Margaret of Anjou. The college spans the River Cam, colloquially referred to as the "light s ..., under the supervision of J. A. Todd. He was a professor of mathematics at the University of East Anglia until his retirement. University of East Anglia School of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branko Grünbaum
Branko Grünbaum ( he, ברנקו גרונבאום; 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 in |
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 (russian: Владимир Александрович Копцик; 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Lindsay Mackay
Alan Lindsay Mackay FRS (born 6 September 1926) is a British crystallographer, born in Wolverhampton. 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 has 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 Nive Quinquangula" in which he used a Penrose tiling in two and three dimensions to predict a new kind of ordered structures not allowed by traditional crystallography. In a later manuscript, in 1982, he took the optica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kristallografija
''Kristallografija'', also transliterated as ''Kristallografiya'' or ''Kristallografiia'', (russian: Кристаллография) is a bimonthly, peer-reviewed, Russian crystallography journal currently published by MAIC "Science/Interperiodica". An English translation ''Crystallography Reports'' is published by Pleiades Publishing, Inc. History The journal was founded in 1956 by Alexei Vasilievich Shubnikov and was initially dedicated to the publication of research from the Institute of Crystallography of the Russian Academy of Sciences. The journal is also available in English translation as ''Soviet Physics Crystallography'' (ISSN 0038-5638) 1956–1992 (volumes 1–37) continued as ''Crystallography Reports'' (ISSN 1063-7745) 1993–present (volumes 38–present). The journal is available in online format (ISSN 1562-689X) from 2000–present. The current publisher of the translated journal is Pleiades Publishing, Inc., and the distributor is Springer Nature. The journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolay Belov (geochemist)
Nikolay Vasilyevich Belov (russian: Никола́й Васи́льевич Бело́в; December 14, 1891 – March 6, 1982) was a Soviet and Russian crystallographer, geochemist, academician (1953), and Hero of Socialist Labour (1969). Honours and awards * Hero of Socialist Labour (1969) * Four Orders of Lenin (1961, 1969, 1971, 1981) * Order of the October Revolution (1975) * Order of the Red Banner of Labour (1953) * Medal "For the Defence of Moscow" (1944) * Medal "For Valiant Labour in the Great Patriotic War 1941–1945" (1946) * Medal "In Commemoration of the 800th Anniversary of Moscow" (1948) * Medal "For Labour Valour" (1967) * Jubilee Medal "In Commemoration of the 100th Anniversary of the Birth of Vladimir Ilyich Lenin" (1970) * Stalin Prize, 1st class (1952) * Lenin Prize (1974) * First Prize Fedorov (USSR, 1948) * Lomonosov Gold Medal (1965) * Gold Medal Exhibition of Economic Achievements of the USSR (1962) * Medal K. Ohridski (Sofia University K. Ohridski, Bul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotient Group
A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo ''n'' can be obtained from the group of integers under addition by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class (known as a congruence class) as a single entity. It is part of the mathematical field known as group theory. For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written G\,/\,N, where G is the original group and N is the normal subgroup. (This is pronounced G\bmod N, where \mbox is short for modulo.) Much of the importan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Symmetry Aspects Of M")
