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Ausdehnungslehre
Hermann Günther Grassmann (, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all ''k''-dimensional linear subspaces of an ''n''-dimensional vector space ''V''. In linguistics he helped free language history and structure from each other. Biography Hermann Grassmann was the third of 12 children of Justus Günter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated. Grassmann was an undistinguished student until he obtained a high mark on the examinations for admission to Prussian universities. Beginning in 1827, he studied theology at the University of Berlin, also ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exterior Algebra
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector v in V. The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol \wedge and the fact that the product of two elements of V is "outside" V. The wedge product of k vectors v_1 \wedge v_2 \wedge \dots \wedge v_k is called a ''blade (geometry), blade of degree k'' or ''k-blade''. The wedge product was introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude (mathematics), magnitude of a bivector, -blade v\wedge w is the area of the parallelogram defined by v and w, and, more generally, the magnitude of a k-blade is the (hyper)volume of the Parallelepiped#Parallelotope, parallelotope defined by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called scalar (mathematics), ''scalars''. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field (mathematics), field. Vector spaces generalize Euclidean vectors, which allow modeling of Physical quantity, physical quantities (such as forces and velocity) that have not only a Magnitude (mathematics), magnitude, but also a Orientation (geometry), direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix (mathematics), matrices, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stettin
Szczecin ( , , ; ; ; or ) is the capital and largest city of the West Pomeranian Voivodeship in northwestern Poland. Located near the Baltic Sea and the German border, it is a major seaport, the largest city of northwestern Poland, and seventh-largest city of Poland. the population was 391,566. Szczecin is located on the Oder River, south of the Szczecin Lagoon and the Bay of Pomerania. The city is situated along the southwestern shore of Dąbie Lake, on both sides of the Oder and on several large islands between the western and eastern branches of the river. It is also surrounded by dense forests, shrubland and heaths, chiefly the Wkrzańska Heath shared with Germany (Ueckermünde) and the Szczecin Landscape Park. Szczecin is adjacent to the town of Police and is the urban centre of the Szczecin agglomeration, an extended metropolitan area that includes communities in the German states of Brandenburg and Mecklenburg-Western Pomerania. The city's recorded histo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mineralogy
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical mineralogy, optical) properties of minerals and mineralized artifact (archaeology), artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization. History Early writing on mineralogy, especially on gemstones, comes from ancient Babylonia, the ancient Greco-Roman world, ancient and medieval History of China, China, and Sanskrit texts from History of India, ancient India and the ancient Islamic world. Books on the subject included the ''Naturalis Historia, Natural History'' of Pliny the Elder, which not only described many different minerals but also explained many of their properties, and Kitab al Jawahir (Book of Precious Stones) by Persian scientist Al-Biruni. The German Renaissance specialist Georgius Agricola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during chemical reaction, reactions with other chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classics
Classics, also classical studies or Ancient Greek and Roman studies, is the study of classical antiquity. In the Western world, ''classics'' traditionally refers to the study of Ancient Greek literature, Ancient Greek and Roman literature and their original languages, Ancient Greek and Latin. Classics may also include as secondary subjects Greco-Roman Ancient philosophy, philosophy, Ancient history, history, archaeology, anthropology, classical architecture, architecture, Ancient art, art, Classical mythology, mythology, and society. In Western culture, Western civilization, the study of the Ancient Greek and Roman classics was considered the foundation of the humanities, and they traditionally have been the cornerstone of an elite higher education. Etymology The word ''classics'' is derived from the Latin adjective ''wikt:classicus, classicus'', meaning "belonging to the highest class of Citizenship, citizens." The word was originally used to describe the members of the Patri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prussia
Prussia (; ; Old Prussian: ''Prūsija'') was a Germans, German state centred on the North European Plain that originated from the 1525 secularization of the Prussia (region), Prussian part of the State of the Teutonic Order. For centuries, the House of Hohenzollern ruled Prussia, expanding its size with the Prussian Army. Prussia, with its capital at Königsberg and then, when it became the Kingdom of Prussia in 1701, History of Berlin, Berlin, decisively shaped the history of Germany. Prussia formed the German Empire when it united the German states in 1871. It was ''de facto'' dissolved by 1932 Prussian coup d'état, an emergency decree transferring powers of the Prussian government to German Chancellor Franz von Papen in 1932 and ''de jure'' by Abolition of Prussia, an Allied decree in 1947. The name ''Prussia'' derives from the Old Prussians who were conquered by the Teutonic Knightsan organized Catholic medieval Military order (religious society), military order of Pru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minister (Christianity)
In Christianity, a minister is a person authorised by a church body, church or other religious organization to perform functions such as teaching of beliefs; leading services such as weddings, baptisms or funerals; or otherwise providing spiritual guidance to the community. The term is taken from Latin ''minister'' ("servant", "attendant"). In some church traditions the term is usually used for people who have been ordained, but in other traditions it can also be used for non-ordained. In the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Church, Anglicanism and Lutheranism, the concept of a priesthood is emphasized, though in the Church of England there are nearly as many non-ordained licensed lay ministers as there are paid clergy. In other traditions such as Baptist, Methodist, and Reformed Christianity, Reformed groups like Congregationalists and Presbyterians, the term "minister" usually refers to a member of the ordination, ordained clergy who leads a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordination
Ordination is the process by which individuals are Consecration in Christianity, consecrated, that is, set apart and elevated from the laity class to the clergy, who are thus then authorized (usually by the religious denomination, denominational hierarchy composed of other clergy) to perform various religious rites and ceremonies. The process and ceremonies of ordination vary by religion and denomination. One who is in preparation for, or who is undergoing the process of ordination is sometimes called an ordinand. The liturgy used at an ordination is commonly found in a book known as an Order of Mass, Ordinal which provides the ordo (ritual and rubrics) for celebrations. Christianity Catholic, Orthodox, Lutheran and Anglican churches In Catholicism and Orthodoxy, ordination is one of the seven sacraments, variously called holy orders or ''Christian laying on of hands, cheirotonia'' ("Laying on of Hands"). Apostolic succession is considered an essential and necessary concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
