|
Otto Hesse
Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. Hesse was born in Königsberg, Prussia, and died in Munich, Bavaria. He worked mainly on algebraic invariants, and geometry. The Hessian matrix, the Hesse normal form, the Hesse configuration, the Hessian group, Hessian pairs, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many of Hesse's research findings were presented for the first time in ''Crelle's Journal'' or Hesse's textbooks. MacTutor History of Mathematics archive and Complete Dictionary of Scientific Biography Life Hesse was born in Königsberg (today Kaliningrad) as the son of Johann Gottlieb Hesse, a businessman and brewery owner and his wife Anna Karoline Reiter (1788–1865). He studied in his hometown at the Albertina under Carl Gustav Jacob Jacobi. Among his teachers were count Friedrich Wilhelm Bessel and Friedrich Julius Richelot. He earned his doctorate in 1840 at the University of K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Königsberg
Königsberg (; ; ; ; ; ; , ) is the historic Germany, German and Prussian name of the city now called Kaliningrad, Russia. The city was founded in 1255 on the site of the small Old Prussians, Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, Baltic Crusades. It was named in honour of King Ottokar II of Bohemia, who led a campaign against the pagan Old Prussians, a Baltic tribe. A Baltic Sea, Baltic port city, it successively became the capital of the State of the Teutonic Order, the Duchy of Prussia and the provinces of East Prussia and Province of Prussia, Prussia. Königsberg remained the coronation city of the Prussian monarchy from 1701 onwards, though the capital was Berlin. From the thirteenth to the twentieth centuries on, the inhabitants spoke predominantly German language, German, although the city also had a profound influence upon the Lithuanian and Polish cultures. It was a publishing center of Lutheranism, Lutheran literatu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hesse Normal Form
In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane \mathbb^2, a plane in Euclidean space \mathbb^3, or a hyperplane in higher dimensions.John Vince: ''Geometry for Computer Graphics''. Springer, 2005, , pp. 42, 58, 135, 273 It is primarily used for calculating distances (see point-plane distance and point-line distance). It is written in vector notation as :\vec r \cdot \vec n_0 - d = 0.\, The dot \cdot indicates the dot product (or scalar product). Vector \vec r points from the origin of the coordinate system, ''O'', to any point ''P'' that lies precisely in plane or on line ''E''. The vector \vec n_0 represents the unit normal vector of plane or line ''E''. The distance d \ge 0 is the shortest distance from the origin ''O'' to the plane or line. Derivation/Calculation from the normal form Note: For simplicity, the following derivation discusses the 3D case. However, it is also applicable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Dictionary Of Scientific Biography
The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It consisted of sixteen volumes. It is supplemented by the ''New Dictionary of Scientific Biography'' (2007). Both these publications are included in a later electronic book, called the ''Complete Dictionary of Scientific Biography''. ''Dictionary of Scientific Biography'' The ''Dictionary of Scientific Biography'' is a scholarly English-language reference work consisting of biographies of scientists from antiquity to modern times but excluding scientists who were alive when the ''Dictionary'' was first published. It includes scientists who worked in the areas of mathematics, physics, chemistry, biology, and earth sciences. The work is notable for being one of the most substantial reference works in the field of history of science, containing exte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Daniel Huybrechts ( Rheinische Friedrich-Wilhelms-Universität Bonn). Past editors * 1826–1856: August Leopold Crelle * 1856–1880: Carl Wilhelm Borchardt * 1881–1888: Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hesse Transfer Principle
Hesse or Hessen ( ), officially the State of Hesse (), is a state in Germany. Its capital city is Wiesbaden, and the largest urban area is Frankfurt, which is also the country's principal financial centre. Two other major historic cities are Darmstadt and Kassel. With an area of 21,114.73 square kilometers and a population of over six million, it ranks seventh and fifth, respectively, among the sixteen German states. Frankfurt Rhine-Main, Germany's second-largest metropolitan area (after Rhine-Ruhr), is mainly located in Hesse. As a cultural region, Hesse also includes the area known as Rhenish Hesse (Rheinhessen) in the neighboring state of Rhineland-Palatinate. Etymology The German name , like the names of other German regions ( "Swabia", "Franconia", "Bavaria", "Saxony"), derives from the dative plural form of the name of the inhabitants or eponymous tribe, the Hessians (, singular ). The geographical name represents a short equivalent of the older compound name ("land ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Invariant
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are ''invariant'', under the transformations from a given linear group. For example, if we consider the action of the special linear group ''SLn'' on the space of ''n'' by ''n'' matrices by left multiplication, then the determinant is an invariant of this action because the determinant of ''A X'' equals the determinant of ''X'', when ''A'' is in ''SLn''. Introduction Let G be a group, and V a finite-dimensional vector space over a field k (which in classical invariant theory was usually assumed to be the complex numbers). A representation of G in V is a group homomorphism \pi:G \to GL(V), which induces a group action of G on V. If k /math> is the space of polynomial functions on V, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hesse Pencil
In mathematics, the syzygetic pencil or Hesse pencil, named for Otto Hesse, is a pencil (one-dimensional family) of cubic plane elliptic curves in the complex projective plane, defined by the equation :\lambda(x^3+y^3+z^3) + \mu xyz =0. Each curve in the family is determined by a pair of parameter values (\lambda,\mu) (not both zero) and consists of the points in the plane whose homogeneous coordinates (x,y,z) satisfy the equation for those parameters. Multiplying both \lambda and \mu by the same scalar does not change the curve, so there is only one degree of freedom in selecting a curve from the pencil, but the two-parameter form given above allows either \lambda or \mu (but not both) to be set to zero. Each curve in the pencil passes through the nine points of the complex projective plane whose homogeneous coordinates are some permutation of 0, –1, and a cube root of unity. There are three roots of unity, and six permutations per root, giving 18 choices for the homogeneous coo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hesse's Theorem
In geometry, Hesse's theorem, named for Otto Hesse, states that if two pairs of opposite vertices of a quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ... are conjugate with respect to some conic, then so is the third pair. A quadrilateral with this property is called a Hesse quadrilateral. References * Theorems in projective geometry {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
