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Julius Plücker
Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves. Biography Early years Plücker was born at Elberfeld (now part of Wuppertal). After being educated at Düsseldorf and at the universities of Bonn, Heidelberg and Berlin he went to Paris in 1823, where he came under the influence of the great school of French geometers, whose founder, Gaspard Monge, had only recently died. In 1825 he returned to Bonn, and in 1828 was made professor of mathematics. In the same year he published the first volume of his ''Analytisch-geometrische Entwicklungen'', which introduced the method of "abridged notation". In 1831 he published the second volume, in which he clearly established on a firm and independent basis projecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elberfeld
Elberfeld is a municipal subdivision of the Germany, German city of Wuppertal; it was an independent town until 1929. History The first official mentioning of the geographic area on the banks of today's Wupper River as "''elverfelde''" was in a document of 1161. Etymologically, ''elver'' is derived from the old Low German word for "river." (See etymology of the name of the German Elbe#Etymology, Elbe River; cf. North Germanic languages, North Germanic ''älv''.) Therefore, the original meaning of "elverfelde" can be understood as "field on the river." Elverfelde received its town charter in 1610. In 1726, Elias Eller and a pastor, Daniel Schleyermacher, founded a Philadelphian Society. They later moved to Ronsdorf in the Duchy of Berg, becoming the Zionites (Germany), Zionites, a fringe sect. In 1826 Friedrich Harkort, a famous German industrialist and politician, had a type of suspension railway built as a trial and ran it on the grounds of what is today the tax office at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johann Hittorf
Johann Wilhelm Hittorf (27 March 1824 – 28 November 1914) was a German physicist who was born in Bonn and died in Münster, Germany. Hittorf was the first to compute the electricity-carrying capacity of charged atoms and molecules ( ions), an important factor for understanding electrochemical reactions. He formulated ion transport numbers and the first method for their measurements. He experimented with tubes containing energy rays extending from a negative electrode. These rays produced a fluorescence when they hit the glass walls of the tubes. In 1876 the effect was named " cathode rays" by Eugen Goldstein. Hittorf's early investigations concerned the allotropes of phosphorus and selenium. Between 1853 and 1859 his most important work concerned ion movement caused by electric current. In 1853 Hittorf revealed that some ions traveled more rapidly than others. This observation resulted in the concept of transport number, the fraction of the electric current carried by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cathode Ray
Cathode rays are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to electrons emitted from the cathode (the electrode connected to the negative terminal of the voltage supply). They were first observed in 1859 by German physicist Julius Plücker and Johann Wilhelm Hittorf, and were named in 1876 by Eugen Goldstein ''Kathodenstrahlen'', or cathode rays. In 1897, British physicist J. J. Thomson showed that cathode rays were composed of a previously unknown negatively charged particle, which was later named the ''electron''. Cathode-ray tubes (CRTs) use a focused beam of electrons deflected by electric or magnetic fields to render an image on a screen. Description Cathode rays are so named because they are emitted by the negative electrode, or cathode, in a vacuum tube. To release electrons into the tube, they first must be detach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Geometry
Analytic or analytical may refer to: Chemistry * Analytical chemistry, the analysis of material samples to learn their chemical composition and structure * Analytical technique, a method that is used to determine the concentration of a chemical compound or chemical element * Analytical concentration Mathematics * Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields * Analytic combinatorics, a branch of combinatorics that describes combinatorial classes using generating functions * Analytic element method, a numerical method used to solve partial differential equations * Analytic expression or analytic solution, a mathematical expression using well-known operations that lend themselves readily to calculation * Analytic geometry, the study of geometry based on numerical coordinates rather than axioms * Analytic number theory, a branch of number theory that uses methods from mathematical analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of Phenomenon, phenomena, and usually frame their understanding in mathematical terms. They work across a wide range of Physics#Research fields, research fields, spanning all length scales: from atom, sub-atomic and particle physics, through biological physics, to physical cosmology, cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: Experimental physics, experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and Theoretical physics, theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their k ... [...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] |
Copley Medal
The Copley Medal is the most prestigious award of the Royal Society of the United Kingdom, conferred "for sustained, outstanding achievements in any field of science". The award alternates between the physical sciences or mathematics and the biological sciences. It is arguably the highest United Kingdom, British and Commonwealth of Nations, Commonwealth award for scientific achievement, and has often been included among the most distinguished international scientific awards. Given annually, the medal is the oldest Royal Society medal awarded and the oldest surviving scientific award in the world, having first been given in 1731 to Stephen Gray (scientist), Stephen Gray, for "his new Electrical Experiments: – as an encouragement to him for the readiness he has always shown in obliging the Society with his discoveries and improvements in this part of Natural Knowledge". The medal is made of silver-gilt and awarded with a £25,000 prize. It is awarded to "senior scientists" irres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. They are also used in fundamental elliptic curve cryptography algorithms. If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Surface
In algebraic geometry, a Plücker surface, studied by , is a quartic surface in 3-dimensional projective space In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally ... with a double line and 8 nodes. Construction For any quadric line complex, the lines of the complex in a plane envelop a quadric in the plane. A Plücker surface depends on the choice of a quadric line complex and a line, and consists of points of the quadrics associated to the planes through the chosen line. References * * * {{DEFAULTSORT:Plucker Surface Algebraic surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Relations
{{disambiguation * Julius Plücker Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the di ..., German mathematician and physicist * 29643 Plücker, main-belt asteroid * Plücker Line * Plücker matrix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Matrix
The Plücker matrix is a special skew-symmetric matrix, skew-symmetric 4 × 4 Matrix (mathematics), matrix, which characterizes a straight line in projective space. The matrix is defined by 6 Plücker coordinates with 4 degrees of freedom. It is named after the German mathematician Julius Plücker. Definition A straight line in space is defined by two distinct points A = \left(A_0, A_1, A_2, A_3\right)^\top \in \mathbb\mathcal^3 and B = \left(B_0, B_1, B_2, B_3\right)^\top \in \mathbb\mathcal^3 in homogeneous coordinates of the projective space. Its Plücker matrix is: : [\mathbf]_ \propto \mathbf\mathbf^ - \mathbf\mathbf^ = \left(\begin 0 & -L_ & -L_ & -L_ \\ L_ & 0 & -L_ & -L_ \\ L_ & L_ & 0 & -L_ \\ L_ & L_ & L_ & 0 \end\right) Where the skew-symmetric matrix, skew-symmetric 4\times 4-matrix is defined by the 6 Plücker coordinates :\mathbf\propto(L_, L_, L_, L_, L_, L_)^\top with :L_ = A_iB_j - B_iA_j. Plücke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Formula
In mathematics, a Plücker formula, named after Julius Plücker, is one of a family of formulae, of a type first developed by Plücker in the 1830s, that relate certain numeric invariants of algebraic curves to corresponding invariants of their dual curves. The invariant called the genus, common to both the curve and its dual, is connected to the other invariants by similar formulae. These formulae, and the fact that each of the invariants must be a positive integer, place quite strict limitations on their possible values. Plücker invariants and basic equations A curve in this context is defined by a non-degenerate algebraic equation in the complex projective plane. Lines in this plane correspond to points in the dual projective plane and the lines tangent to a given algebraic curve ''C'' correspond to points in an algebraic curve ''C''* called the dual curve. In the correspondence between the projective plane and its dual, points on ''C'' correspond to lines tangent ''C''*, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
