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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 projective ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elberfeld
Elberfeld is a municipal subdivision of the 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 River; cf. 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, 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 Elberfeld. In fact the railway, the Schwebebahn Wuppertal, was eventu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker's Conoid
In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder. Plücker's conoid is the surface defined by the function of two variables: : z=\frac. This function has an essential singularity at the origin. By using cylindrical coordinates in space, we can write the above function into parametric equations : x=v\cos u,\quad y=v\sin u,\quad z=\sin 2u. Thus Plücker's conoid is a right conoid, which can be obtained by rotating a horizontal line about the with the oscillatory motion (with period 2''π'') along the segment of the axis (Figure 4). A generalization of Plücker's conoid is given by the parametric equations : x=v \cos u,\quad y=v \sin u,\quad z= \sin nu. where denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cathode Ray
Cathode rays or electron beam (e-beam) 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, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to ... [...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 phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies (also known as applie ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copley Medal
The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, 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". __TOC__ History The medal was created following a donation of Pound sterling, £100 to be used for carrying out experiments by Sir Godfrey Copley, 2nd Baronet, Sir Godfrey Copley, for which the interest on the amount was used for several years. The conditions for the medal have been changed several times; in 1736, it was suggested that "a medal or other honorary prize s ... [...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. 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 infinity, the number of coordinates required to allow this extension is one more than ... [...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 with a double line and 8 nodes. Construction For any quadric line complex In algebraic geometry, a line complex is a 3-fold given by the intersection of the Grassmannian ''G''(2, 4) (embedded in projective space ''P''5 by Plücker coordinates) with a hypersurface. It is called a line complex because points of ''G''( ..., 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, German mathematician and physicist * 29643 Plücker, main-belt asteroid * Plücker Line * Plücker matrix The Plücker matrix is a special skew-symmetric 4 × 4 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 mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Matrix
The Plücker matrix is a special skew-symmetric 4 × 4 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 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. Plücker coordinates fulfill the Graßmann–Plücker relations :L_ L_ - L_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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