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Gustav Von Escherich
Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician. Biography Born in Mantua, he studied mathematics and physics at the University of Vienna. From 1876 to 1879 he was professor at the University of Graz. In 1882 he went to the Graz University of Technology and in 1884 he went to the University of Vienna, where he also was president of the university in 1903/04. Together with Emil Weyr he founded the journal '' Monatshefte für Mathematik und Physik'' and together with Ludwig Boltzmann and Emil Müller he founded the Austrian Mathematical Society. Escherich died in Vienna. Work on hyperbolic geometry Following Eugenio Beltrami's (1868) discussion of hyperbolic geometry, Escherich in 1874 published a paper named "The geometry on surfaces of constant negative curvature". He used coordinates initially introduced by Christoph Gudermann (1830) for spherical geometry, which were adapted by Escherich using hyperbolic functions. For the case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mantua
Mantua ( ; it, Mantova ; Lombard language, Lombard and la, Mantua) is a city and ''comune'' in Lombardy, Italy, and capital of the Province of Mantua, province of the same name. In 2016, Mantua was designated as the Italian Capital of Culture. In 2017, it was named as the European Capital of Gastronomy, included in the Eastern Lombardy District (together with the cities of Bergamo, Brescia, and Cremona). In 2008, Mantua's ''centro storico'' (old town) and Sabbioneta were declared by UNESCO to be a World Heritage Site. Mantua's historic power and influence under the Gonzaga family has made it one of the main artistic, culture, cultural, and especially musical hubs of Northern Italy and the country as a whole. Having one of the most splendid courts of Europe of the fifteenth, sixteenth, and early seventeenth centuries. Mantua is noted for its significant role in the history of opera; the city is also known for its architectural treasures and artifacts, elegant palaces, and the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Müller (mathematician)
Emil Adalbert Müller (22 April 1861 – 1 September 1927) was an Austrian mathematician. Biography Born in Lanškroun, he studied mathematics and physics at the University of Vienna and Vienna University of Technology. In 1898 he defended his dissertation (''Die Geometrie orientierter Kugeln nach Grassmann’schen Methoden'') at the University of Königsberg with Wilhelm Franz Meyer. One year later he received his habilitation at the same university. Since 1902 he was professor for descriptive geometry at the Vienna University of Technology and founder of the Vienna school of descriptive geometry. He also served as dean and president (1912–13). In 1903 he founded the Austrian Mathematical Society together with Ludwig Boltzmann and Gustav von Escherich. In 1904 Müller was an Invited Speaker of the ICM in Heidelberg. He was a member of the Austrian Academy of Sciences and the German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (german: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1935 Deaths
Events January * January 7 – Italian premier Benito Mussolini and French Foreign Minister Pierre Laval conclude an agreement, in which each power agrees not to oppose the other's colonial claims. * January 12 – Amelia Earhart becomes the first person to successfully complete a solo flight from Hawaii to California, a distance of 2,408 miles. * January 13 – A plebiscite in the Territory of the Saar Basin shows that 90.3% of those voting wish to join Germany. * January 24 – The first canned beer is sold in Richmond, Virginia, United States, by Gottfried Krueger Brewing Company. February * February 6 – Parker Brothers begins selling the board game Monopoly in the United States. * February 13 – Richard Hauptmann is convicted and sentenced to death for the kidnapping and murder of Charles Lindbergh Jr. in the United States. * February 15 – The discovery and clinical development of Prontosil, the first broadly effective antibiotic, is published in a se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1849 Births
Events January–March * January 1 – France begins issue of the Ceres series, the nation's first postage stamps. * January 5 – Hungarian Revolution of 1848: The Austrian army, led by Alfred I, Prince of Windisch-Grätz, enters in the Hungarian capitals, Buda and Pest. The Hungarian government and parliament flee to Debrecen. * January 8 – Hungarian Revolution of 1848: Romanian armed groups massacre 600 unarmed Hungarian civilians, at Nagyenyed.Hungarian HistoryJanuary 8, 1849 And the Genocide of the Hungarians of Nagyenyed/ref> * January 13 ** Second Anglo-Sikh War – Battle of Tooele: British forces retreat from the Sikhs. ** The Colony of Vancouver Island is established. * January 21 ** General elections are held in the Papal States. ** Hungarian Revolution of 1848: Battle of Nagyszeben – The Hungarian army in Transylvania, led by Josef Bem, is defeated by the Austrians, led by Anton Puchner. * January 23 – Elizabeth Blackwell is awarded her M.D. by the Medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homersham Cox (mathematician)
Homersham Cox (1857–1918) was an English mathematician. Life He was the son of Homersham Cox (1821–1897) and brother of Harold Cox and was educated at Tonbridge School (1870–75). At Trinity College, Cambridge, he graduated B.A. as 4th wrangler in 1880, and MA in 1883. He became a fellow in 1881. His younger sister Margaret, described him as a man often completely lost in his thoughts. He was married to Amy Cox. Later they separated and she started working as a governess in Russia in 1907. Cox wrote four papers applying algebra to physics, and then turned to mathematics education with a book on arithmetic in 1885. His ''Principles of Arithmetic'' included binary numbers, prime numbers, and permutations. Contracted to teach mathematics at Muir Central College, Cox became a resident of Allahabad, Uttar Pradesh from 1891 till his death in 1918. He was married to Amy Cox, by whom he had a daughter, Ursula Cox. Work on non-Euclidean geometry 1881–1883 he publishe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperboloid Model
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of ''n''-dimensional hyperbolic geometry in which points are represented by points on the forward sheet ''S''+ of a two-sheeted hyperboloid in (''n''+1)-dimensional Minkowski space or by the displacement vectors from the origin to those points, and ''m''-planes are represented by the intersections of (''m''+1)-planes passing through the origin in Minkowski space with ''S''+ or by wedge products of ''m'' vectors. Hyperbolic space is embedded isometrically in Minkowski space; that is, the hyperbolic distance function is inherited from Minkowski space, analogous to the way spherical distance is inherited from Euclidean distance when the ''n''-sphere is embedded in (''n''+1)-dimensional Euclidean space. Other models of hyperbolic space can be thought of as map projections of ''S''+: the Beltrami–Klein model is the projection of ''S''+ through the origin onto a plane perpendic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beltrami–Klein Model
In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or ''n''-dimensional unit ball) and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere. The Beltrami–Klein model is named after the Italian geometer Eugenio Beltrami and the German Felix Klein while "Cayley" in Cayley–Klein model refers to the English geometer Arthur Cayley. The Beltrami–Klein model is analogous to the gnomonic projection of spherical geometry, in that geodesics (great circles in spherical geometry) are mapped to straight lines. This model is not conformal, meaning that angles and circles are distorted, whereas the Poincaré disk model preserves these. In this model, lines and segments are straight Euclidean segments, whereas in the Poincaré disk model, lines ... [...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] |
Lorentz Boost
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the origins coinciding at 0, where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \left ( \sqrt\right )^ is the Lorentz factor. When speed is much smaller than , the Lorentz factor is negligibly different from 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where ''c'' is the velocity of light. For low speeds, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps onto . History In 1908 Hermann Minkowski expl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Addition Formula
In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost. Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment. The notation employs as velocity of a body within a Lorentz frame , and as velocity of a second frame , as measured in , and as the transformed velocity of the body within the second frame. History The speed of light in a fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Function
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: * hyperbolic sine "" (), * hyperbolic cosine "" (),''Collins Concise Dictionary'', p. 328 from which are derived: * hyperbolic tangent "" (), * hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
