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Werner Boy
Werner Boy (; 4 May 1879 − 6 September 1914) was a German mathematician. He was the discoverer and eponym of Boy's surface—a three-dimensional projection of the real projective plane without singularities, the first of its kind. He discovered it in 1901 after his thesis adviser, David Hilbert, asked him to prove that it was not possible to immerse the real projective plane in three-dimensional space. Boy sketched several models of the surface, and discovered that it could have 3-fold rotational symmetry, but was unable to find a parametric model for the surface. It was not until 1978 that Bernard Morin found the first parametrisation, with the aid of computers. After completing his dissertation, Boy worked as a high school teacher in Krefeld, Germany. He later returned to his birth town of Barmen (today Wuppertal) to teach. He died as a soldier in the first weeks of World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barmen
Barmen is a former industrial metropolis of the region of Bergisches Land, Germany, which merged with four other towns in 1929 to form the city of Wuppertal. Barmen, together with the neighbouring town of Elberfeld founded the first electric suspended monorail tramway system, the Schwebebahn ''floating tram''. History Barmen was a pioneering centre for both the early industrial revolution on the European mainland, and for the socialist movement and its theory. It was the location of one of the first concentration camps in Nazi Germany, KZ Wuppertal-Barmen, later better known as Kemna concentration camp. Oberbarmen (Upper Barmen) is the eastern part of Barmen, and Unterbarmen (Lower Barmen) the western part. One of its claims to fame is the fact that Friedrich Engels, co-author of ''The Communist Manifesto'', was born in Barmen. Another of its claims is the fact that Bayer AG was founded there by Friedrich Bayer and master dyer Johann Friedrich Weskott with the express pur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Projective Plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in passing through the origin. The plane is also often described topologically, in terms of a construction based on the Möbius strip: if one could glue the (single) edge of the Möbius strip to itself in the correct direction, one would obtain the projective plane. (This cannot be done in three-dimensional space without the surface intersecting itself.) Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane. Topologically, it has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. Since the Möbius strip, in turn, can be constructed from a square by glui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1914 Deaths
This year saw the beginning of what became known as World War I, after Archduke Franz Ferdinand of Austria, heir to the Austrian throne was Assassination of Archduke Franz Ferdinand, assassinated by Serbian nationalist Gavrilo Princip. It also saw the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with the St. Petersburg–Tampa Airboat Line. Events January * January 1 – The St. Petersburg–Tampa Airboat Line in the United States starts services between St. Petersburg, Florida, St. Petersburg and Tampa, Florida, becoming the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with Tony Jannus (the first federally-licensed pilot) conveying passengers in a Benoist XIV flying boat. Abram C. Pheil, mayor of St. Petersburg, is the first airline passenger, and over 3,000 people witness the first departure. * January 11 – The Sakurajima volcano in Japan b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1879 Births
Events January–March * January 1 – The Specie Resumption Act takes effect. The United States Note is valued the same as gold, for the first time since the American Civil War. * January 11 – The Anglo-Zulu War begins. * January 22 – Anglo-Zulu War – Battle of Isandlwana: A force of 1,200 British soldiers is wiped out by over 20,000 Zulu warriors. * January 23 – Anglo-Zulu War – Battle of Rorke's Drift: Following the previous day's defeat, a smaller British force of 140 successfully repels an attack by 4,000 Zulus. * February 3 – Mosley Street in Newcastle upon Tyne (England) becomes the world's first public highway to be lit by the electric incandescent light bulb invented by Joseph Swan. * February 8 – At a meeting of the Royal Canadian Institute, engineer and inventor Sandford Fleming first proposes the global adoption of standard time. * March 3 – United States Geological Survey is founded. * March 11 – Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fighting occurring throughout Europe, the Middle East, Africa, the Pacific, and parts of Asia. An estimated 9 million soldiers were killed in combat, plus another 23 million wounded, while 5 million civilians died as a result of military action, hunger, and disease. Millions more died in genocides within the Ottoman Empire and in the 1918 influenza pandemic, which was exacerbated by the movement of combatants during the war. Prior to 1914, the European great powers were divided between the Triple Entente (comprising France, Russia, and Britain) and the Triple Alliance (containing Germany, Austria-Hungary, and Italy). Tensions in the Balkans came to a head on 28 June 1914, following the assassination of Archduke Franz Ferdin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wuppertal
Wuppertal (; "''Wupper Dale''") is, with a population of approximately 355,000, the seventh-largest city in North Rhine-Westphalia as well as the 17th-largest city of Germany. It was founded in 1929 by the merger of the cities and towns of Elberfeld, Barmen, Ronsdorf, Cronenberg and Vohwinkel, and was initially "Barmen-Elberfeld" before adopting its present name in 1930. It is regarded as the capital and largest city of the Bergisches Land (historically this was Düsseldorf). The city straddles the densely populated banks of the River Wupper, a tributary of the Rhine called ''Wipper'' in its upper course. Wuppertal is located between the Ruhr (Essen) to the north, Düsseldorf to the west, and Cologne to the southwest, and over time has grown together with Solingen, Remscheid and Hagen. The stretching of the city in a long band along the narrow Wupper Valley leads to a spatial impression of Wuppertal being larger than it actually is. The city is known for its steep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krefeld, Germany
Krefeld ( , ; li, Krieëvel ), also spelled Crefeld until 1925 (though the spelling was still being used in British papers throughout the World War II, Second World War), is a city in North Rhine-Westphalia, Germany. It is located northwest of Düsseldorf, its center lying just a few kilometers to the west of the river Rhine; the borough of Uerdingen is situated directly on the Rhine. Because of its economic past, Krefeld is often referred to as the "Velvet and Silk City". It is accessed by the autobahns Bundesautobahn 57, A57 (Cologne–Nijmegen) and Bundesautobahn 44, A44 (Aachen–Düsseldorf–Dortmund–Kassel). Krefeld's residents now speak ', or standard German, but the native dialect is a Low Franconian variety, sometimes locally called ', ', ', or sometimes simply '. The Uerdingen line isogloss, separating general dialectical areas in Germany and neighboring Germanic-speaking countries, runs through and is named after Krefeld's Uerdingen district, originally an independ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer-assisted Proof
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program. Attempts have also been made in the area of artificial intelligence research to create smaller, explicit, new proofs of mathematical theorems from the bottom up using automated reasoning techniques such as heuristic search. Such automated theorem provers have proved a number of new results and found new proofs for known theorems. Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which are nonetheless formally verified for correctness. Since these proofs ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Morin
Bernard Morin (; 3 March 1931 in Shanghai, China – 12 March 2018) was a French mathematician, specifically a topologist. Early life and education Morin lost his sight at the age of six due to glaucoma, but his blindness did not prevent him from having a successful career in mathematics. He received his Ph.D. in 1972 from the Centre National de la Recherche Scientifique. Career Morin was a member of the group that first exhibited an eversion of the sphere, i.e., a homotopy which starts with a sphere and ends with the same sphere but turned inside-out. He also discovered the Morin surface, which is a half-way model for the sphere eversion, and used it to prove a lower bound on the number of steps needed to turn a sphere inside out. Morin discovered the first parametrization of Boy's surface (earlier used as a half-way model), in 1978. His graduate student François Apéry, in 1986, discovered another parametrization of Boy's surface, which conforms to the general method for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. For example, the equations :\begin x &= \cos t \\ y &= \sin t \end form a parametric representation of the unit circle, where ''t'' is the parameter: A point (''x'', ''y'') is on the unit circle if and only if there is a value of ''t'' such that these two equations generate that point. Sometimes the parametric equations for the individual scalar output variables are combined into a single parametric equation in vectors: :(x, y)=(\cos t, \sin t). Parametric representations are generally nonunique (see the "Examples in two dimensions" section belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the real function : f(x) = \frac has a singularity at x = 0, where the numerical value of the function approaches \pm\infty so the function is not defined. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory. Real analysis In real analysis, singularities are either discontinuities, or discontinuities of the derivative (sometimes also discontinuities of higher order derivatives). There are four kinds of discon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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