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Schoenflies Theorem
Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology. Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland). Arthur Schoenflies married Emma Levin (1868–1939) in 1896. He studied under Ernst Kummer and Karl Weierstrass, and was influenced by Felix Klein. The Schoenflies problem is to prove that an (n - 1)-sphere in Euclidean ''n''-space bounds a topological ball, however embedded. This question is much more subtle than it initially appears. He studied at the University of Berlin from 1870 to 1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar to teach. Schoenflies was a frequent contributor to Klein's encyclopedia: In 1898 he wrote on set theory, in 1902 on kinematics, and on projective geometry in 1910. He wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landsberg An Der Warthe
Landsberg may refer to: * Landsberg (surname) * Margraviate of Landsberg, a march of the Holy Roman Empire * Palatinate-Landsberg, a state of the Holy Roman Empire Places * Landsberg (district), Bavaria, Germany * Landsberg, Saxony-Anhalt, Germany * Landsberg am Lech, Bavaria, Germany ** Landsberg-Lech Air Base, Germany ** Landsberg Prison, a prison in Landsberg am Lech ** Kaufering concentration camp complex * Landsberg an der Warthe, German name of Gorzów Wielkopolski, Poland * Landsberg in Oberschlesien/Upper Silesia, German name of Gorzów Śląski, Poland * Landsberg in Ostpreußen/East Prussia, German name of Górowo Iławeckie, Poland * Landsberg Castle (other) See also * Altlandsberg * Deutschlandsberg * Landsberge * Landsberger * Landsbergis, a surname * Margraviate of Landsberg The Margraviate of Landsberg (german: Mark Landsberg) was a march of the Holy Roman Empire that existed from the 13th to the 14th century under the rule of the Wettin dynasty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time. Life Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents. His father, Caspar Klein (1809–1889), was a Prussian government official's secretary stationed in the Rhine Province. His mother was Sophie Elise Klein (1819–1890, née Kayser). He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walther Nernst
Walther Hermann Nernst (; 25 June 1864 – 18 November 1941) was a German chemist known for his work in thermodynamics, physical chemistry, electrochemistry, and solid state physics. His formulation of the Nernst heat theorem helped pave the way for the third law of thermodynamics, for which he won the 1920 Nobel Prize in Chemistry. He is also known for developing the Nernst equation in 1887. Life and career Early years Nernst was born in Briesen in West Prussia (now Wąbrzeźno, Poland) to Gustav Nernst (1827–1888) and Ottilie Nerger (1833–1876). His father was a country judge. Nernst had three older sisters and one younger brother. His third sister died of cholera. Nernst went to elementary school at Graudenz. He studied physics and mathematics at the universities of Zürich, Berlin, Graz and Würzburg, where he received his doctorate 1887. In 1889, he finished his habilitation at University of Leipzig. Personal attributes It was said that Nernst was mechanically min ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Benjamin
Walter Bendix Schönflies Benjamin (; ; 15 July 1892 – 26 September 1940) was a German Jewish philosopher, cultural critic and essayist. An eclectic thinker, combining elements of German idealism, Romanticism, Western Marxism, and Jewish mysticism, Benjamin made enduring and influential contributions to aesthetic theory, literary criticism, and historical materialism. He was associated with the Frankfurt School, and also maintained formative friendships with thinkers such as playwright Bertolt Brecht and Kabbalah scholar Gershom Scholem. He was also related to German political theorist and philosopher Hannah Arendt through her first marriage to Benjamin's cousin Günther Anders. Among Benjamin's best known works are the essays " The Work of Art in the Age of Mechanical Reproduction" (1935), and "Theses on the Philosophy of History" (1940). His major work as a literary critic included essays on Baudelaire, Goethe, Kafka, Kraus, Leskov, Proust, Walser, and trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called " points at infinity") to Euclidean points, and vice-versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. It is not possible to refer to angles in projective geometry as it is in Euclidean geometry, because a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein's Encyclopedia
Felix Klein's ''Encyclopedia of Mathematical Sciences'' is a German mathematical encyclopedia published in six volumes from 1898 to 1933. Klein and Wilhelm Franz Meyer were organizers of the encyclopedia. Its full title in English is ''Encyclopedia of Mathematical Sciences Including Their Applications'', which is ''Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen'' (EMW). It is 20,000 pages in length (6 volumes, ''i.e. Bände'', published in 23 separate books, 1-1, 1-2, 2-1-1, 2-1-2, 2-2, 2-3-1, 2-3-2, 3-1-1, 3-1-2, 3-2-1, 3-2-2a, 3-2-2b, 3-3, 4-1, 4-2, 4-3, 4-4, 5-1, 5-2, 5-3, 6-1, 6-2-1, 6-2-2) and was published by B.G. Teubner Verlag, publisher of '' Mathematische Annalen''. Today, Göttinger Digitalisierungszentrum provides online access to all volumes, while archive.org hosts some particular parts. Overview Walther von Dyck acted as chairman of the commission to publish the encyclopedia. In 1904 he contributed a preparatory report on the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colmar
Colmar (, ; Alsatian: ' ; German during 1871–1918 and 1940–1945: ') is a city and commune in the Haut-Rhin department and Grand Est region of north-eastern France. The third-largest commune in Alsace (after Strasbourg and Mulhouse), it is the seat of the prefecture of the Haut-Rhin department and of the subprefecture of the Colmar-Ribeauvillé arrondissement. The city is renowned for its well-preserved old town, its numerous architectural landmarks, and its museums, among which is the Unterlinden Museum, which houses the '' Isenheim Altarpiece''. Colmar is situated on the Alsatian Wine Route and considers itself to be the "capital of Alsatian wine" ('). History Colmar was first mentioned by Charlemagne in his chronicle about Saxon wars. This was the location where the Carolingian Emperor Charles the Fat held a diet in 884. Colmar was granted the status of a free imperial city by Emperor Frederick II in 1226. In 1354 it joined the Décapole city league.G. Köb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Berlin
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Ernst Daniel Schleiermacher as the University of Berlin () in 1809, and opened in 1810, making it the oldest of Berlin's four universities. From 1828 until its closure in 1945, it was named Friedrich Wilhelm University (german: Friedrich-Wilhelms-Universität). During the Cold War, the university found itself in East Berlin and was ''de facto'' split in two when the Free University of Berlin opened in West Berlin. The university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties including its medical school shared with the Freie Universität Berlin. The university has a student enrollment of aroun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the centre of the sphere, and is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings. Basic terminology As mentioned earlier is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gorzów Wielkopolski
Gorzów Wielkopolski (; german: Landsberg an der Warthe) often abbreviated to Gorzów Wlkp. or simply Gorzów, is a city in western Poland, on the Warta river. It is the second largest city in the Lubusz Voivodeship with 120,087 inhabitants (December 2021) and one of its two capitals with a seat of a voivode, with the other being Zielona Góra. Around Gorzów, there are two large forest areas: Gorzów Woods to the north, where the Barlinek-Gorzów Landscape Park is situated, and Noteć Woods to the southeast. The biggest oil fields in Poland are located near Gorzów. Etymology The pre-1945 German name ''Landsberg an der Warthe'', dating back to 1257, derived from the German words ''land'' or 'state' and ''berg'' or 'mountain' combined with ''Warthe''the German name for the river Warta. The Polish name Gorzów, written as Gorzew, is known from Polish maps and historical books dating back to the 19th century or perhaps earlier.Henryk M. Wozniak, Gazeta Zachodnia "Gorzów tak - W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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