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Julius Weingarten
Julius Weingarten (2 March 1836 – 16 June 1910) was a German mathematician. He received his doctorate in 1864 from Martin-Luther-Universität Halle-Wittenberg. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations The Weingarten equations give the expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of a point on the surface. These formulas were established in 1861 by the German mathematic .... Notes References * External links * * 19th-century German mathematicians 1836 births 1910 deaths 20th-century German mathematicians {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freiburg Im Breisgau
Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic German, Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as of 31 December 2018), Freiburg is the List of cities in Baden-Württemberg by population, fourth-largest city in Baden-Württemberg after Stuttgart, Mannheim, and Karlsruhe. The population of the Freiburg metropolitan area was 656,753 in 2018. In the Southern Germany, south-west of the country, it straddles the Dreisam river, at the foot of the Schlossberg (Freiburg), Schlossberg. Historically, the city has acted as the hub of the Breisgau region on the western edge of the Black Forest in the Upper Rhine Plain. A famous old German university town, and Roman Catholic Archdiocese of Freiburg, archiepiscopal seat, Freiburg was incorporated in the early twelfth century and developed into a major commercial, intellectual, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germans
, native_name_lang = de , region1 = , pop1 = 72,650,269 , region2 = , pop2 = 534,000 , region3 = , pop3 = 157,000 3,322,405 , region4 = , pop4 = 21,000 3,000,000 , region5 = , pop5 = 125,000 982,226 , region6 = , pop6 = 900,000 , region7 = , pop7 = 142,000 840,000 , region8 = , pop8 = 9,000 500,000 , region9 = , pop9 = 357,000 , region10 = , pop10 = 310,000 , region11 = , pop11 = 36,000 250,000 , region12 = , pop12 = 25,000 200,000 , region13 = , pop13 = 233,000 , region14 = , pop14 = 211,000 , region15 = , pop15 = 203,000 , region16 = , pop16 = 201,000 , region17 = , pop17 = 101,000 148,00 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin-Luther-Universität Halle-Wittenberg
Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university in the German state of Saxony-Anhalt. MLU offers German and international (English) courses leading to academic degrees such as BA, BSc, MA, MSc, doctoral degrees, and Habilitation. The university was created in 1817 through the merger of the University of Wittenberg (founded in 1502) and the University of Halle (founded in 1694). MLU is named after Protestant reformer Martin Luther, who was a professor in Wittenberg. Today, the university campus is located in Halle, while ''Leucorea Foundation'' in Wittenberg serves as MLU's convention centre. Both Halle and Wittenberg are about one hour from Berlin via the Berlin–Halle railway, which offers Intercity-Express (ICE) trains. History University of Wittenberg (''Universität Wittenb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Stäckel
Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term ''twin prime'' (in its German form, "Primzahlzwilling") for the first time. After passing his ''Abitur'' in 1880 he studied mathematics and physics at the University of Berlin, but also listened to lectures on philosophy, psychology, education, and history. A year later he qualified for teaching in higher education and then taught at ''Gymnasien'' in Berlin. In 1885 he wrote his doctoral dissertation under Leopold Kronecker and Karl Weierstraß. In 1891 he completed his ''Habilitation'' at the University of Halle. Later he worked as a professor at the University of Königsberg (''außerordentlicher Professor'' from 1895 to 1897), the University of Kiel (''ordentlicher Professor'', 1897 to 1905), University of Hannover (1905 to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weingarten Equations
The Weingarten equations give the expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of a point on the surface. These formulas were established in 1861 by the German mathematician Julius Weingarten. Statement in classical differential geometry Let ''S'' be a surface in three-dimensional Euclidean space that is parametrized by the position vector r(''u'', ''v''). Let ''P'' = ''P''(''u'', ''v'') be a point on the surface. Then : \mathbf_ = \frac , \quad \mathbf_ = \frac are two tangent vectors at point ''P''. Let n(''u'', ''v'') be the unit normal vector and let (''E'', ''F'', ''G'') and (''L'', ''M'', ''N'') be the coefficients of the first and second fundamental forms of this surface, respectively. The Weingarten equation gives the first derivative of the unit normal vector n at point ''P'' in terms of the tangent vectors r''u'' and r''v'': :\mathbf_u = \frac \mathbf_u + \frac \mathbf_v :\mathbf_v ... [...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] |
Differential Geometry Of Surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: ''extrinsically'', relating to their embedding in Euclidean space and ''intrinsically'', reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space. Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves. An important role in their study has been played by Lie groups (in the spirit of the Erlangen program), namely the symmetry groups of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1836 Births
Events January–March * January 1 – Queen Maria II of Portugal marries Prince Ferdinand Augustus Francis Anthony of Saxe-Coburg-Gotha. * January 5 – Davy Crockett arrives in Texas. * January 12 ** , with Charles Darwin on board, reaches Sydney. ** Will County, Illinois, is formed. * February 8 – London and Greenwich Railway opens its first section, the first railway in London, England. * February 16 – A fire at the Lahaman Theatre in Saint Petersburg kills 126 people."Fires, Great", in ''The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance'', Cornelius Walford, ed. (C. and E. Layton, 1876) p76 * February 23 – Texas Revolution: The Battle of the Alamo begins, with an American settler army surrounded by the Mexican Army, under Santa Anna. * February 25 – Samuel Colt receives a United States patent for the Colt revolver, the first revolving barrel multishot firearm. * March 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1910 Deaths
Year 191 ( CXCI) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Bradua (or, less frequently, year 944 ''Ab urbe condita''). The denomination 191 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Parthia * King Vologases IV of Parthia dies after a 44-year reign, and is succeeded by his son Vologases V. China * A coalition of Chinese warlords from the east of Hangu Pass launches a punitive campaign against the warlord Dong Zhuo, who seized control of the central government in 189, and held the figurehead Emperor Xian Emperor Xian of Han (2 April 181 – 21 April 234), personal name Liu Xie (劉協), courtesy name Bohe, was the 14th and last emperor of the Eastern Han dynasty in China. He reigned from 28 September 189 until 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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