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Delfino Codazzi
Delfino Codazzi (7 March 1824 in Lodi – 21 July 1873 in Pavia) was an Italian mathematician.U. Amaldi, in Enciclopedia italiana, app. 1, Rome, (1938), 438. He made some important contributions to the differential geometry of surfaces, such as the Codazzi–Mainardi equations. Biography He graduated in mathematics at the University of Pavia, where he was a pupil of Antonio Bordoni. For a long period Codazzi taught first at the Ginnasio Liceale of Lodi, then at the liceo of Pavia. Meanwhile, he devoted himself to research in differential geometry. In 1865, he was appointed professor of complementary algebra and analytic geometry at University of Pavia. He remained in his position at Pavia until his death in 1873. He also obtained results concerning isometric lines, geodesic triangles, equiareal mapping and the stability of floating bodies. See also * Gauss–Codazzi equations * Codazzi tensor In the mathematical field of differential geometry, a Codazzi tensor (named a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lodi, Lombardy
Lodi ( , ; Ludesan: ) is a city and ''comune'' in Lombardy, northern Italy, primarily on the western bank of the River Adda. It is the capital of the province of Lodi. History Lodi was a Celtic village; in Roman times it was called, in Latin, Laus Pompeia (probably in honour of the consul Gnaeus Pompeius Strabo) and was known also because its position allowed many Gauls of ''Gallia Cisalpina'' to obtain Roman citizenship. It was in an important position where a vital Roman road crossed the River Adda. Lodi became the see of a diocese in the 3rd century. Saint Bassianus (San Bassiano) is the patron saint of the town. A free commune around 1000, it fiercely resisted the Milanese, who destroyed it in 1111. The old town corresponds to the modern Lodi Vecchio. Frederick Barbarossa rebuilt it on its current location in 1158. From 1220, the ''Lodigiani'' (inhabitants of Lodi) spent decades in constructing a system of miles of artificial rivers and channels (called ''Consorzio di M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pavia
Pavia (, , , ; la, Ticinum; Medieval Latin: ) is a town and comune of south-western Lombardy in northern Italy, south of Milan on the lower Ticino river near its confluence with the Po. It has a population of c. 73,086. The city was the capital of the Ostrogothic Kingdom from 540 to 553, of the Kingdom of the Lombards from 572 to 774, of the Kingdom of Italy from 774 to 1024 and seat of the Visconti court from 1365 to 1413. Pavia is the capital of the fertile province of Pavia, which is known for a variety of agricultural products, including wine, rice, cereals, and dairy products. Although there are a number of industries located in the suburbs, these tend not to disturb the peaceful atmosphere of the town. It is home to the ancient University of Pavia (founded in 1361 and recognized in 2022 by the Times Higher Education among the top 10 in Italy and among the 300 best in the world), which together with the IUSS (Institute for Advanced Studies of Pavia), Ghislieri College, B ... [...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
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Codazzi Equations
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi Formulas) are fundamental formulas which link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold. The equations were originally discovered in the context of surfaces in three-dimensional Euclidean space. In this context, the first equation, often called the Gauss equation (after its discoverer Carl Friedrich Gauss), says that the Gauss curvature of the surface, at any given point, is dictated by the derivatives of the Gauss map at that point, as encoded by the second fundamental form. The second equation, called the Codazzi equation or Codazzi-Mainardi equation, states that the covariant derivative of the second fundamental form is fully symmetric. It is named for Gaspare Mainardi (1856) and Delfino Codazzi (1868†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pavia
The University of Pavia ( it, Università degli Studi di Pavia, UNIPV or ''Università di Pavia''; la, Alma Ticinensis Universitas) is a university located in Pavia, Lombardy, Italy. There was evidence of teaching as early as 1361, making it one of the oldest universities in the world. It was the sole university in Milan and the greater Lombardy region until the end of the 19th century. In 2022 the University was recognized by the Times Higher Education among the top 10 in Italy and among the 300 best in the world. Currently, it has 18 departments and 9 faculties. It does not have a main campus; its buildings and facilities are scattered around the city, which is in turn called "a city campus." The university caters to more than 20,000 students who come from Italy and all over the world. The university offers more than 80 undergraduate programs; over 40 master programs, and roughly 20 doctoral programs (including 8 in English). About 1,500 students who enter the university every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antonio Maria Bordoni
Antonio Maria Bordoni (19 July 1789 – 26 March 1860) was an Italian mathematician who did research on mathematical analysis, geometry, and mechanics. Joining the faculty of the University of Pavia in 1817, Bordoni is generally considered to be the founder of the mathematical school of Pavia. He was a member of various learned academies, notably the Accademia nazionale delle scienze detta dei XL, Accademia dei XL. Bordoni's famous students were Francesco Brioschi, Luigi Cremona, Eugenio Beltrami, Felice Casorati and Delfino Codazzi. Biography Antonio Bordoni was born in Mezzana Corti (province of Pavia) on 19 July 1788, and graduated in Mathematics from Pavia on 7 June 1807. After just two months he was appointed teacher of mathematics at the military School of Pavia, established by Napoleon, and held such office until 1816 when the school was closed due to the political situation of the times. On 1 November 1817 he became full professor of Elementary Pure mathematics at the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic 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, Aerospace engineering, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including Algebraic geometry, algebraic, Differential geometry, differential, Discrete geometry, 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 defin ... [...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] |
Equiareal Map
In differential geometry, an equiareal map, sometimes called an authalic map, is a smooth map from one surface to another that preserves the areas of figures. Properties If ''M'' and ''N'' are two Riemannian (or pseudo-Riemannian) surfaces, then an equiareal map ''f'' from ''M'' to ''N'' can be characterized by any of the following equivalent conditions: * The surface area of ''f''(''U'') is equal to the area of ''U'' for every open set ''U'' on ''M''. * The pullback of the area element ''μ''''N'' on ''N'' is equal to ''μ''''M'', the area element on ''M''. * At each point ''p'' of ''M'', and tangent vectors ''v'' and ''w'' to ''M'' at ''p'',\bigl, df_p(v)\wedge df_p(w)\bigr, = , v\wedge w, \,where \wedge denotes the Euclidean wedge product of vectors and ''df'' denotes the pushforward along ''f''. Example An example of an equiareal map, due to Archimedes of Syracuse, is the projection from the unit sphere to the unit cylinder outward from their common axis. An explicit for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codazzi Tensor
In the mathematical field of differential geometry, a Codazzi tensor (named after Delfino Codazzi) is a symmetric 2-tensor whose covariant derivative is also symmetric. Such tensors arise naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold. Also, the second fundamental form of an immersed hypersurface in a space form (relative to a local choice of normal field) is a Codazzi tensor. Definition Let (M,g) be a n-dimensional Riemannian manifold for n \geq 3, let T be a symmetric 2-tensor field, and let \nabla be the Levi-Civita connection. We say that the tensor T is a Codazzi tensor if : (\nabla_X T)(Y,Z) = (\nabla_Y T)(X,Z) for all X,Y,Z\in T_pM. Examples * Any parallel -tensor field is, trivially, Codazzi. * Let (N,\overline) be a space form, let M be a smooth manifold with 1+\dim M=\dim N, and let F:M\to N be an immersion. If the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1824 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
