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Gregorio Ricci-Curbastro
Gregorio Ricci-Curbastro (; 12January 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus. With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. This appears to be the only time that Ricci-Curbastro used the shortened form of his name in a publication, and continues to cause confusion. Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis, and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind. Early life and education Completing privately his high school studies at only 16 years of age, he enrolled on the course of philosophy-mathematics at Rome University (1869). The following year the Papal State fell and so Gregorio was called by his father to the city of his birth, Lugo di Romagna. Subsequently he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lugo, Emilia-Romagna
Lugo ( rgn, Lùgh) is a town and ''comune'' in the northern Italian region of Emilia-Romagna, in the province of Ravenna. History A settlement in where is now the city is mentioned for the first time in 782 AD, but the names Lucus appears only in 1071. In 1161 it was a fief of the Counts of Cunio, but in 1202 it returned to the Papal States. It was later a possession of the da Polenta, Pepoli, Visconti and Este; the latter maintained it until 1597, when the city was again annexed to the Papal States. In 1424 the Castle of Zagonara (now destroyed) was the seat of the homonymous battle, in which a Milanese army defeated the Florentines. When in 1797 the French revolutionary forces invaded northern Italy, Barnaba Chiaramonti (later pope as Pius VII), then still Bishop of Imola, addressed his flock to refrain from useless resistance to the overwhelming and threatening forces of the enemy. The town of Lugo refused to submit to the invaders and was delivered up to a pillage which ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Calculus
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold. Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:In our subject of differenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lingua Franca
A lingua franca (; ; for plurals see ), also known as a bridge language, common language, trade language, auxiliary language, vehicular language, or link language, is a language systematically used to make communication possible between groups of people who do not share a native language or dialect, particularly when it is a third language that is distinct from both of the speakers' native languages. Lingua francas have developed around the world throughout human history, sometimes for commercial reasons (so-called "trade languages" facilitated trade), but also for cultural, religious, diplomatic and administrative convenience, and as a means of exchanging information between scientists and other scholars of different nationalities. The term is taken from the medieval Mediterranean Lingua Franca, a Romance-based pidgin language used especially by traders in the Mediterranean Basin from the 11th to the 19th centuries. A world language – a language spoken internationally and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemannian Geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "''Ueber die Hypothesen, welche der Geometrie zu Grunde liegen''" ("On the Hypotheses on which Geometry is Based.") It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Munich
The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Established in 1868 by King Ludwig II of Bavaria, the university now has additional campuses in Garching, Freising, Heilbronn, Straubing, and Singapore, with the Garching campus being its largest. The university is organized into eight schools and departments, and is supported by numerous research centers. It is one of the largest universities in Germany, with 50,000 students and an annual budget of €1,770.3 million (including university hospital). A ''University of Excellence'' under the German Universities Excellence Initiative, TUM is considered the top university in Germany according to major rankings as of 2022 and is among the leading universities in the European Union. Its researchers and alumni include 18 Nobel laureates and 23 Leibniz ... [...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] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pisa
Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the city contains more than twenty other historic churches, several medieval palaces, and bridges across the Arno. Much of the city's architecture was financed from its history as one of the Italian maritime republics. The city is also home to the University of Pisa, which has a history going back to the 12th century, the Scuola Normale Superiore di Pisa, founded by Napoleon in 1810, and its offshoot, the Sant'Anna School of Advanced Studies.Scuola Superiore Sant'Anna di Pisa Information statistics History |
Vatican State
Vatican City (), officially the Vatican City State ( it, Stato della Città del Vaticano; la, Status Civitatis Vaticanae),—' * german: Vatikanstadt, cf. '—' (in Austria: ') * pl, Miasto Watykańskie, cf. '—' * pt, Cidade do Vaticano—' * es, Ciudad del Vaticano—' is an independent city-state, microstate and enclave within Rome, Italy. Also known as The Vatican, the state became independent from Italy in 1929 with the Lateran Treaty, and it is a distinct territory under "full ownership, exclusive dominion, and sovereign authority and jurisdiction" of the Holy See, itself a sovereign entity of international law, which maintains the city state's temporal, diplomatic, and spiritual independence. With an area of and a 2019 population of about 453, it is the smallest state in the world both by area and population. As governed by the Holy See, Vatican City State is an ecclesiastical or sacerdotal-monarchical state ruled by the Pope who is the bishop of Rome and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as '' Logicism''. Life Dedekind's father was Julius Levin Ulrich Dedekind, an administrator of Collegium Carolinum in Braunschweig. His mother was Caroline Henriette Dedekind (née Emperius), the daughter of a professor at the Collegium. Richard Dedekind had three older siblings. As an adult, he never used the names Julius Wilhelm. He was born in Braunschweig (often called "Brunswick" in English), which is where he lived most of his life and died. He first attended the Collegium Carolinum in 1848 before transferring to the Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers is denoted or \mathbb and is sometimes called "the reals". The adjective ''real'' in this context was introduced in the 17th century by René Descartes to distinguish real numbers, associated with physical reality, from imaginary numbers (such as the square roots of ), which seemed like a theoretical contrivance unrelated to physical reality. The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
