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Eugenio Beltrami

Index Eugenio Beltrami

Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. [1]

65 relations: Accademia dei Lincei, American Mathematical Society, Austrian Empire, Beltrami equation, Beltrami identity, Beltrami vector field, Beltrami's theorem, Beltrami–Klein model, Bernhard Riemann, Constant curvature, Cremona, Cylinder, Delfino Codazzi, Differential calculus, Differential geometry, Equiconsistency, Euclidean geometry, Euclidean space, Felix Klein, Ferdinand Minding, Francesco Brioschi, Gaspard Monge, Gaussian curvature, Geodesic, Ghislieri College, Giovanni Frattini, Gregorio Ricci-Curbastro, Horocycle, Horosphere, Hyperbolic function, Hyperbolic space, Italian unification, Italy, János Bolyai, Jeremy Gray, Joseph Liouville, Kingdom of Italy, Kingdom of Lombardy–Venetia, Laplace–Beltrami operator, Lombardy, Luigi Cremona, Manifold, Mathematical physics, Mathematician, Matrix (mathematics), Nikolai Lobachevsky, Non-Euclidean geometry, Parallel postulate, Poincaré disk model, Poincaré half-plane model, ..., Pseudosphere, Riemannian manifold, Rome, Sapienza University of Rome, Singular-value decomposition, Singularity theory, Spherical trigonometry, Tensor calculus, Trigonometric functions, Tullio Levi-Civita, Unit disk, Unit sphere, University of Bologna, University of Pavia, University of Pisa. Expand index (15 more) »

Accademia dei Lincei

The Accademia dei Lincei (literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Austrian Empire

The Austrian Empire (Kaiserthum Oesterreich, modern spelling Kaisertum Österreich) was a Central European multinational great power from 1804 to 1919, created by proclamation out of the realms of the Habsburgs.

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Beltrami equation

In mathematics, the Beltrami equation, named after Eugenio Beltrami, is the partial differential equation for w a complex distribution of the complex variable z in some open set U, with derivatives that are locally L2, and where μ is a given complex function in L∞(U) of norm less than 1, called the Beltrami coefficient.

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Beltrami identity

The Beltrami identity, named after Eugenio Beltrami, is a simplified and less general version of the Euler–Lagrange equation in the calculus of variations.

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Beltrami vector field

In vector calculus, a Beltrami vector field, named after Eugenio Beltrami, is a vector field in three dimensions that is parallel to its own curl.

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Beltrami's theorem

In mathematics — specifically, in Riemannian geometry — Beltrami's theorem is a result named after the Italian mathematician Eugenio Beltrami which states that geodesic maps preserve the property of having constant curvature.

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Beltrami–Klein model

In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere.

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Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

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Constant curvature

In mathematics, constant curvature is a concept from differential geometry.

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Cremona

Cremona is a city and comune in northern Italy, situated in Lombardy, on the left bank of the Po River in the middle of the Pianura Padana (Po Valley).

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Cylinder

A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

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Delfino Codazzi

Delfino Codazzi (March 7, 1824 in Lodi – July 21, 1873 in Pavia) was an Italian mathematician.

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Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Equiconsistency

In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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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.

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Ferdinand Minding

Ferdinand Minding (Фердинанд Готлибович Миндинг; &ndash) was a German-Russian mathematician known for his contributions to differential geometry.

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Francesco Brioschi

Francesco Brioschi (22 December 1824 – 13 December 1897) was an Italian mathematician.

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Gaspard Monge

Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, the inventor of descriptive geometry (the mathematical basis of technical drawing), and the father of differential geometry.

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.

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Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

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Ghislieri College

The Ghislieri College (Italian: Collegio Ghislieri), founded in 1567 by Pope Pius V, is the second most ancient college in Pavia and co-founder of the IUSS, located in Pavia as well.

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Giovanni Frattini

Giovanni Frattini (8 January 1852 – 21 July 1925) was an Italian mathematician, noted for his contributions to group theory.

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Gregorio Ricci-Curbastro

Gregorio Ricci-Curbastro (12January 1925) was an Italian mathematician born in Lugo di Romagna.

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Horocycle

In hyperbolic geometry, a horocycle (ὅριον + κύκλος — border + circle, sometimes called an oricycle, oricircle, or limit circle) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction.

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Horosphere

In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic ''n''-space.

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Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

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Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

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Italian unification

Italian unification (Unità d'Italia), or the Risorgimento (meaning "the Resurgence" or "revival"), was the political and social movement that consolidated different states of the Italian peninsula into the single state of the Kingdom of Italy in the 19th century.

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Italy

Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.

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János Bolyai

János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.

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Jeremy Gray

Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics.

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Joseph Liouville

Joseph Liouville FRS FRSE FAS (24 March 1809 – 8 September 1882) was a French mathematician.

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Kingdom of Italy

The Kingdom of Italy (Regno d'Italia) was a state which existed from 1861—when King Victor Emmanuel II of Sardinia was proclaimed King of Italy—until 1946—when a constitutional referendum led civil discontent to abandon the monarchy and form the modern Italian Republic.

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Kingdom of Lombardy–Venetia

The Kingdom of Lombardy–Venetia (Regno Lombardo-Veneto, Königreich Lombardo–Venetien; Regnum Langobardiae et Venetiae), commonly called the Lombardo-Venetian Kingdom, was a constituent land (crown land) of the Austrian Empire.

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Laplace–Beltrami operator

In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.

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Lombardy

Lombardy (Lombardia; Lumbardia, pronounced: (Western Lombard), (Eastern Lombard)) is one of the twenty administrative regions of Italy, in the northwest of the country, with an area of.

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Luigi Cremona

Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Nikolai Lobachevsky

Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.

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Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

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Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.

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Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.

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Poincaré half-plane model

In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H \, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.

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Pseudosphere

In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Rome

Rome (Roma; Roma) is the capital city of Italy and a special comune (named Comune di Roma Capitale).

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Sapienza University of Rome

The Sapienza University of Rome (Italian: Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, is a collegiate research university located in Rome, Italy.

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Singular-value decomposition

In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.

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Singularity theory

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite.

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Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

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Tensor calculus

In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Tullio Levi-Civita

Tullio Levi-Civita, FRS (29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas.

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Unit disk

In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.

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Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

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University of Bologna

The University of Bologna (Università di Bologna, UNIBO), founded in 1088, is the oldest university in continuous operation, as well as one of the leading academic institutions in Italy and Europe.

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University of Pavia

The University of Pavia (Università degli Studi di Pavia, UNIPV or Università di Pavia; Ticinensis Universitas) is a university located in Pavia, Lombardy, Italy.

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University of Pisa

The University of Pisa (Università di Pisa, UniPi) is an Italian public research university located in Pisa, Italy.

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References

[1] https://en.wikipedia.org/wiki/Eugenio_Beltrami

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