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# Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory. [1]

93 relations: Adrien-Marie Legendre, Alfred Clebsch, Algebraic solution, Ashkenazi Jews, August Böckh, Augustin-Louis Cauchy, , Berlin, Bernhard Riemann, Canon arithmeticus, Carl Friedrich Gauss, Celestial mechanics, Classical mechanics, Continued fraction, Crelle's Journal, Differential equation, Differential geometry of curves, Differential geometry of surfaces, Dynamics (mechanics), Elliptic function, Equations of motion, Euclidean vector, Fermat's theorem on sums of two squares, Friedrich Bessel, Friedrich Julius Richelot, Friedrich Wilhelm Argelander, Fundamenta nova theoriae functionum ellipticarum, Germans, Gravitational field, Gymnasium (Germany), Haaretz, Habilitation, Hamilton–Jacobi equation, Humboldt University of Berlin, Hypergeometric function, Italy, Jacobi (crater), Jacobi ellipsoid, Jacobi elliptic functions, Jacobi identity, Jacobi integral, Jacobi method, Jacobi operator, Jacobi polynomials, Jacobi sum, Jacobi symbol, Jacobi transform, Jacobi triple product, Jacobian matrix and determinant, Jacobian variety, ... Expand index (43 more) »

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.

## Alfred Clebsch

Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory.

## Algebraic solution

An algebraic solution or solution in radicals is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of an algebraic equation in terms of the coefficients, relying only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots).

## Ashkenazi Jews

Ashkenazi Jews, also known as Ashkenazic Jews or simply Ashkenazim (אַשְׁכְּנַזִּים, Ashkenazi Hebrew pronunciation:, singular:, Modern Hebrew:; also), are a Jewish diaspora population who coalesced in the Holy Roman Empire around the end of the first millennium.

## August Böckh

August Böckh or Boeckh (24 November 1785 – 3 August 1867) was a German classical scholar and antiquarian.

## Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

## ∂

The character ∂ (HTML element: &amp;#8706; or &amp;part;, Unicode: U+2202) or \partial is a stylized d mainly used as a mathematical symbol to denote a partial derivative such as \frac (read as "the partial derivative of z with respect to x").

## Berlin

Berlin is the capital and the largest city of Germany, as well as one of its 16 constituent states.

## 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.

## Canon arithmeticus

In mathematics, Canon arithmeticus is a table of indices and powers with respect to primitive roots for prime powers less than 1000, originally published by.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

## Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

## Differential geometry of curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

## 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.

## Dynamics (mechanics)

Dynamics is the branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to these forces.

## Elliptic function

In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions.

## Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.

## Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

## Fermat's theorem on sums of two squares

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p.

## Friedrich Bessel

Friedrich Wilhelm Bessel (22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist and geodesist.

## Friedrich Julius Richelot

Friedrich Julius Richelot (6 November 1808 – 31 March 1875) was a German mathematician, born in Königsberg.

## Friedrich Wilhelm Argelander

Friedrich Wilhelm August Argelander (22 March 1799 – 17 February 1875) was a German astronomer.

## Fundamenta nova theoriae functionum ellipticarum

Fundamenta nova theoriae functionum ellipticarum (New Foundations of the Theory of Elliptic Functions) is a book on Jacobi elliptic functions by Carl Gustav Jacob Jacobi.

## Germans

Germans (Deutsche) are a Germanic ethnic group native to Central Europe, who share a common German ancestry, culture and history.

## Gravitational field

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.

## Gymnasium (Germany)

Gymnasium (German plural: Gymnasien), in the German education system, is the most advanced of the three types of German secondary schools, the others being Realschule and Hauptschule. Gymnasium strongly emphasizes academic learning, comparable to the British grammar school system or with prep schools in the United States.

## Haaretz

Haaretz (הארץ) (lit. "The Land ", originally Ḥadashot Ha'aretz – חדשות הארץ, – "News of the Land ") is an Israeli newspaper.

## Habilitation

Habilitation defines the qualification to conduct self-contained university teaching and is the key for access to a professorship in many European countries.

## Hamilton–Jacobi equation

In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation.

## Humboldt University of Berlin

The Humboldt University of Berlin (Humboldt-Universität zu Berlin, abbreviated HU Berlin), is a university in the central borough of Mitte in Berlin, Germany.

## Hypergeometric function

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.

## Italy

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

## Jacobi (crater)

Jacobi is a lunar impact crater that is located in the southern highlands on the near side of the Moon.

## Jacobi ellipsoid

A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under equilibrium which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity.

## Jacobi elliptic functions

In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance.

## Jacobi identity

In mathematics the Jacobi identity is a property of a binary operation which describes how the order of evaluation (the placement of parentheses in a multiple product) affects the result of the operation.

## Jacobi integral

In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem.

## Jacobi method

In numerical linear algebra, the Jacobi method (or Jacobi iterative method) is an algorithm for determining the solutions of a diagonally dominant system of linear equations.

## Jacobi operator

A Jacobi operator, also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix.

## Jacobi polynomials

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials.

## Jacobi sum

In mathematics, a Jacobi sum is a type of character sum formed with Dirichlet characters.

## Jacobi symbol

Jacobi symbol for various k (along top) and n (along left side).

## Jacobi transform

In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P_n^(x) as kernels of the transform.

## Jacobi triple product

In mathematics, the Jacobi triple product is the mathematical identity: \left(1 - x^\right) \left(1 + x^ y^2\right) \left(1 +\frac\right).

## Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

## Jacobian variety

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.

## Jews

Jews (יְהוּדִים ISO 259-3, Israeli pronunciation) or Jewish people are an ethnoreligious group and a nation, originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The people of the Kingdom of Israel and the ethnic and religious group known as the Jewish people that descended from them have been subjected to a number of forced migrations in their history" and Hebrews of the Ancient Near East.

## Johann Franz Encke

Johann Franz Encke (23 September 1791 – 26 August 1865) was a German astronomer.

## Johann Friedrich Herbart

Johann Friedrich Herbart (4 May 1776 – 14 August 1841) was a German philosopher, psychologist and founder of pedagogy as an academic discipline.

## Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

## Karl Weierstrass

Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".

## Kingdom of Prussia

The Kingdom of Prussia (Königreich Preußen) was a German kingdom that constituted the state of Prussia between 1701 and 1918.

## Kreuzberg

Kreuzberg, a part of the combined Friedrichshain-Kreuzberg borough located south of Mitte since 2001, is one of the best-known areas of Berlin, Germany.

## Lagrange's four-square theorem

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Liberalism

Liberalism is a political and moral philosophy based on liberty and equality.

## Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

## Lie bracket of vector fields

In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi&ndash;Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X and Y on a smooth manifold M a third vector field denoted.

## List of things named after Carl Gustav Jacob Jacobi

These are things named after Carl Gustav Jacob Jacobi (1804–1851), a German mathematician.

## Mathematician

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

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Mental breakdown

A mental breakdown (also known as a nervous breakdown) is an acute, time-limited mental disorder that manifests primarily as severe stress-induced depression, anxiety, Paranoia, or dissociation in a previously functional individual, to the extent that they are no longer able to function on a day-to-day basis until the disorder is resolved.

## Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

## Moritz Cantor

Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics.

## Moritz von Jacobi

Moritz Hermann (Boris Semyonovich) von Jacobi (Борис Семёнович (Морис-Герман) Якоби) (21 September 1801 – 10 March 1874) was a German and Russian engineer and physicist born in Potsdam.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Otto Hesse

Ludwig Otto Hesse (22 April 1811 &ndash; 4 August 1874) was a German mathematician.

## Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

## Partial fraction decomposition

In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

## Paul Gordan

Paul Albert Gordan (27 April 1837 &ndash; 21 December 1912) was a German mathematician, a student of Carl Jacobi at the University of Königsberg before obtaining his Ph.D. at the University of Breslau (1862),.

## Pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely.

## Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

## Philology

Philology is the study of language in oral and written historical sources; it is a combination of literary criticism, history, and linguistics.

## Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

## Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

## Potsdam

Potsdam is the capital and largest city of the German federal state of Brandenburg.

The Royal Prussian Academy of Sciences (Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Akademie der Künste, or "Arts Academy," to which "Berlin Academy" may also refer.

## Q-Pochhammer symbol

In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

## Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

## Random House Webster's Unabridged Dictionary

Random House Webster's Unabridged Dictionary is a large American dictionary, first published in 1966 as The Random House Dictionary of the English Language: The Unabridged Edition.

## Rational function

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Revolutions of 1848

The Revolutions of 1848, known in some countries as the Spring of Nations, People's Spring, Springtime of the Peoples, or the Year of Revolution, were a series of political upheavals throughout Europe in 1848.

## Royal Swedish Academy of Sciences

The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden.

## Smallpox

Smallpox was an infectious disease caused by one of two virus variants, Variola major and Variola minor.

## Theta function

In mathematics, theta functions are special functions of several complex variables.

## University of Königsberg

The University of Königsberg (Albertus-Universität Königsberg) was the university of Königsberg in East Prussia.

## References

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