|
Carl Gustav Jacob Jacobi (December 10, 1804 - February 18, 1851) was a German mathematician, widely considered to be the most inspiring teacher of his time[1] and one of the greatest mathematicians of all time [2][3]. Carl Jacobi (1804-1851), picture obviously in the public domain This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ...
is the 344th day of the year (345th in leap years) in the Gregorian calendar. ...
1804 was a leap year starting on Sunday (see link for calendar). ...
Potsdam is the capital city of the federal state of Brandenburg in Germany. ...
is the 49th day of the year in the Gregorian calendar. ...
1851 (MDCCCLI) was a common year starting on Wednesday (see link for calendar) of the Gregorian calendar (or a common year starting on Friday of the 12-day-slower Julian calendar). ...
This article is about the capital of Germany. ...
Image File history File links Flag_of_Germany. ...
Image File history File links Flag_of_Germany. ...
Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...
The Königsberg University Albertina was opened in 1544 by Albrecht or Albert of Brandenburg Prussia, first duke of a Protestant Prussia. ...
There is no institution called the University of Berlin, but there are four universities in Berlin, Germany: Humboldt University of Berlin (Humboldt-Universität zu Berlin) Technical University of Berlin (Technische Universität Berlin) Free University of Berlin (Freie Universität Berlin) Berlin University of the Arts (Universität der...
Paul Albert Gordan (April 27, 1837 – December 21, 1912) was a German mathematician. ...
Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. ...
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that have historical importance with also many features that show up important structure, and have direct relevance to some applications (e. ...
In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ...
The Jacobi symbol generalises the Legendre symbol. ...
In mathematics the Jacobi identity is a property that a binary operation can satisfy which determines how the order of evaluation behaves for the given operation. ...
For other uses, see Christian (disambiguation). ...
This article or section does not cite its references or sources. ...
is the 344th day of the year (345th in leap years) in the Gregorian calendar. ...
1804 was a leap year starting on Sunday (see link for calendar). ...
is the 49th day of the year in the Gregorian calendar. ...
1851 (MDCCCLI) was a common year starting on Wednesday (see link for calendar) of the Gregorian calendar (or a common year starting on Friday of the 12-day-slower Julian calendar). ...
Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...
Biography
He was born of Jewish parentage in Potsdam. He studied at Berlin University, where he obtained the degree of Doctor of Philosophy in 1825, his thesis being an analytical discussion of the theory of fractions. In 1827 he became ordinary and in 1829 extraordinary professor of mathematics at Königsberg University, and this chair he filled until 1842. For other uses, see Jew (disambiguation). ...
Potsdam is the capital city of the federal state of Brandenburg in Germany. ...
Alternative meaning: Humboldt State University, located in Arcata, California German Humboldt-Universität zu Berlin) is the successor to Berlins oldest university, the Friedrich Wilhelm University (Friedrich-Wilhelms-Universität), founded in 1810 by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt whose university model has strongly...
Doctor of Philosophy, abbreviated Ph. ...
Year 1825 (MDCCCXXV) was a common year starting on Saturday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Thursday of the 12-day slower Julian calendar). ...
For other meanings of the word fraction, see fraction (disambiguation) A cake with one quarter removed. ...
Year 1827 (MDCCCXXVII) was a common year starting on Monday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Wednesday of the 12-day slower Julian calendar). ...
Johann Wolfgang von Goethe 1829 was a common year starting on Thursday (see link for calendar). ...
The meaning of the word professor (Latin: [1]) varies. ...
Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
The Königsberg University Albertina was opened in 1544 by Albrecht or Albert of Brandenburg Prussia, first duke of a Protestant Prussia. ...
1842 was a common year starting on Saturday (see link for calendar). ...
Jacobi suffered a breakdown from overwork in 1843. He then visited Italy for a few months to regain his health. On his return he moved to Berlin, where he lived as a royal pensioner until his death. During the Revolution of 1848 Jacobi was politically involved and unsuccessfully presented his parliamentary candidature on behalf of a Liberal club. This led, after the suppression of the revolution, to his royal grant being cut off - but his fame and reputation were such that it was soon resumed. Year 1843 (MDCCCXLIII) was a common year starting on Sunday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Friday of the 12-day slower Julian calendar). ...
This article is about the capital of Germany. ...
—Alexis de Tocqueville, Recollections The European Revolutions of 1848, in some countries known as the Spring of Nations, were the bloody consequences of a variety of changes that had been taking place in Europe in the first half of the 19th century. ...
Look up liberal on Wiktionary, the free dictionary Liberal may refer to: Politics: Liberalism American liberalism, a political trend in the USA Political progressivism, a political ideology that is for change, often associated with liberal movements Liberty, the condition of being free from control or restrictions Liberal Party, members of...
Jacobi is buried at a cemetery in the Kreuzberg section of Berlin, the Friedhof II der Jerusalems- und Neuen Kirchengemeinde (61 Baruther Street). His grave is close to that of Johann Encke, the astronomer. Johann Franz Encke (September 23, 1791 – August 26, 1865) was a German astronomer, born in Hamburg. ...
The Jacobi crater, on the Moon, is named after him. Jacobi is a lunar crater that is located in the southern highlands on the near side of the Moon. ...
This article is about Earths moon. ...
Scientific contributions Jacobi wrote the classic treatise (1829) on elliptic functions, of great importance in mathematical physics, because of the need to "integrate second order kinetic energy equations". The motion equations in rotational form are integrable only for the three cases of the pendulum, the symmetric top in a gravitational field, and a freely spinning body, wherein solutions are in terms of elliptic functions. See Jacobi's elliptic functions. Johann Wolfgang von Goethe 1829 was a common year starting on Thursday (see link for calendar). ...
In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ...
In mathematical physics, Jacobis integral represents a solution to the circular restricted three-body problem of celestial mechanics. ...
For other uses, see Pendulum (disambiguation). ...
A gravitational field is a model used within physics to explain how gravity exists in the universe. ...
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that have historical importance with also many features that show up important structure, and have direct relevance to some applications (e. ...
Jacobi was also the first mathematician to apply elliptic functions to number theory, for example, proving the 2 square and four-square theorems of Pierre de Fermat. He also proved similar results for 6 and 8 squares. The Jacobi theta functions, so frequently applied in the study of hypergeometric series, were named in his honor. Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...
Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
In mathematics, Pierre de Fermats theorem on sums of two squares states that an odd prime number p is expressible as with x and y integers, if and only if For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and...
Lagranges four-square theorem, also known as Bachets conjecture, was proved in 1770 by Joseph Louis Lagrange. ...
Pierre de Fermat Pierre de Fermat IPA: (August 17, 1601–January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. ...
In mathematics, theta functions are special functions of several complex variables. ...
In mathematics, a hypergeometric series is a power series in which the ratios of successive coefficients k is a rational function of k. ...
He proved the functional equation for the theta function.
He proved the Jacobi triple product formula and many other results in q-series. In mathematics, the Jacobi triple product is a relation that re-expresses the Jacobi theta function, normally written as a series, as a product. ...
In mathematics, a q-series, also sometimes called a q-shifted factorial, is defined as It is usually considered first as a formal power series; it is also an analytic function of q, in the unit disc. ...
He gave new proofs of quadratic reciprocity, made contributions to higher reciprocity laws, investigated continued fractions and invented Jacobi sums. In number theory, the law of quadratic reciprocity connects the solvability of two related quadratic equations in modular arithmetic. ...
In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ...
In mathematics, a Jacobi sum is a type of character sum formed with one or more Dirichlet characters. ...
In 1841 he reintroduced the partial derivative ∂ notation of Legendre, which was to become standard. 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). ...
Adrien-Marie Legendre (September 18, 1752–January 10, 1833) was a French mathematician. ...
Karl Gustav Jacob Jacobi. His investigations in elliptic functions, the theory of which he established upon quite a new basis, and more particularly his development of the theta function, as given in his great treatise Fundamenta nova theoriae functionum ellipticarum (1829), and in later papers in Crelle's Journal, constitute his grandest analytical discoveries. Second in importance only to these are his researches in differential equations, notably the theory of the last multiplier, which is fully treated in his Vorlesungen über Dynamik, edited by Alfred Clebsch (1866). Image File history File links No higher resolution available. ...
Image File history File links No higher resolution available. ...
In mathematics, theta functions are special functions of several complex variables. ...
Johann Wolfgang von Goethe 1829 was a common year starting on Thursday (see link for calendar). ...
Crelles Journal, or just Crelle, is the common name for the Journal für die reine und angewandte Mathematik founded by August Leopold Crelle. ...
Alfred Clebsch (1832-1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. ...
1866 (MDCCCLXVI) is a common year starting on Monday of the Gregorian calendar or a common year starting on Wednesday of the 12-day-slower Julian calendar. ...
It was in analytical development that Jacobi’s peculiar power mainly lay, and he made many important contributions of this kind to other departments of mathematics, as a glance at the long list of papers that were published by him in Crelle’s Journal and elsewhere from 1826 onwards will sufficiently indicate. He was one of the early founders of the theory of determinants; in particular, he invented the functional determinant formed of the n² differential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations. The oldest surviving photograph, Nicéphore Niépce, circa 1826 1826 (MDCCCXXVI) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar (or a common year starting on Tuesday of the 12-day-slower Julian calendar). ...
In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ...
In his 1835 paper, Jacobi proved the following: | Come and take it, slogan of the Texas Revolution 1835 was a common year starting on Thursday (see link for calendar). ...
- If a univariate single-value function is periodic, then the ratio of the periods cannot be a real number, and that such a function cannot have more than two periods.
Jacobi reduced the general quintic equation to the form, In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable. ...
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...
Graph of a polynomial of degree 5, with 4 critical points. ...
- x5 − 10q2x = p.
Valuable also are his papers on Abelian transcendents, and his investigations in the theory of numbers, in which latter department he mainly supplements the labours of K. F. Gauss. For the purposes of algebraic geometry over the complex numbers, an abelian variety is a complex torus (a torus of real dimension 2n that is a complex manifold) that is also a projective algebraic variety of dimension n, i. ...
Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 - February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ...
The planetary theory and other particular dynamical problems likewise occupied his attention from time to time. While contributing to celestial mechanics, Jacobi (1836) introduced the Jacobi integral for a sidereal coordinate system. Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ...
Year 1836 (MDCCCXXXVI) was a leap year starting on Friday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Wednesday of the 12-day slower Julian calendar). ...
In mathematical physics, Jacobis integral represents a solution to the circular restricted three-body problem of celestial mechanics. ...
He left a vast store of manuscripts, portions of which have been published at intervals in Crelle's Journal. His other works include Comnienlatio de transformatione integralis duplicis indefiniti in formam simpliciorem (1832), Canon arithmeticus (1839), and Opuscula mathematica (1846–1857). His Gesammelte Werke (1881–1891) were published by the Berlin Academy. Perhaps his most publicized work is Hamilton-Jacobi theory in rational mechanics. Year 1832 (MDCCCXXXII) was a leap year starting on Sunday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Friday of the 12-day slower Julian calendar). ...
1839 (MDCCCXXXIX) was a common year starting on Tuesday (see link for calendar). ...
1846 was a common year starting on Thursday (see link for calendar). ...
1857 was a common year starting on Thursday (see link for calendar). ...
Year 1881 (MDCCCLXXXI) was a common year starting on Saturday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day slower Julian calendar). ...
Year 1891 (MDCCCXCI) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Saturday of the 12-day slower Julian calendar). ...
The Prussian Academy of Sciences (German: ) was an academy established in Berlin on July 11, 1700. ...
In physics and mathematics, the Hamilton-Jacobi equation (HJE) is a particular canonical transformation of the classical Hamiltonian which results in a first order, non-linear differential equation whose solution describes the behavior of the system. ...
Classical mechanics is a model of the physics of forces acting upon bodies. ...
Students of vector theory often encounter the Jacobi identity, those studying differential equations often encounter the Jacobian determinant, and those working in number theory and cryptography use the Jacobi symbol. A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ...
In mathematics the Jacobi identity is a property that a binary operation can satisfy which determines how the order of evaluation behaves for the given operation. ...
A simulation of airflow into a duct using the Navier-Stokes equations A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. ...
Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Cryptography (or cryptology; derived from Greek κÏυπτός kryptós hidden, and the verb γÏάφω gráfo write or λεγειν legein to speak) is the study of message secrecy. ...
The Jacobi symbol generalises the Legendre symbol. ...
The phrase 'Invert, always invert,' is associated with Jacobi for he believed that it is in the nature of things that many hard problems are best solved when they are addressed backwards.
See also In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ...
In mathematics the Jacobi identity is a property that a binary operation can satisfy which determines how the order of evaluation behaves for the given operation. ...
In matrix calculus, Jacobis formula expresses the differential of the determinant of a matrix A in terms of the adjugate of A and the differential of A. The formula is It is named after the mathematician C.G.J. Jacobi. ...
The Jacobi symbol generalises the Legendre symbol. ...
In mathematical physics, Jacobis integral represents a solution to the circular restricted three-body problem of celestial mechanics. ...
In mathematics, Jacobi polynomials are a class of orthogonal polynomials. ...
The Carathéodory-Jacobi-Lie theorem is a theorem in symplectic topology which generalizes Darbouxs theorem. ...
The Jacobi method is an algorithm in linear algebra for determining the solutions of a system of linear equations with largest absolute values in each row and column dominated by the diagonal element. ...
Citations - ^ (Bell, p. 330)
- ^ Retrieved from [1]
- ^ [2]
References - Temple Bell, Eric (1937). Men of Mathematics. New York: Simon and Schuster.
- Hestenes, David (1986). New Foundations of Classical Mechanics. Dordrecht: Kluwer Adademic Publishers.
- This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
Encyclopædia Britannica, the eleventh edition The Encyclopædia Britannica Eleventh Edition (1910–1911) is perhaps the most famous edition of the Encyclopædia Britannica. ...
The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...
External links Wikiquote has a collection of quotations related to: Carl Gustav Jacob Jacobi |
Feeds |
Contact