Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...

(1777–1855) is the

eponym An eponym is a noun after which or for which someone or something is, or is believed to be, named. Adjectives derived from the word ''eponym'' include ''eponymous'' and ''eponymic''. Eponyms are commonly used for time periods, places, innovati ...

of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous adjective ''Gaussian'' is pronounced .

Mathematics

Algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
and
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

Geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
and
differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

Number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Cyclotomic field In algebraic number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to \Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory ...
s

Gaussian period In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of root of unity, roots of unity. The periods permit explicit calculations in cyclotomic fields connected with Galois theory and with harmonic analysis (discre ...

Gaussian rational In mathematics, a Gaussian rational number is a complex number of the form ''p'' + ''qi'', where ''p'' and ''q'' are both rational numbers. The set of all Gaussian rationals forms the Gaussian rational field, denoted Q(''i''), obtained b ...

Gauss sum In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically :G(\chi) := G(\chi, \psi)= \sum \chi(r)\cdot \psi(r) where the sum is over elements of some finite commutative ring , is ...

, an

exponential sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typi ...

over

Dirichlet character In analytic number theory and related branches of mathematics, a complex-valued arithmetic function \chi: \mathbb\rightarrow\mathbb is a Dirichlet character of modulus m (where m is a positive integer) if for all integers a and b: # \chi(ab) = \ch ...

s ** Elliptic Gauss sum, an analog of a

Quadratic Gauss sum In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; f ...

Analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
,
numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
,
vector calculus Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a ...
and
calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

Complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
and
convex analysis Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex optimization, convex minimization, a subdomain of optimization (mathematics), optimization theor ...

Gauss–Lucas theorem In complex analysis, a branch of mathematics, the Gauss–Lucas theorem gives a geometry, geometric relation between the root of a function, roots of a polynomial and the roots of its derivative . The set of roots of a real or complex polynomial ...

* Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions * Gauss's criterion – described o
Encyclopedia of Mathematics
* Gauss's hypergeometric theorem, an identity on

hypergeometric series In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

* Gauss plane

Statistics

* Gauss–Kuzmin distribution, a

discrete probability distribution In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample spa ...

* Gauss–Markov process *

Gauss–Markov theorem In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in ...

* Gaussian copula *

Gaussian measure In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space \mathbb^n, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are na ...

** Gaussian correlation inequality **

Gaussian isoperimetric inequality Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

* Gauss's inequality * Gauss-Helmert model

Gaussian function and topics named for it

Knot theory

* Gauss code – described o
website of University of Toronto
* Gauss linking integral (

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

)

Other mathematical areas

* Gauss's algorithm for

determination of the day of the week The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the ...

* Gauss's Easter algorithm *

Gaussian brackets In mathematics, Gaussian brackets are a special notation invented by Carl Friedrich Gauss to represent the convergents of a simple continued fraction in the form of a simple fraction. Gauss used this notation in the context of finding solutions of ...

– described o
WolframMathWorld
*Gaussian's

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...

Gaussian integer In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as \mathbf ...

, usually written as :*

Gaussian prime In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as \mathbf /ma ...

* Gaussian logarithms (also known as addition and subtraction logarithms) * Gauss congruence for integer sequences

Cartography

Gauss–Krüger coordinate system The transverse Mercator map projection (TM, TMP) is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercat ...

* Gaussian grid

Physics

Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

* Gauss lens * Double-Gauss lens *

Gaussian optics Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. ...

Classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...

Gauss's principle of least constraint The principle of least constraint is one variational formulation of classical mechanics enunciated by Carl Friedrich Gauss in 1829, equivalent to all other formulations of analytical mechanics. Intuitively, it says that the acceleration of a ...

*For

orbit determination Orbit determination is the estimation of orbits of objects such as moons, planets, and spacecraft. One major application is to allow tracking newly observed asteroids and verify that they have not been previously discovered. The basic methods wer ...

orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal ...

: **

Gauss's law for gravity In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integ ...

Gaussian gravitational constant The Gaussian gravitational constant (symbol ) is a parameter used in the orbital mechanics of the Solar System. It relates the orbital period to the orbit's semi-major axis and the mass of the orbiting body in Solar masses. The value of histor ...

Gaussian year A Gaussian year is defined as 365.2568983 days. It was adopted by Carl Friedrich Gauss as the length of the sidereal year in his studies of the dynamics of the Solar System. A slightly different value is now accepted as the length of the sidereal ...

** Gauss's method

Quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

* Gaussian orbital

Electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

Gaussian units Gaussian units constitute a metric system of units of measurement. This system is the most common of the several electromagnetic unit systems based on the centimetre–gram–second system of units (CGS). It is also called the Gaussian unit syst ...

gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

, the CGS unit for

magnetic flux density A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

Degaussing Degaussing, or deperming, is the process of decreasing or eliminating a remnant magnetic field. It is named after the gauss, a unit of magnetism, which in turn was named after Carl Friedrich Gauss. Due to magnetic hysteresis, it is generally not ...

, to demagnetize an object * Gauss rifle or coilgun *

Gauss's law for magnetism In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field has divergence equal to zero, in other words, that it is a solenoidal vector field. It is ...

* Gaussian surface ** Gauss's law, giving the relationship between

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phe ...

through a closed surface and the enclosed source * Gauss gun

Awards and recognitions

Carl Friedrich Gauss Prize The Carl Friedrich Gauss Prize for Applications of Mathematics is a mathematics award, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found signific ...

, a mathematics award * Gauss Lectureship, a mathematical distinction * The Gauss Mathematics Competition in Canadian junior high schools, an annual national mathematics competition administered by the Centre for Education in Mathematics and Computing

Other things named for him

Biology

160px, Gaussia maya * '' Gaussia'', a palm genus described by

Hermann Wendland Hermann Wendland (October 11, 1825 in Herrenhausen – January 12, 1903 in Hanover) was a German botanist and gardener. He was a noted authority on the family Arecaceae The Arecaceae () is a family (biology), family of perennial plant, peren ...

with the then new species '' Gaussia princeps'', collected by Charles Wright in western Cuba. Named in "memoriam astronomi Caroli Friderici Gauss". * '' Gaussia'', a genus of

copepod Copepods (; meaning 'oar-feet') are a group of small crustaceans found in nearly every freshwater and saltwater habitat (ecology), habitat. Some species are planktonic (living in the water column), some are benthos, benthic (living on the sedimen ...

Informatics

Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

, a computational chemistry software program *

GAUSS Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

, a matrix programming language for mathematics and statistics

Place names and expedition named in his honour

Terrestrial *The

Gauss expedition The ''Gauss'' expedition of 1901–1903 (also known as the ''Deutsche Südpolar-Expedition 1901–1903)'' was the first German expedition to Antarctica. It was led by geologist Erich von Drygalski in the ship , named after the mathematician and p ...

, the first German expedition to Antarctica (1901–1903) ** The ship ''

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

'', used in the

to the Antarctic *

Gaussberg Gaussberg (or Schwarzen Berg, Mount Gauss) is an extinct, high volcanic cone in East Antarctica fronting on Davis Sea immediately west of Posadowsky Glacier (Antarctica), Posadowsky Glacier. It is ice-free and conical in nature, having formed s ...

in Antarctica, an extinct volcano discovered by the Gauss expedition * Mount Gauss, in Antarctica * Gauss Peninsula, East Greenland * Gaussberg, a hill in

Braunschweig Braunschweig () or Brunswick ( ; from Low German , local dialect: ) is a List of cities and towns in Germany, city in Lower Saxony, Germany, north of the Harz Mountains at the farthest navigable point of the river Oker, which connects it to the ...

Celestial * Crater

on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

Asteroid An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...

1001 Gaussia

Institutions and buildings named in his honour

* The ''Carl-Friedrich-Gauss Fakultät'' of Braunschweig University of Technology * Several schools in Germany named after Gauss * Several buildings named "Gauss Haus" or "Gauss Building": ** Gauss Tower, an observation tower in Dransfeld, Germany ** The Gauss Building at the

University of Idaho The University of Idaho (U of I, or UIdaho) is a public land-grant research university in Moscow, Idaho, United States. Established in 1889 and opened three years later, it was the state's sole university for 71 years, until 1963. The un ...

(College of Engineering) ** Gauss Haus, an

NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which atomic nucleus, nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near and far field, near field) and respond by producing ...

center at the

University of Utah The University of Utah (the U, U of U, or simply Utah) is a public university, public research university in Salt Lake City, Utah, United States. It was established in 1850 as the University of Deseret (Book of Mormon), Deseret by the General A ...

** The 'Gauss House', a common room in the University of Sussex Mathematical and Physical Sciences department. ** A dormitory building is named after him in University of California, Santa Cruz, in Crown College

Monuments, busts, and memorial plaques

Gauss Monuments were erected in Brunswick and Göttingen (the last together with Weber). Busts of Gauss were placed in the Walhalla hall of fame near

Regensburg Regensburg (historically known in English as Ratisbon) is a city in eastern Bavaria, at the confluence of the rivers Danube, Naab and Regen (river), Regen, Danube's northernmost point. It is the capital of the Upper Palatinate subregion of the ...

and in the German Research Centre for Geosciences in

Potsdam Potsdam () is the capital and largest city of the Germany, German States of Germany, state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the Havel, River Havel, a tributary of the Elbe, downstream of B ...

. Several places where Gauss has stayed in Germany are marked with plaques. File:Carl.Friedrich.Gauss.Bueste.vor1900.GFZ.jpg, Bust by ''Hans Weddo von Glümer'' (1895) in the German Research Centre for Geosciences in

File:Carl Friedrich Gauß, Büste von Friedrich Künkler, 001.jpg, Bust by Friedrich Künkler (1810) File:Gauss Stein Wilseder Berg.jpg, Gauss memorial on the

Wilseder Berg At , the Wilseder Berg is the highest point on the Lüneburg Heath in North Germany. Due to its position in the middle of the nature reserve Lüneburg Heath it is a popular tourist destination, especially in the period when the Ericaceae, heather ...

, highest point in the Luneburg Heath File:Walhalla wie Parthenon zu Ehren bedeutender Personen - erbaut 1842 - König Ludwig I - Foto Wolfgang Pehlemann DSCN2430.jpg, A bust of Gauss is placed in the Walhalla since 2007

Other commemorations

Germany issued three postage stamps honoring Gauss, one in 1955 on the hundredth anniversary of his death and two others in 1977, the 200th anniversary of his birth. File:DBP 1955 204 Carl Friedrich Gauß.jpg, Stamp (West Germany) 1955 File:DBP 1977 928 Carl Friedrich Gauß.jpg, Stamp (West Germany) 1977 File:Stamp Carl Friedrich Gauß.jpg, Stamp (East Germany) 1977 File:1856 Friedrich Brehmer Denkmünze auf Gauss nach Christian Heinrich Hesemann im Auftrag von Georg. V. von Hannover, Medaille Avers mit Portrait.jpg, Medal for Gauss (1856, front) File:1856 Friedrich Brehmer Denkmünze auf Gauss nach Christian Heinrich Hesemann im Auftrag von Georg. V. von Hannover, Medaille Revers mit Efeukranz, Gipsmodell.jpg, Medal for Gauss (1856, back) "mathematicorum principi"

References

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List of things