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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 eponymous adjective Gaussian is pronounced /ˈɡaʊsiən/.

Mathematics

Algebra and linear algebra

• Gaussian elimination, also known as row reduction or Gaussian method
• Gauss–Jordan elimination
• Gauss–Seidel method
• Gauss's cyclotomic formula
• Gauss's lemma in relation to polynomials
• Gaussian binomial coefficient, also called Gaussian polynomial or Gaussian coefficient
• Gauss transformation, also called Frobenius matrix

Geometry and differential geometry

• Gauss–Bodenmiller theorem – described on website of University of Crete
• Gauss–Bolyai–Lobachevsky space, a hyperbolic geometry
• Gauss–Bonnet theorem, a theorem about curvature in differential geometry for 2d surfaces
  • Chern–Gauss–Bonnet theorem in differential geometry, Shiing-Shen Chern's generalization of the above theorem to higher dimensions
• Gauss's braid in braid theory – a four-strand braid
• Gauss–Codazzi equations
• Gauss–Manin connection, a connection on a vector bundle over a family of algebraic varieties
• Gauss–Newton line – described in Journal for Geometry and Graphics, see also Newton line
• Gauss's area formula
• Gauss's lemma in Riemannian geometry
• Gauss map in differential geometry
• Gaussian curvature, defined in his Theorema egregium
• Gauss circle problem

Number theory

• Gauss–Kuzmin–Wirsing constant, a constant in number theory
• Gauss's constant, the reciprocal of the AGM of 1 and ${\displaystyle \scriptstyle {\sqrt {2}}}$
• Gauss's digamma theorem, a theorem about the digamma function
• Gauss's generalization of Wilson's theorem
• Gauss's lemma in number theory
• Gauss composition law – described on website of University of Université de Montréal
• Gauss map in number theory
• Gaussian moat
• Gauss class number problem
• Gauss's multiplication formula

Cyclotomic fields

• Gaussian period
• Gaussian rational
• Gauss sum, an exponential sum over Dirichlet characters
  • Elliptic Gauss sum, an analog of a Gauss sum
  • Quadratic Gauss sum

Analysis, numerical analysis, vector calculus and calculus of variations

• Gaussian quadrature
• Gauss–Hermite quadrature
• Gauss–Jacobi quadrature
• Gauss–Kronrod quadrature formula
• Gauss–Newton algorithm
• Gauss–Legendre algorithm
• Gauss's complex multiplication algorithm
• Gauss's theorem may refer to the divergence theorem, which is also known as the Ostrogradsky–Gauss theorem
• Gauss pseudospectral method
• Gauss transform, also known as Weierstrass transform.

Complex analysis and convex analysis

• Gauss–Lucas theorem
• Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions
• Gauss's criterion – described on Encyclopedia of Mathematics
• Gauss's hypergeometric theorem, an identity on hypergeometric series
• Gauss plane

Statistics

• Gauss–Kuzmin distribution, a discrete probability distribution
• Gauss–Markov process
• Gauss–Markov theorem
• Gaussian copula
• Gaussian measure
  • Gaussian correlation inequality
  • Gaussian isoperimetric inequality
• Gauss's inequality
• Gauss-Helmert model

Gaussian function and topics named for it

• The normal distribution, also known as the Gaussian distribution, the most common bell curve in statistics
• The Gaussian function, the function used in the normal distribution, but also used elsewhere
• The exponentially modified Gaussian distribution or function, used for description of peak shape in many techniques
• Gauss error function
• Gaussian process
• Gaussian filter
• Gauss iterated map (dynamical systems)
• Additive white Gaussian noise
• Gaussian beam
• Gaussian blur, a technique in image processing
• Gaussian fixed point
• Gaussian random field
  • Gaussian free field
• Gaussian integral
• Gaussian variogram model
• Gaussian mixture model
• Gaussian network model
• Gaussian noise
• Gaussian smoothing
• The inverse Gaussian distribution, also known as the Wald distribution

Knot theory

• Gauss code – described on website of University of Toronto
• Gauss linking integral (knot theory)

Other mathematical areas

• Gauss's algorithm for determination of the day of the week
• Gauss's Easter algorithm
• Gaussian brackets – described on WolframMathWorld
• Gaussian's modular arithmetic
• Gaussian integer, usually written as Z

• Gaussian prime

• Gaussian logarithms (also known as addition and subtraction logarithms)

Cartography

• Gauss–Krüger coordinate system
• Gaussian grid

Physics

Optics

• Gauss lens
• Double-Gauss lens
• Gaussian optics

Classical mechanics

• Gauss's principle of least constraint
• For orbit determination in orbital mechanics:
  • Gauss's law for gravity
  • Gaussian gravitational constant
  • Gaussian year
  • Gauss's method

Quantum mechanics

• Gaussian orbital

Electromagnetism

• Gaussian units
• gauss, the CGS unit for magnetic flux density
• Degaussing, to demagnetize an object
• Gauss rifle or coilgun
• Gauss's law for magnetism
• Gaussian surface
  • Gauss's law, giving the relationship between flux through a closed surface and the enclosed source

• Gauss gun

Awards and recognitions

• Carl Friedrich Gauss Prize, 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

• Gaussia, a palm genus described by Hermann Wendland 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 copepods

Informatics

• Gaussian, a computational chemistry software program
• GAUSS, a matrix programming language for mathematics and statistics

Place names and expedition named in his honour

Terrestrial

• The Gauss expedition, the first German expedition to Antarctica (1901–1903)
  • The ship Gauss, used in the Gauss expedition to the Antarctic
• Gaussberg in Antarctica, an extinct volcano discovered by the Gauss expedition
• Mount Gauss, in Antarctica
• Gauss Peninsula, East Greenland
• Gaussberg, a hill in Braunschweig

Celestial

• Crater Gauss on the Moon
• Asteroid 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 (College of Engineering)
  • Gauss Haus, an NMR center at the University of Utah
  • 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 and in the German Research Centre for Geosciences in Potsdam. Several places where Gauss has stayed in Germany are marked with plaques.

• Bust by Hans Weddo von Glümer (1895) in the German Research Centre for Geosciences in Potsdam
• Bust by Friedrich Künkler (1810)
• Gauss memorial on the Wilseder Berg, highest point in the Luneburg Heath
• 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.

• Stamp (West Germany) 1955
• Stamp (West Germany) 1977
• Stamp (East Germany) 1977
• Medal for Gauss (1856, front)
• Medal for Gauss (1856, back) "mathematicorum principi"
• Commemorative coin (Federal Republic of Germany, 1977)
• Commemorative coin (German Democratic Republic, 1977)

References

1. Wells, John (2008). Longman Pronunciation Dictionary (3rd ed.). Pearson Longman. ISBN 978-1-4058-8118-0.
2. Wendland, H., 1865. Ueber die neue Palmengatung Gaussia. Nachr. Königl. Ges. Wiss. Georg-Augusts-Univ. 1865.
3. Andersson, L. E.; Whitaker, E. A., (1982). NASA Catalogue of Lunar Nomenclature. NASA RP-1097.
4. Carl-Friedrich-Gauß-Fakultät
5. Reich, Karin (2019). "Bessel, Gauß und Baeyer: Drei Büsten im ehemalig Königlich Geodätischen Institut Potsdam, heute Helmert-Haus, im 'Wissenschaftspark Albert Einstein, Telegrafenberg Potsdam'". Mitteilungen der Gauss-Gesellschaft (in German) (56): 67–74.
6. Michling, Horst (1966). "Zur Gaußbüste von Friedrich Künkler". Mitteilungen der Gauss-Gesellschaft (in German) (3): 3–4.

• Lists of things named after mathematicians
• Carl Friedrich Gauss