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Carl Friedrich Gauss (1777–1855)
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/ GOWSS-ee-ən.[1]
Mathematics
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Various Gaussian curvatures
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
Geometry and differential geometry
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Gauss map
- 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
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Gaussian moat
- Gauss–Kuzmin–Wirsing constant, a constant in number theory
- Gauss's constant, the reciprocal of the AGM of 1 and
- 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 – 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
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Comparison between 2-point Gaussian and trapezoidal quadrature.
- 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
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Gaussian copula
- 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
Gaussian function and topics named for it
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Gaussian curve with a 2-dimensional domain
- 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
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Linking integral
- 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 bracket – described on WolframMathWorld
- Gaussian's modular arithmetic
- Gaussian integer, usually written as Z[i]
- Gaussian prime
- Gaussian logarithms (also known as addition and subtraction logarithms)
Cartography
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Gaussian grid points
- Gauss–Krüger coordinate system
- Gaussian grid
Physics
- 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
Quantum mechanics
Electromagnetism
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Gauss gun
- gauss, the CGS unit for magnetic field
- 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
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
Place names and expedition named in his honour
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The Gaußberg in Braunschweig, Germany with the Gauss memorial in front
- The Gauss expedition, the first German expedition to Antarctica
- The crater Gauss on the Moon[2]
- Asteroid 1001 Gaussia
- Gauss Peninsula, East Greenland
- Mount Gauss, in Antarctica, not to be confused with the aforementioned Gaussberg
- Gauss Tower, an observation tower in Dransfeld, Germany
- Gaußberg, a hill in Braunschweig
- Several buildings named "Gauss Haus" or "Gauss Building":
- 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
Institutions named in his honour
- The Carl-Friedrich-Gauß School for Mathematics, Computer Science, Business Administration, Economics, and Social Sciences of Braunschweig University of Technology
- The Carl-Friedrich-Gauss Gymnasium (a school for grades 5–13) in Worms, Germany
Other things named for him
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- 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”.[3]
- Gaussia, a genus of copepods
- Gaussian, a computational chemistry software program
- GAUSS, a matrix programming language for mathematics and statistics
References
- ^ Wells, John (2008). Longman Pronunciation Dictionary (3rd ed.). Pearson Longman. ISBN 978-1-4058-8118-0.
- ^ Andersson, L. E.; Whitaker, E. A., (1982). NASA Catalogue of Lunar Nomenclature. NASA RP-1097.
- ^ Wendland, H., 1865. Ueber die neue Palmengatung Gaussia. Nachr. Königl. Ges. Wiss. Georg-Augusts-Univ. 1865.