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/.^[1]

Mathematics

Various Gaussian curvatures

Geometry and differential geometry

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

Gaussian moat

• 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

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

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

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

Linking integral

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

Cartography

Gaussian grid points

• Gauss–Krüger coordinate system
• Gaussian grid

Physics

Electromagnetism

Gauss gun

• 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

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 maya

• 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".^[2]
• Gaussia, a genus of copepods

Place names and expedition named in his honour

The Gaussberg in Braunschweig, Germany with the Gauss memorial in front

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^[3]
• Asteroid 1001 Gaussia

Institutions and buildings named in his honour

• The Carl-Friedrich-Gauss Fakultät of Braunschweig University of Technology^[4]
• Several school 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 and memorial plaques

Gauss Monuments were erected in Brunswick and Göttingen (the last together with Weber). Busts of Gauss were placed in the Walhalla temple 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^[5]
• 
  Gauss memorial on the Wilseder Berg, highest point in the Luneburg Heath

Other commemorations

From 1989 through 2001, Gauss' portrait, a normal distribution curve and some prominent Göttingen buildings, were featured on the front-side of a German ten-mark banknote. The reverse featured a part of the Hanoverian triangulation and his invention of a vice heliotrope.^[6] Germany has also 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.

• 
  German 10-Deutsche Mark Banknote (1993) with formula and graph of normal distribution; portrait as mirror image of the Jensen portrait (background: some Göttingen buildings)
• 
  Back of German 10-Deutsche Mark Banknote (1993) with vice heliotrope and a section of the triangulation network (background: mathematical signs)

References