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  2. Divergence theorem - Wikipedia

    en.wikipedia.org/wiki/Divergence_theorem

    In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, [1] is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface ...

  3. Gauss's law - Wikipedia

    en.wikipedia.org/wiki/Gauss's_law

    Here, the electric field outside (r > R) and inside (r < R) of a charged sphere is being calculated (see Wikiversity). In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the ...

  4. Gauss's law for gravity - Wikipedia

    en.wikipedia.org/wiki/Gauss's_law_for_gravity

    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 integral) of the gravitational field over any closed surface is proportional to ...

  5. Four-gradient - Wikipedia

    en.wikipedia.org/wiki/Four-gradient

    As a component of the 4D Gauss' Theorem / Stokes' Theorem / Divergence Theorem [ edit ] In vector calculus , the divergence theorem , also known as Gauss's theorem or Ostrogradsky's theorem, is a result that relates the flow (that is, flux ) of a vector field through a surface to the behavior of the vector field inside the surface.

  6. Gauss–Markov theorem - Wikipedia

    en.wikipedia.org/wiki/Gauss–Markov_theorem

    t. e. In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) [1] states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. [2]

  7. Gauss–Bonnet theorem - Wikipedia

    en.wikipedia.org/wiki/Gauss–Bonnet_theorem

    In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology. In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. [1] The Gauss–Bonnet theorem extends this ...

  8. Carl Friedrich Gauss - Wikipedia

    en.wikipedia.org/wiki/Carl_Friedrich_Gauss

    This is an accepted version of this page This is the latest accepted revision, reviewed on 20 September 2024. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...

  9. Shell theorem - Wikipedia

    en.wikipedia.org/wiki/Shell_theorem

    The shell theorem is an immediate consequence of Gauss's law for gravity saying that ∫ S g ⋅ d S = − 4 π G M {\displaystyle \int _{S}{\mathbf {g} }\cdot \,d{\mathbf {S} }=-4\pi GM} where M is the mass of the part of the spherically symmetric mass distribution that is inside the sphere with radius r and