The Gauss–Markov theorem in mathematical statistics (In this theorem, one does not assume the probability distributions are Gaussian.)
Carl Friedrich Gauss | Liouville's theorem | Gauss | Markov process | Markov chain | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Markov chain Monte Carlo | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Markov | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Hidden Markov model | Gauss–Seidel method | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem |
Many famous mathematicians have studied such problems, including Euler, Legendre, and Gauss.
Gauss influenced and corresponded frequently with F. Scott Fitzgerald and Edmund Wilson.
Probably Gauss first realized this, and used it to prove the impossibility of some constructions; only much later did Hilbert find a complete set of axioms for geometry.
The evaluation of these inequalities/inclusions is commonly done by solving linear (or nonlinear) complementarity problems, by quadratic programming or by transforming the inequality/inclusion problems into projective equations which can be solved iteratively by Jacobi or Gauss–Seidel techniques.
A digital form of the Gauss–Bonnet theorem is: Let M be a closed digital 2D manifold in direct adjacency (i.e. a (6,26)-surface in 3D).
Two examples are Gauss' law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss' law for gravity, which follows from the inverse-square Newton's law of universal gravitation.
Mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold, and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability for the solar system.
The Gauss-Matuyama Reversal was a geologic event approximately 2.588 million years ago when the Earth's magnetic field underwent reversal.
In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.
Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electricity bears to Coulomb's law.
In the mid nineteenth century, the Gauss–Bonnet theorem linked the Euler characteristic to the Gaussian curvature.
In 2006, Karl-Markus Gauß was accepted as member of the German Academy for Language and Poetry.
She has undertaken a number of sabbaticals which have given her experience of NASA’s Goddard Space Flight Center, Harvard University, the University of California at San Diego (where she was a Green Scholar), Victoria University of Wellington, and Göttingen University (as Gauss Professor), funded by the Fulbright Foundation, NASA, the Cecil H and Ida M Green Foundation, and Göttingen Academy of Sciences.
Many famous mathematicians studied mathematical chess problems, for example, Euler, Legendre and Gauss.
Homoscedasticity, one of the basic Gauss–Markov assumptions of ordinary least squares linear regression modeling, refers to equal variance in the random error terms regardless of the trial or observation, such that
Skinner has delivered many prestigious lecture-series, including the Christian Gauss Seminars in Criticism at Princeton (1980), the Carlyle Lectures at Oxford (1980), the Messenger Lectures at Cornell (1983), the Tanner Lectures on Human Values at Harvard (1984), the T. S. Eliot Memorial Lectures at Kent (1995), the Ford Lectures at Oxford (2003), the Clarendon Lectures at Oxford (2011) and the Clark Lectures at Cambridge (2012).
In most applications the Gauss–Krüger is applied to a narrow strip near the central meridians where the differences between the spherical and ellipsoidal versions are small, but nevertheless important in accurate mapping.