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Gauss and discovered
Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the famous note: " ΕΥΡΗΚΑ!
Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it.
Gauss usually declined to present the intuition behind his often very elegant proofs — he preferred them to appear " out of thin air " and erased all traces of how he discovered them.
This method ( and the general idea of an FFT ) was popularized by a publication of J. W. Cooley and J. W. Tukey in 1965, but it was later discovered ( Heideman & Burrus, 1984 ) that those two authors had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805 ( and subsequently rediscovered several times in limited forms ).
Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path ; Carl Friedrich Gauss ; Jean-Baptiste Biot and Félix Savart, both of which in 1820 came up with the Biot-Savart Law giving an equation for the magnetic field from a current-carrying wire ; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity.
as discovered by Gauss.
* Theorema Egregium − The " remarkable theorem " discovered by Gauss which showed there is an intrinsic notion of curvature for surfaces.
Five years later, on March 29, 1807, he discovered the asteroid Vesta, which he allowed Carl Friedrich Gauss to name.
Legendre and Gauss both applied the method to the problem of determining, from astronomical observations, the orbits of bodies about the Sun ( mostly comets, but also later the then newly discovered minor planets ).
He also discovered the presence of new constraints which he suggested to be interpreted as the equivalent of Gauss constraint of Yang Mills field theories.
It was discovered by the British National Antarctic Expedition, 1901 – 04, which named this feature after Professor Carl Friedrich Gauss, a German mathematician and astronomer.
The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered that

Gauss and law
Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.
The second law of error is called the normal distribution or the Gauss law.
" It is difficult historically to attribute that law to Gauss, who in spite of his well-known precocity had probably not made this discovery before he was two years old.
* О суммахъ Гаусса и о законе взаимности символа Лежандра ( About Gauss sums and the reciprocity law of the Legendre symbol ) ( 1877 ),
The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867.
These groups appeared in the theory of quadratic forms: in the case of binary integral quadratic forms, as put into something like a final form by Gauss, a composition law was defined on certain equivalence classes of forms.
which contains Gauss ' law for gravity, and Poisson's equation for gravity.
Newton's and Gauss ' law are mathematically equivalent, and are related by the divergence theorem.
In the case of a gravitational field g due to an attracting massive object, of density ρ, Gauss ' law for gravity in differential form can be used to obtain the corresponding Poisson equation for gravity.
Gauss ' law for gravity is:
substituting into Gauss ' law
Starting with Gauss ' law for electricity ( also one of Maxwell's equations ) in differential form, we have:
Substituting this into Gauss ' law and assuming ε is spatially constant in the region of interest obtains:
While in Breslau, Dirichlet continued his number theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gauss ' research.
The latter property is called the global reciprocity law and is a far reaching generalization of the Gauss quadratic reciprocity law.
The origins of class field theory lie in the quadratic reciprocity law proved by Gauss.
The Artin reciprocity law, which is a high level generalization of the Gauss quadratic reciprocity law, states that the product vanishes on the multiplicative group of the number field.
Let and substitute into Gauss ' law.
Gauss ' law states that " the total electric flux through any closed hypothetical surface of any shape drawn in an electric field is proportional to the total electric charge enclosed within the surface ".
When it came to deriving the electromagnetic wave equation from displacement current in his 1865 paper A Dynamical Theory of the Electromagnetic Field, he got around the problem of the non-zero divergence associated with Gauss's law and dielectric displacement by eliminating the Gauss term and deriving the wave equation exclusively for the solenoidal magnetic field vector.
One has the following analogue of the quadratic reciprocity law for ( even more general ) Gauss sums

Gauss and biquadratic
The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
The two monographs Gauss published on biquadratic reciprocity have consecutively-numbered sections: the first contains §§ 1 – 23 and the second §§ 24 – 76.
The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws.
In his second monograph on biquadratic reciprocity, Gauss used a fourth-power lemma to derive the formula for the biquadratic character of 1 + i in Z, the ring of Gaussian integers.

Gauss and reciprocity
The first section of this article does not use the Legendre symbol and gives the formulations of quadratic reciprocity found by Legendre and Gauss.
The ring of Gaussian integers was introduced by Carl Friedrich Gauss in his second monograph on quartic reciprocity ( 1832 ) ( see ).
Carl Friedrich Gauss introduced the square bracket notation for the floor function in his third proof of quadratic reciprocity ( 1808 ).
* German mathematician Carl Friedrich Gauss publishes Theorematis arithmetici demonstratio nova, introducing Gauss's lemma in the third proof of quadratic reciprocity.
That the zeta function of a quadratic field is a product of the Riemann zeta function and a certain Dirichlet L-function is an analytic formulation of the quadratic reciprocity law of Gauss.

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