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 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.

Though Gauss had up to that point been financially supported by his stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support.

Gauss proved the method under the assumption of normally distributed errors ( see Gauss – Markov theorem ; see also Gaussian ).

Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it.

See also the letter from Robert Gauss to Felix Klein on 3 September 1912.

Germany has also issued three postage stamps honoring Gauss.

He was a contemporary of Carl Gauss, also a mathematician and physicist.

Gauss – Jordan elimination, an extension of this algorithm, reduces the matrix further to diagonal form, which is also known as reduced row echelon form.

Its major part resembles the field of a bar magnet (" dipole field ") inclined by about 10 ° to the rotation axis of Earth, but more complex parts (" higher harmonics ") also exist, as first shown by Carl Friedrich Gauss.

Other standard iterative methods for matrix equation solutions can also be used, for example the Gauss – Seidel method, where updated values for each patch are used in the calculation as soon as they are computed, rather than all being updated synchronously at the end of each sweep.

Gauss has also found some of Vega's errors in the calculations in the range of numbers, of which there are more than a million.

He also has a South African spider named after him, Araneus drygalskii ( Strand, 1909 ), based on material collected on the Gauss expedition.

Gauss conjectured that this condition was also necessary, but he offered no proof of this fact, which was provided by Pierre Wantzel in 1837.

The Riemann – Roch theorem can also be seen as a generalization of Gauss – Bonnet.

In fact, although Gauss also conjectured that there are infinitely many primes such that the ring of integers of is a PID, to this day we do not even know whether there are infinitely many number fields ( of arbitrary degree ) such that is a PID!

X ( f ( t )) is also a Gauss – Markov process

In mathematics, the error function ( also called the Gauss error function ) is a special function ( non-elementary ) of sigmoid shape which occurs in probability, statistics and partial differential equations.

Starting with Gauss ' law for electricity ( also one of Maxwell's equations ) in differential form, we have:

Another interpretation of the metric tensor, also considered by Gauss, is that it provides a way in which to compute the length of tangent vectors to the surface, as well as the angle between two tangent vectors.

Humboldt also secured a recommendation letter from Gauss, who upon reading his memoir on Fermat's theorem wrote with an unusual amount of praise that " Dirichlet showed excellent talent ".

Riemann later named this approach the Dirichlet principle, although he knew it had also been used by Gauss and by Lord Kelvin.

Bolzano also gave the first purely analytic proof of the fundamental theorem of algebra, which had originally been proven by Gauss from geometrical considerations.

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.

Hadamard described the experiences of the mathematicians / theoretical physicists Carl Friedrich Gauss, Hermann von Helmholtz, Henri Poincaré and others as viewing entire solutions with " sudden spontaneity.

There he attended classes at the Collège de France and at the Faculté des sciences de Paris, learning mathematics from Hachette among others, while undertaking private study of Gauss ' Disquisitiones Arithmeticae, a book he kept close for his entire life.

In fact, it was the only prior FFT work cited by them, as they were not then aware of the earlier research by Gauss and others.

Gauss, amongst others, after computing a large list of primes, conjectured that the number of primes less than or equal to a large number N is close to the value of the integral

Having studied under Carl Friedrich Gauss, he became a teacher at the gymnasium in Hof, tutoring, among others, Carl Culmann and Philipp Ludwig von Seidel.

Johann Carl Friedrich Gauss (;, ) ( 30 April 177723 February 1855 ) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.

Gauss, who was 23 at the time, heard about the problem and tackled it.

" Four normal distribution | Gaussian distributions in statisticsThis unproved statement put a strain on his relationship with János Bolyai ( who thought that Gauss was " stealing " his idea ), but it is now generally taken at face value.

" 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.

In Göttingen Reuter met Carl Friedrich Gauss who experimented with the transmission of electrical signals via wire.

It was Gauss who coined the term " non-euclidean geometry ".

It is named after Carl Friedrich Gauss who was aware of a version of the theorem but never published it, and Pierre Ossian Bonnet who published a special case in 1848.

Mathematical studies of knots began in the 19th century with Gauss, who defined the linking integral.

According to Gauss, who first described it, it is the " mathematical figure of the Earth ", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations.

While the notion of a metric tensor was known in some sense to mathematicians such as Carl Gauss from the early 19th century, it was not until the early 20th century that its properties as a tensor were understood by, in particular, Gregorio Ricci-Curbastro and Tullio Levi-Civita who first codified the notion of a tensor.

As Germany provided little opportunity to study higher mathematics at the time, with only Gauss at the University of Göttingen who was nominally a professor of astronomy and anyway disliked teaching, Dirichlet decided to go to Paris in May 1822.

He became interested in Gauss through one of his elementary school teachers, Minna Waldeck Gauss Reeves, who was a great-granddaughter of Gauss.

The name Gauss gun is sometimes used for such devices in reference to Carl Friedrich Gauss, who formulated mathematical descriptions of the magnetic effect used by magnetic accelerators.

Developed by Carl Gauss, who began research on the treatment in 1903, it was also sometimes known as the " Freiburg method ".

This algorithm, including its recursive application, was invented around 1805 by Carl Friedrich Gauss, who used it to interpolate the trajectories of the asteroids Pallas and Juno, but his work was not widely recognized ( being published only posthumously and in neo-Latin ).

This function was first studied in detail by Carl Friedrich Gauss, who explored the conditions for its convergence.

Since the time of Gauss ( who knew of the lemniscate function case ) the special role has been known of the A with extra automorphisms, and more generally endomorphisms.