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.

James Clerk Maxwell and Elihu Thomson ( through the British Association for the Advancement of Science-BAAS ) introduced the Centimetre gram second system of units ( cgs ) in 1874, in order to derive electric and magnetic metric units, following the recommendation of Carl Friedrich Gauss in 1832.

Engineers often measure magnetic fields in Gauss ( 1 Gauss

In 1833, Carl Friedrich Gauss, head of the Geomagnetic Observatory in Göttingen, published a paper on measurement of the Earth's magnetic field.

The average magnetic field strength in the Earth's outer core was measured to be 25 Gauss, 50 times stronger than the magnetic field at the surface.

The average magnetic field in the Earth's outer core was calculated to be 25 Gauss, 50 times stronger than the field at the surface.

The Earth's magnetic field strength was measured by Carl Friedrich Gauss in 1835 and has been repeatedly measured since then, showing a relative decay of about 10 % over the last 150 years.

* Milligauss ( mG ) and megagauss ( MG ), multiples of a unit of magnetic field Gauss ( unit ), equivalent to 1. 0 × 10 < sup >− 7 </ sup > tesla and 100 teslas, respectively.

Also, the application of the theories of Carl Friedrich Gauss to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin.

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.

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.

Since the Germans used the Gauss as the unit of the strength of the magnetic field in their mines ' triggers ( this was not yet a standard measure ), Goodeve referred to the various processes to counter the mines as degaussing.

The Earth's magnetic field is only 0. 5 Gauss and so it is difficult to conceive of a mechanism by which such a field could lead to any chemical changes other than those affecting the weak magnetic fields between radical pairs.

After Gauss ' death in 1855, the mathematician W. E. Weber replaced him as director, but Klinkerfues was to be temporarily responsible for the observatory from 1861.

He attended the University of Göttingen from 1818 to 1822 where he studied with Gauss who was director of the observatory.

While at university, Gauss independently rediscovered several important theorems ; his breakthrough occurred in 1796 when he showed that any regular polygon with a number of sides which is a Fermat prime ( and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2 ) can be constructed by compass and straightedge.

Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

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.

Among his results, Gauss showed that under a paraxial approximation an optical system can be characterized by its cardinal points and he derived the Gaussian lens formula.

He further asserts that although Gauss firmly believed in the immortality of the soul and in some sort of life after death, it was not in a fashion that could be interpreted as Christian.

This is justified, if unsatisfactorily, by Gauss in his " Disquisitiones Arithmeticae ", where he states that all analysis ( i. e., the paths one travelled to reach the solution of a problem ) must be suppressed for sake of brevity.

However, the Theorema Egregium of Carl Friedrich Gauss showed that already for surfaces, the existence of a local isometry imposes strong compatibility conditions on their metrics: the Gaussian curvatures at the corresponding points must be the same.

The most well-known use of the Cooley – Tukey algorithm is to divide the transform into two pieces of size at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general ( as was known to both Gauss and Cooley / Tukey ).

Archimedes ( 287-212 BC ), of Syracuse, Sicily, when it was a Greek city-state, is often considered to be the greatest of the Greek mathematicians, and occasionally even named as one of the three greatest of all time ( along with Isaac Newton and 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.

The row-echelon form of A produced by the Gauss algorithm has the same rank as A, and its rank can be read off as the number of non-zero rows.

This can be confirmed with the Gauss algorithm.

Gauss replied with a counterexample: 15 < sup > 11 </ sup > + 8 < sup > 11 </ sup > can be written as h < sup > 2 </ sup > + 11f < sup > 2 </ sup >, but 15 + 8 cannot.

If we choose the volume to be a ball of radius a around the source point, then Gauss ' divergence theorem implies that

For example, it follows that any closed oriented Riemannian surface can be C < sup > 1 </ sup > isometrically embedded into an arbitrarily small ε-ball in Euclidean 3-space ( there is no such C < sup > 2 </ sup >- embedding since from the formula for the Gauss curvature an extremal point of such an embedding would have curvature ≥ ε < sup >- 2 </ sup >).

Carl Friedrich Gauss in 1796 showed that a regular n-sided polygon can be constructed with ruler and compass if the odd prime factors of n are distinct Fermat primes.

LLSQ solutions can be computed using direct methods, although problems with large numbers of parameters are typically solved with iterative methods, such as the Gauss – Seidel method.

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

Property ( 3 ) means that every Gauss – Markov process can be synthesized from the standard Wiener process ( SWP ).

Gauss observed that if a primitive nth root of unity can be expressed using only square roots, then it is possible to construct the regular n-gon using only ruler and compass, and that if the root of unity requires third or fourth or higher radicals the regular polygon cannot be constructed.

Carl Friedrich Gauss and Wilhelm Weber built and first used for regular communication the electromagnetic telegraph in 1833 in Göttingen, connecting Göttingen Observatory and the Institute of Physics, covering a distance of about 1 km.

The main equipment Hook used during the early days of New Order was an Alembic F-2B preamp / Roland rack unit / Amcron DC-300A power amp fed through two large custom built 2 x 15 Gauss loaded flightcase cabinets designed and built by Chris Hewitt of Tractor Music.

The target space for the Gauss map N is a Grassmann bundle built on the tangent bundle TM.

In 1818 Gauss, putting his calculation skills to practical use, carried out a geodesic survey of the Kingdom of Hanover, linking up with previous Danish surveys.

His friend Farkas Wolfgang Bolyai with whom Gauss had sworn " brotherhood and the banner of truth " as a student, had tried in vain for many years to prove the parallel postulate from Euclid's other axioms of geometry.

" 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.

In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, leading to new knowledge in magnetism ( including finding a representation for the unit of magnetism in terms of mass, length and time ) and the discovery of Kirchhoff's circuit laws in electricity.

Bühler writes that, according to correspondence with Rudolf Wagner, Gauss did not appear to believe in a personal god.

Gauss also upheld religious tolerance, believing it wrong to disturb others who were at peace with their own beliefs.

Gauss eventually had conflicts with his sons.

The method is based on the individual work of Carl Friedrich Gauss ( 1777 – 1855 ) and Adrien-Marie Legendre ( 1752 – 1833 ) combined with modern algorithms for multiplication and square roots.

By the 1830s mathematics, physics, chemistry, and biology had emerged with world class science, led by Alexander von Humboldt ( 1769 – 1859 ) in natural science and Carl Friedrich Gauss ( 1777 – 1855 ) in mathematics.

In 1838 Johann Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li ( x ) ( under the slightly different form of a series, which he communicated to Gauss ).

Despite initial opposition from her parents and difficulties presented by a sexist society, she gained education from books in her father's library and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss.

General Pernety sent a chief of a battalion to meet with Gauss personally to see that he was safe.

When Germain's correspondence with Gauss ceased, she took interest in a contest sponsored by the Paris Academy of Sciences concerning Ernst Chladni's experiments with vibrating metal plates.