After seeing it, Gauss wrote to Farkas Bolyai: " To praise it would amount to praising myself.

Mathematical historian Eric Temple Bell estimated that, had Gauss published all of his discoveries in a timely manner, he would have advanced mathematics by fifty years.

When the matter of honorary degrees came up at the University of Göttingen six years after Germain's death, Gauss lamented, “ proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree.

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 >).

One of the chief aims of Gauss ' investigations was to deduce those features of the surface which could be described by a function which would remain unchanged if the surface underwent a transformation in space ( such as bending the surface without stretching it ), or a change in the particular parametric form of the same geometrical surface.

Since the discrete logarithm problem reduces to Gauss sum estimation, an efficient classical algorithm for estimating Gauss sums would imply an efficient classical algorithm for computing discrete logarithms, which is considered unlikely.

This produced the work on the Hasse – Davenport relations for Gauss sums, and contact with Hans Heilbronn, with whom Davenport would later collaborate.

Current was run through each of the coils, but only one would a 5 Gauss magnetic field at a time.

The problem of their multiplicity was solved by McClellan and Parks ( 1972 ), although it was later shown to have been equivalent to a problem solved by Gauss ( Dickinson and Steiglitz, 1982 ).

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 ).

Carl Friedrich Gauss considered the same question: " Ins Jahr 1792 oder 1793 ", according to his own recollection nearly sixty years later in a letter to Encke ( 1849 ), he wrote in his logarithm table ( he was then 15 or 16 ) the short note " Primzahlen unter ".

William Cooke and Professor Charles Wheatstone learned of the Wilhelm Weber and Carl Gauss electromagnetic telegraph in 1833, and reached the stage of launching a commercial telegraph prior to Morse, despite starting later.

She used the name of a former student Monsieur Antoine-August Le Blanc, “ fearing ,” as she later explained to Gauss, “ the ridicule attached to a female scientist.

The concepts of later tensor analysis arose from the work of Carl Friedrich Gauss in differential geometry, and the formulation was much influenced by the theory of algebraic forms and invariants developed during the middle of the nineteenth century.

In fact even though Gauss redid this proof 50 years later, the gap remained.

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.

( Gauss ' conjecture was proven more than one hundred years later by Heegner, Baker and Stark.

Five years later, on March 29, 1807, he discovered the asteroid Vesta, which he allowed Carl Friedrich Gauss to name.

Although generalized to triple integrals by Lagrange in 1773, and used by Legendre, Laplace, Gauss, and first generalized to n variables by Mikhail Ostrogradski in 1836, it resisted a fully rigorous formal proof for a surprisingly long time, and was first satisfactorily resolved 125 years later, by Élie Cartan in a series of papers beginning in the mid-1890s (; ).

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

Dunnington wrote several articles about Gauss and later a biography entitled Gauss: Titan of Science ( ISBN 0-88385-547-X ).

In the earlier days of Joy Division, Hook used a Hiwatt Custom 100 Watt head initially on top of a Vox Bass Cabinet and then later on top of a 4x15 Gauss loaded Marshall cabinet put together by Tractor.

His proof was incomplete, leaving a gap which was later filled by Carl Friedrich Gauss.

Work in this area was later carried on by those such as Gauss and Galois who succeeded in such a proof.

* the tendency for an initial segment of data to show some bias that drops out later ( one example in number theory being Kummer's conjecture on cubic Gauss sums )

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 did not conclude on the issue at hand, but his work was later completed by Carl Friedrich Gauss.

Carl Friedrich Gauss had also studied the subject before Tissot's contributions later in the nineteenth century.

In 1851, at the instigation of Gauss, he was elected to the Academy of Göttingen ; one year later, this time at the recommendation of Dirichlet, he was also elected to the Academy of Berlin.

This is later supplemented by long-range rifles, medium-range Gauss guns, and a variety of directed-energy weapons, from a basic pulse laser to the highly destructive Graviton Gun.

Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th century by professional hand computers to solve the normal equations of least-squares problems.

The Gauss – Newton algorithm is a method used to solve non-linear least squares problems.

Knowing that, we can solve for,,, using the Gauss elimination method which yields

The puzzle was originally proposed in 1848 by the chess player Max Bezzel, and over the years, many mathematicians, including Gauss, have worked on this puzzle and its generalized n-queens problem.

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

Gauss ( aged about 26 ) on East German Postage stamp | stamp produced in 1977.

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.

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.

Gauss discovered that the law of biquadratic reciprocity and its supplements were more easily stated and proved as statements about " whole complex numbers " ( i. e. the Gaussian integers ) than they are as statements about ordinary whole numbers ( i. e. the integers ).

The Gauss – Bonnet theorem or Gauss – Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry ( in the sense of curvature ) to their topology ( in the sense of the Euler characteristic ).

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.

Mordell's book starts with a remark on homogeneous equations f = 0 over the rational field, attributed to C. F. Gauss, that non-zero solutions in integers ( even primitive lattice points ) exist if non-zero rational solutions do, and notes a caveat of L. E. Dickson, which is about parametric solutions.

Fraenkel also was interested in the history of mathematics, writing in 1920 and 1930 about Gauss ' works in algebra, and he published a biography of Georg Cantor.

As a consequence, the scale variation within a Gauss – Krüger zone is about 1 / 6 of what it is in a UTM zone.

Hardy expounds by commenting about a phrase attributed to Carl Friedrich Gauss that " Mathematics is the queen of the sciences and number theory is the queen of mathematics ".

Some people believe that it is the extreme non-applicability of number theory that led Gauss to the above statement about number theory ; however, Hardy points out that this is certainly not the reason.

The biographical sections give relevant information about the lives of mathematicians who worked in these areas, including Euler, Gauss, Dirichlet, Lobachevsky, Chebyshev, Vallée-Poussin, Hadamard, as well as Riemann himself.

E. T. Bell in his 1937 book Men of Mathematics ( page 237 ) claims that Gauss said " There have been but three epoch-making mathematicians, Archimedes, Newton, and Eisenstein ", and this has been widely quoted in writings about Eisenstein.

, one of Gauss's last students and a historian of mathematics, who was summarizing a remark made by Gauss about Eisenstein in a conversation many years earlier.

The famous mathematician Carl Friedrich Gauss commented that someone skilled in calculation could have done the 100-digit calculation in about half that time with pencil and paper.

*-Discussion of Waltershausen as source on Gauss numbers story including partial translation of Waltershausen book on Gauss Scientist online Volume 94 Number: 3 Page 200 Gauss's Day of Reckoning: A famous story about the boy wonder of mathematics has taken on a life of its own, Brian Hayes

On the other hand, using the universal Elias gamma coding for the Gauss – Kuzmin distribution results in an expected codeword length ( about 3. 51 bits ) near entropy ( about 3. 43 bits ).