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His attempts clarified the concept of complex numbers considerably along the way. It appears that Gauss already knew the class number formula in Piazzi could only track Ceres for somewhat more than a month, following it for three degrees across the night sky.

Then it disappeared temporarily behind the glare of the Sun. Gauss heard about the problem and tackled it. After three months of intense work, he predicted a position for Ceres in December —just about a year after its first sighting—and this turned out to be accurate within a half-degree when it was rediscovered by Franz Xaver von Zach on 31 December at Gotha , and one day later by Heinrich Olbers in Bremen.

Gauss's method involved determining a conic section in space, given one focus the Sun and the conic's intersection with three given lines lines of sight from the Earth, which is itself moving on an ellipse, to the planet and given the time it takes the planet to traverse the arcs determined by these lines from which the lengths of the arcs can be calculated by Kepler's Second Law.

This problem leads to an equation of the eighth degree, of which one solution, the Earth's orbit, is known. The solution sought is then separated from the remaining six based on physical conditions.

In this work, Gauss used comprehensive approximation methods which he created for that purpose. One such method was the fast Fourier transform.

While this method is attributed to a paper by James Cooley and John Tukey , [55] Gauss developed it as a trigonometric interpolation method.

His paper, Theoria Interpolationis Methodo Nova Tractata , [56] was only published posthumously in Volume 3 of his collected works. This paper predates the first presentation by Joseph Fourier on the subject in Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again".

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.

Thus he sought a position in astronomy, and in was appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen , a post he held for the remainder of his life.

The discovery of Ceres led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in as Theoria motus corporum coelestium in sectionibus conicis solem ambientum Theory of motion of the celestial bodies moving in conic sections around the Sun.

In the process, he so streamlined the cumbersome mathematics of 18th-century orbital prediction that his work remains a cornerstone of astronomical computation.

Gauss proved the method under the assumption of normally distributed errors see Gauss—Markov theorem ; see also Gaussian. The method had been described earlier by Adrien-Marie Legendre in , but Gauss claimed that he had been using it since or In Gauss, putting his calculation skills to practical use, carried out a geodetic survey of the Kingdom of Hanover , linking up with previous Danish surveys.

To aid the survey, Gauss invented the heliotrope , an instrument that uses a mirror to reflect sunlight over great distances, to measure positions.

Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.

Research on these geometries led to, among other things, Einstein 's theory of general relativity, which describes the universe as non-Euclidean.

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.

After seeing it, Gauss wrote to Farkas Bolyai: "To praise it would amount to praising myself. For the entire content of the work Letters from Gauss years before reveal him obscurely discussing the problem of parallel lines.

Waldo Dunnington , a biographer of Gauss, argues in Gauss, Titan of Science that Gauss was in fact in full possession of non-Euclidean geometry long before it was published by Bolyai, but that he refused to publish any of it because of his fear of controversy.

The geodetic survey of Hanover, which required Gauss to spend summers traveling on horseback for a decade, [64] fueled Gauss's interest in differential geometry and topology , fields of mathematics dealing with curves and surfaces.

Among other things, he came up with the notion of Gaussian curvature. This led in to an important theorem, the Theorema Egregium remarkable theorem , establishing an important property of the notion of curvature.

Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface.

That is, curvature does not depend on how the surface might be embedded in 3-dimensional space or 2-dimensional space.

In , he was made a foreign member of the Royal Swedish Academy of Sciences. In , 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, charge, and time and the discovery of Kirchhoff's circuit laws in electricity.

They constructed the first electromechanical telegraph in , [18] which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic observatory to be built in the garden of the observatory, and with Weber founded the "Magnetischer Verein" magnetic association , which supported measurements of Earth's magnetic field in many regions of the world.

He developed a method of measuring the horizontal intensity of the magnetic field which was in use well into the second half of the 20th century, and worked out the mathematical theory for separating the inner and outer magnetospheric sources of Earth's magnetic field.

If we except the great name of Newton it is probable that no mathematicians of any age or country have ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied.

It may seem paradoxical, but it is probably nevertheless true that it is precisely the efforts after logical perfection of form which has rendered the writings of Gauss open to the charge of obscurity and unnecessary difficulty.

Gauss says more than once that, for brevity, he gives only the synthesis, and suppresses the analysis of his propositions. If, on the other hand, we turn to a memoir of Euler 's, there is a sort of free and luxuriant gracefulness about the whole performance, which tells of the quiet pleasure which Euler must have taken in each step of his work.

It is not the least of Gauss's claims to the admiration of mathematicians, that, while fully penetrated with a sense of the vastness of the science, he exacted the utmost rigorousness in every part of it, never passed over a difficulty, as if it did not exist, and never accepted a theorem as true beyond the limits within which it could actually be demonstrated.

There are several stories of his early genius. According to one, his gifts became very apparent at the age of three when he corrected, mentally and without fault in his calculations, an error his father had made on paper while calculating finances.

Another story has it that in primary school after the young Gauss misbehaved, his teacher, J. Büttner, gave him a task: add a list of integers in arithmetic progression ; as the story is most often told, these were the numbers from 1 to The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels.

However, the details of the story are at best uncertain see [12] for discussion of the original Wolfgang Sartorius von Waltershausen source and the changes in other versions ; some authors, such as Joseph Rotman in his book A first course in Abstract Algebra , question whether it ever happened.

He referred to mathematics as "the queen of sciences" [67] and supposedly once espoused a belief in the necessity of immediately understanding Euler's identity as a benchmark pursuant to becoming a first-class mathematician.

From through , Gauss's portrait, a normal distribution curve and some prominent Göttingen buildings were featured on the German ten-mark banknote. Germany has also issued three postage stamps honoring Gauss.

One no. Daniel Kehlmann 's novel Die Vermessung der Welt , translated into English as Measuring the World , explores Gauss's life and work through a lens of historical fiction, contrasting them with those of the German explorer Alexander von Humboldt.

A film version directed by Detlev Buck was released in In a bust of Gauss was placed in the Walhalla temple. The numerous things named in honor of Gauss include:.

In the Polish mathematician Marian Rejewski , who helped to solve the German Enigma cipher machine in December , began studying actuarial statistics at Göttingen.

From Wikipedia, the free encyclopedia. This is the latest accepted revision , reviewed on 7 October For other persons or things named Gauss, see Gauss disambiguation.

German mathematician and physicist — Brunswick , Principality of Brunswick-Wolfenbüttel. Göttingen , Kingdom of Hanover , German Confederation.

Johanna Osthoff — Minna Waldeck — This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. July Learn how and when to remove this template message. Main article: List of things named after Carl Friedrich Gauss.

A full proof of necessity was given by Pierre Wantzel. See the Constructible polygon article for further discussion. He did not believe literally in all Christian dogmas.

Officially he was a member of St. Albans Church Evangelical Lutheran in Gottingen. All baptisms, burials, and weddings in his family occurred there.

It is also not known whether he attended church regularly or contributed financially. A faculty colleague called Gauss a deist, but there is good reason to believe that this label did not fit well.

Gauss possessed strong religious tolerance which he carried over to every belief originating in the depths of the human heart. This tolerance is not to be confused with religious indifference.

He took a special interest in the religious development of the human race, especially in his own century. I am not, and, he added, with the expression of great inner emotion, you are much happier than I.

I must say that so often in earlier times when I saw people of the lower classes, simple manual laborers who could believe so rightly with their hearts, I always envied them, and now, he continued, with soft voice and that naive childlike manner peculiar to him, while a tear came to his eye, tell me how does one begin this?

Berlin: Dudenverlag. Berlin: Walter de Gruyter. Retrieved 17 September Oxford Users' Guide to Mathematics. Scientific Monthly.

Bibcode : SciMo.. Archived from the original on 26 February Magoo Theatrical Collection , containing all Mr. Magoo theatrical shorts and Arabian Nights , was released on April 22, From Wikipedia, the free encyclopedia.

For the television series, see Mr. Magoo TV series. Magoo,' Dies at ". The Hollywood Reporter. Retrieved June 28, Kaufman claimed in a interview that the character was based on his uncle.

Walter , the archivist for the Walter J. BearManor Media. The Encyclopedia of Animated Cartoons. Checkmark Books. Retrieved June 6, New American Library.

Magoo' Blunders Into Live-Action". Los Angeles Times. Retrieved June 3, Magoo film ". Chicago Sun-Times. Animation World Network. Retrieved March 10, Retrieved January 21, Retrieved December 25, Retrieved May 22, Magoo Archived April 28, , at the Wayback Machine.

Cox, A Century of Light , , p. Archived from the original on March 5, Retrieved June 13, August 13, Retrieved January 5, Magoo on TV Collection: —".

Archived from the original on October 20, Stu's Show. Retrieved Magoo- The Theatrical Collection: — " ". DVD Talk. Retrieved June 30, Magoo — What's New, Mr.

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