Versions of the Gauss Schoolroom Anecdote Collected by Brian Hayes with a lot of help from my friends Transcribed below are tellings of the story about Carl Friedrich Gauss's boyhood discovery of the "trick" for summing an arithmetic progression.
He was rare among mathematicians in that he was a calculating prodigyand he retained the ability to do elaborate calculations in his head most of his life. Its significance lies not in the result but in the proof, which rested on a profound analysis of the factorization of polynomial equations and opened the door to later ideas of Galois theory.
His doctoral thesis of gave a proof of the fundamental theorem of algebra: Gauss later gave three more proofs of this major result, the last on the 50th anniversary of the first, which shows the importance he attached to the topic.
Foremost was his publication of the first systematic textbook on algebraic number theoryDisquisitiones Arithmeticae. This book begins with the first account of modular arithmeticgives a thorough account of the solutions of quadratic polynomials in two variables in integers, and ends with the theory of factorization mentioned above.
The second publication was his rediscovery of the asteroid Ceres.
Its original discovery, by the Italian astronomer Giuseppe Piazzi inhad caused a sensation, but it vanished behind the Sun before enough observations could be taken to calculate its orbit with sufficient accuracy to know where it would reappear. Many astronomers competed for the honour of finding it again, Johann carl fredrich gauss Gauss won.
His success rested on a novel method for dealing with errors in observations, today called the method of least squares. Thereafter Gauss worked for many years as an astronomer and published a major work on the computation of orbits—the numerical side of such work was much less onerous for him than for most people.
Similar motives led Gauss to accept the challenge of surveying the territory of Hanoverand he was often out in the field in charge of the observations. The project, which lasted from toencountered numerous difficulties, but it led to a number of advancements.
Another was his discovery of a way of formulating the concept of the curvature of a surface. Gauss showed that there is an intrinsic measure of curvature that is not altered if the surface is bent without being stretched. For example, a circular cylinder and a flat sheet of paper have the same intrinsic curvature, which is why exact copies of figures on the cylinder can be made on the paper as, for example, in printing.
But a sphere and a plane have different curvatures, which is why no completely accurate flat map of the Earth can be made.
Gauss published works on number theory, the mathematical theory of map construction, and many other subjects. Instead, he drew important mathematical consequences from this work for what is today called potential theoryan important branch of mathematical physics arising in the study of electromagnetism and gravitation.
Gauss also wrote on cartographythe theory of map projections. For his study of angle-preserving maps, he was awarded the prize of the Danish Academy of Sciences in Gauss also had other unpublished insights into the nature of complex functions and their integralssome of which he divulged to friends.
In fact, Gauss often withheld publication of his discoveries. For this to be the case, there must exist an alternative geometric description of space. Rather than publish such a description, Gauss confined himself to criticizing various a priori defenses of Euclidean geometry.
It would seem that he was gradually convinced that there exists a logical alternative to Euclidean geometry. It is possible to draw these ideas together into an impressive whole, in which his concept of intrinsic curvature plays a central role, but Gauss never did this.
Some have attributed this failure to his innate conservatismothers to his incessant inventiveness that always drew him on to the next new idea, still others to his failure to find a central idea that would govern geometry once Euclidean geometry was no longer unique.
All these explanations have some merit, though none has enough to be the whole explanation.
Another topic on which Gauss largely concealed his ideas from his contemporaries was elliptic functions. He published an account in of an interesting infinite seriesand he wrote but did not publish an account of the differential equation that the infinite series satisfies.Johann Carl Friedrich Gauss (April 30, - February 23, ) was a German mathematician who made significant contributions to a variety of fields.
These include number theory, algebra, statistics, differential geometry, electrostatics, astronomy, and . Share How Johann Carl Friedrich Gauss rediscovered a lost dwarf planet tweet share Reddit Pocket Flipboard Email Johann Carl Friedrich Gauß (or Gauss) is honored today with a Google Doodle.
Enlightenment mathematician Johann Carl Friedrich Gauss () was born on this day in Brunswick, Germany, years ago.
Gauss is the subject of Google's latest Doodle, celebrating. Johann Carl Friedrich Gauss was born on April 30, in the city of Brunswick, Germany. His mother was Dorothea Benze and his father was Gebhard Dietrich Gauss. Carl’s mother was intelligent, but illiterate; she had received no education was a housemaid before marriage.
Apr 30, · Today’s Doodle celebrates the birthday of Johann Carl Friedrich Gauß, one of history's most influential mathematicians — and it was the scholar, himself, who worked out the date.
While his mother couldn’t read or write, she knew her son was born eight days before the Feast of the Ascension (39 days after Easter).
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