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(His name rhymes with "house", and is sometimes spelled Gauß in German.)
Gauss was born in Braunschweig, Duchy of Brunswick-Lüneburg (now part of Germany) as the only son of lower-class uneducated parents. According to legend, his genius became apparent at the age of three, when he corrected, in his head, an error his father had made on paper while calculating finances. It is also said that while in elementary school, his teacher tried to occupy pupils by making them add up the (whole) numbers from 1 to 100. A few seconds later, to the astonishment of all, the young Gauss produced the correct answer, having realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1+100=101, 2+99=101, 3+98=101, etc., for a total sum of 50 × 101 = 5050. (see: summation)
Gauss earned a scholarship and in college, he independently rediscovered several important theorems; his breakthrough occurred in 1796 when he was able to show that any regular polygon, each of whose odd factors are distinct Fermat primes, can be constructed by ruler and compass alone, thereby adding to work started by classical Greek mathematicians. Gauss was so pleased by this result that he requested that a regular 17-gon be inscribed on his tombstone.
Gauss was the first to prove the fundamental theorem of algebra; in fact, he produced four entirely different proofs for this theorem over his lifetime, clarifying the concept of complex numberThe complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. The complex numbers contain a number , the imaginary unit with , i. is a square root of. Every complex number can be represented in the form , wher considerably along the way.
Gauss also made important contributions to number theoryTraditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wide with his 1801Events January 1 Legislative union of Great Britain and Ireland completed under the Act of Union 1800, bringing about the United Kingdom of Great Britain and Ireland. January 1 Giuseppe Piazzi discovers the first (and largest) asteroid Ceres. January 20 J book Disquisitiones ArithmeticaeThe Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. In this book Gauss brings together results in number theory obtained by mathematicians such, which contained a clean presentation of modular arithmeticModular arithmetic Group theory In mathematics, modular arithmetic is a system of arithmetic for certain equivalence classes of integers, called congruence classes . In modular arithmetic, numbers 'wrap around' after they reach a certain value (the modulu and the first proof of the law of quadratic reciprocity.
He had been supported by a stipend from the Duke of Brunswick, but he did not appreciate the insecurity of this arrangement and also did not believe mathematics to be important enough to deserve support; he therefore aimed for a position in astronomy, and in 1807 he was appointed professor of astronomy and director of the astronomical observatory in Göttingen.
In 1809, Gauss published a major work about the motion of celestial bodies. Among other things, he introduced the gaussian gravitational constant. It also contains an influential treatment of the method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error. He was able to prove the correctness of 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 1805, but Gauss claimed that he had been using it since 1795.
Gauss discovered the possibility of non-Euclidean geometries but never published it. His friend Farkos Wolfgang Bolyai had tried in vain for many years to prove the parallel postulate from Euclid's other axioms of geometry and failed. Bolyai's son, János Bolyai, rediscovered non-Euclidean geometry in the 1820s; his work was published in 1832.
In 1818, Gauss started a geodesic survey of the state of Hanover, work which later lead to the development of the normal distribution for describing measurement errors and an interest in differential geometry and his theorema egregrium establishing an important property of the notion of curvature.
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