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Branch of Science
">Mathematicians
Nationality">German
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Gauss, Karl Friedrich (1777-1855)
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German mathematician who is sometimes called the "prince of mathematics." He was a prodigious child, at the age ofthree informing his father of an arithmetical error in a complicated payroll calculation & stating the correct answer.In school, when his teacher gave the problem of summing the integers from 1 to lớn 100 (an arithmetic series ) tohis students lớn keep them busy, Gauss immediately wrote down the correct answer 5050 on his slate. At age 19, Gaussdemonstrated a method for constructing a heptadecagon using only a straightedge andcompass which had eluded the Greeks. (The explicit construction of the heptadecagon wasaccomplished around 1800 by Erchinger.) Gauss also showed that only regular polygons ofa certain number of sides could be in that manner (a heptagon, for example, could not be constructed.)Gauss proved the fundamental theorem of algebra, which states that every polynomial has aroot of the khung a+bi. In fact, he gave four different proofs, the first of which appeared in his dissertation. In1801, he proved the fundamental theorem of arithmetic, which states that every naturalnumber can be represented as the product of primes in only one way.At age 24, Gauss published one of the most brilliant achievements in mathematics, Disquisitiones Arithmeticae(1801). In it, Gauss systematized the study of number theory (properties of theintegers ). Gauss proved that every number is the sum of at most three triangularnumbers & developed the algebra of congruences. In 1801, Gauss developed the method of least squares fitting, 10 years before Legendre, but didnot publish it. The method enabled him to lớn calculate the orbit of the asteroid
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Ceres, which had beendiscovered by Piazzi from only three observations. However, after his independent discovery, Legendreaccused Gauss of plagiarism. Gauss published his monumental treatise on celestial mechanics Theoria Motus in 1806.He became interested in the compass through surveying and developed the magnetometer and, with WilhelmWeber measured the intensity of magnetic forces. With Weber, he also builtthe first successful telegraph.Gauss is reported lớn have said "There have been only three epoch-making mathematicians: Archimedes, Newtonand Eisenstein" (Boyer 1968, p.553). Most historians are puzzled by the inclusion of Eisenstein in the sameclass as the other two. There is also a story that in 1807 he was interrupted in the middle of a problem and told that hiswife was dying. He is purported khổng lồ have said, "Tell her to wait a moment "til I"m through" (Asimov 1972, p.280).Gauss arrived at important results on the parallel postulate, but failed to publish them. Credit forthe discovery of non-Euclidean geometry therefore went khổng lồ Janos Bolyai andLobachevsky. However, he did publish his seminal work on differential geometry in Disquisitionescirca superticies curvas. The Gaussian curvature (or "second" curvature) is named for him. He alsodiscovered the Cauchy integral theorem


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for analytic functions, but did not publish it. Gauss solved the general problemof making a conformal map of one surface onto another.Unfortunately for mathematics, Gauss reworked & improved papers incessantly, therefore publishing only a fraction ofhis work, in keeping with his motto "pauca sed matura" (few but ripe). Many of his results were subsequently repeatedby others, since his terse diary remained unpublished for years after his death. This diary was only 19 pages long, butlater confirmed his priority on many results he had not published. Gauss wanted a heptadecagon placed on hisgravestone, but the carver refused, saying it would be indistinguishable from a circle. The heptadecagon appears, however, as the shape of a pedestal with a statue erected in his honor in his home town of Braunschweig.Bolyai (Janos), Eisenstein, Kovalevskaya, Legendre, Weber (Wilhelm) Additional biographies: MacTutor (St. Andrews), Bonn
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Asimov, I. Biographical Encyclopedia of Science và Technology; the Lives and Achievements of 1195 Great Scientists from Ancient Times to lớn the Present, Chronologically Arranged. Garden City, NY: Doubleday, 1972. Bell, E.T. "The Prince of Mathematicians: Gauss." Ch.14 in Men of Mathematics: The Lives & Achievements of the Great Mathematicians from Zeno to lớn Poincaré. New York: Simon and Schuster, pp.218-269, 1986. Boyer, C.B. A History of Mathematics, 2nd ed. New York: Wiley, 1968.Bühler, W. Gauss: A Biographical Study Berlin: Springer-Verlag, 1981.Cung, N. "Carl Friedrich Gauss." http://www.geocities.com/RainForest/Vines/2977/gauss/gauss.html. Dunnington, G.W. Carl Friedrich Gauss, Titan of Science: A Study of his Life & His Work. 1959.Gauss, C.F. Disquisitiones Arithmeticae. New York: Springer-Verlag, 1986.Hall, T. Carl Friedrich Gauss: A Biography. Cambridge, MA: MIT Press, 1970.Merzbach, U.C.

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Carl Friedrich Gauss: A Bibliography. Scholarly Resources, 1984.