carl friedrich gauß formel

. Carl Friedrich Gauss is sometimes referred to as the \"Prince of Mathematicians\" and the \"greatest mathematician since antiquity\". The discovery of Ceres led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in 1809 as Theoria motus corporum coelestium in sectionibus conicis solem ambientum (Theory of motion of the celestial bodies moving in conic sections around the Sun). During an austere childhood in a poor and unlettered family he showed extraordinary precocity. Gauss was born on 30 April, 1777 in Brunswick, Germany, into a humble family and attended a squalid school. {\displaystyle n} Gauß-Poisson-Verteilung {f} Gauss-Poisson distributionmath.stat. The solution sought is then separated from the remaining six based on physical conditions. Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. {\displaystyle 0,1,3,6,10,\dotsc } 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. + April 1777 in Braunschweig; † 23. Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the note: "ΕΥΡΗΚΑ! 51. 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. Die Aufgabe war indess kaum ausgesprochen als Gauss die Tafel mit den im niedern Braunschweiger Dialekt gesprochenen Worten auf den Tisch wirft: »Ligget se’.« (Da liegt sie.)“. + [13] This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day. 6 Danach ruhte die Formel im Verborgenen. n Lemma {n} von Gauß Gauss's lemmamath. God's revelation is continuous, not contained in tablets of stone or sacred parchment. werden Dreieckszahlen genannt. They constructed the first electromechanical telegraph in 1833,[18] which connected the observatory with the institute for physics in Göttingen. Marko Petkovsek, Herbert Wilf, Doron Zeilberger: Beweis der Gaußschen Summenformel mit vollständiger Induktion, Wikibooks: Mathe für Nicht-Freaks: Gaußsche Summenformel, Herleitung der gaußschen Summenformel auf zwei Arten einfach erklärt, Geometrischer Beweis der gaußschen Summenformel, https://de.wikipedia.org/w/index.php?title=Gaußsche_Summenformel&oldid=208015845, „Creative Commons Attribution/Share Alike“. n [a] This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career. Eugene shared a good measure of Gauss's talent in languages and computation. This is the book up on which this paper Jahrhundert. He did not want any of his sons to enter mathematics or science for "fear of lowering the family name", as he believed none of them would surpass his own achievements. Gauss's proofs of the fundamental theorem of Algebra Highly developed convolutions were also found, which in the early 20th century were suggested as the explanation of his genius.[27]. {\displaystyle 50+51.} On 1 October he published a result on the number of solutions of polynomials with coefficients in finite fields, which 150 years later led to the Weil conjectures. 101 Diese Summenformel wie auch die Summenformel für die ersten A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Stephen M. Stigler, "Gauss and the Invention of Least Squares,". {\displaystyle n} {\displaystyle n\cdot (n+1)} Um die Summe der Zahlen einer Zeile zu ermitteln, wird das Ergebnis halbiert, und es ergibt sich die obige Formel: Im Bild unten werden die einzelnen Summanden als grüne Kästchenreihen zu einem Dreieck angeordnet, das durch die weißen Kästchen zu einem Quadrat mit Seitenlänge Germany has also issued three postage stamps honoring Gauss. {\displaystyle n} Gauss was born on April 30, 1777 in a small German city north of the Harz mountains named Braunschweig. "[29] One of his biographers, G. Waldo Dunnington, described Gauss's religious views as follows: For him science was the means of exposing the immortal nucleus of the human soul. liefert die Summe der ersten Beginnings. 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. + {\displaystyle n+1.} Gauss supported the monarchy and opposed Napoleon, whom he saw as an outgrowth of revolution. Gauss viste tidligt mere end almindelig flair for tal, da han i en alder af tre år som en anden tallenes Mozart rettede fejl i sin fars regnskaber. To aid the survey, Gauss invented the heliotrope, an instrument that uses a mirror to reflect sunlight over great distances, to measure positions. , Gauss contributed to many areas of learning. Thus he sought a position in astronomy, and in 1807 was appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen, a post he held for the remainder of his life. Diese Seite wurde zuletzt am 24. der ungeraden Zahlen. , It appears that Gauss already knew the class number formula in 1801.[51]. 3 [59] In the history of statistics, this disagreement is called the "priority dispute over the discovery of the method of least squares."[60]. Two people gave eulogies at his funeral: Gauss's son-in-law Heinrich Ewald, and Wolfgang Sartorius von Waltershausen, who was Gauss's close friend and biographer. In this work, Whewell had discarded the possibility of existing life in other planets, on the basis of theological arguments, but this was a position with which both Wagner and Gauss disagreed. Work 3. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.[50]. [b], In connection to this, there is a record of a conversation between Rudolf Wagner and Gauss, in which they discussed William Whewell's book Of the Plurality of Worlds. In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Felix Klein, Vorlesungen über die Entwicklung der Mathematik im 19. The ‘Prince of Mathematicians’ is hailed for contributions to number theory, geometry, probability theory and astronomy. Also musste das gesuchte Ergebnis gleich dem Produkt This problem leads to an equation of the eighth degree, of which one solution, the Earth's orbit, is known. Während nun seine Mitschüler fleißig zu addieren begannen, stellte Gauß fest, dass sich die 100 zu addierenden Zahlen zu 50 Paaren gruppieren lassen, die jeweils die Summe 101 haben: Carl Friedrich Gauss (1777–1855), one of the most prolific mathematicians of all time, displayed a talent for mathematics at an early age. Two religious works which Gauss read frequently were Braubach's Seelenlehre (Giessen, 1843) and Süssmilch's Gottliche (Ordnung gerettet A756); he also devoted considerable time to the New Testament in the original Greek.[35]. Scottish-American mathematician and writer Eric Temple Bell said that if Gauss had published all of his discoveries in a timely manner, he would have advanced mathematics by fifty years.[45]. 1. {\displaystyle 1+100,2+99,3+98} Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. In 1831, 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. Carl Friedrich Gauss 1. Johann Carl Friedrich Gauss was an amazing and truly outstanding mathematician who lived in the Holy Roman Empire (nowadays Germany) in the XVIII and XIX centuries. On Gauss's recommendation, Friedrich Bessel was awarded an honorary doctor degree from Göttingen in March 1811. [54], One such method was the fast Fourier transform. n [citation needed] This is justified, if unsatisfactorily, by Gauss in his Disquisitiones Arithmeticae, where he states that all analysis (i.e., the paths one traveled to reach the solution of a problem) must be suppressed for sake of brevity. See also the letter from Robert Gauss to Felix Klein on 3 September 1912. Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again". ⋅ Piazzi could track Ceres for only somewhat more than a month, following it for three degrees across the night sky. Published April 1999,October 2009,September 2012,February 2011. [52][53], 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). Gauss summarized his views on the pursuit of knowledge in a letter to Farkas Bolyai dated 2 September 1808 as follows: It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. [13][17] He further advanced modular arithmetic, greatly simplifying manipulations in number theory. ( Bell, author of Men of Mathematics, while Gauss’s father, Gerhard, was calculating the payroll for some laborers under his charge, little Gauss was … {\displaystyle n\cdot (n+1).} , In addition, he proved the following conjectured theorems: On 1 January 1801, Italian astronomer Giuseppe Piazzi discovered the dwarf planet Ceres. Religion is not a question of literature, but of life. n The British mathematician Henry John Stephen Smith (1826–1883) gave the following appraisal of Gauss: 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. In the days of his full strength, it furnished him recreation and, by the prospects which it opened up to him, gave consolation. To man is not vouchsafed that fullness of knowledge which would warrant his arrogantly holding that his blurred vision is the full light and that there can be none other which might report the truth as does his. 3 Gauss was a Lutheran Protestant, a member of the St. Albans Evangelical Lutheran church in Göttingen. Der kleine Gauss ist eine Figur, angelehnt an den Mathematiker Carl Friedrich Gauß, der mit neun Jahren eine Formel für die Summe der ersten n aufeinanderfolgenden natürlichen Zahlen entdeckte. Aus der Gaußschen Summenformel ergeben sich durch Anwenden des Distributivgesetzes und anderer ähnlich elementarer Rechenregeln leicht auch Formeln für die Summe der geraden bzw. Several months later, when Ceres should have reappeared, Piazzi could not locate it: the mathematical tools of the time were not able to extrapolate a position from such a scant amount of data—three degrees represent less than 1% of the total orbit. [6] His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). With Johanna (1780–1809), his children were Joseph (1806–1873), Wilhelmina (1808–1846) and Louis (1809–1810). Gauss remained mentally active into his old age, even while suffering from gout and general unhappiness. 1 Erst 1976 wurde sie von Eugene Salamin [103] und Richard Brent [36] unabhängig voneinander erneut gefunden, und ist … Later Wagner explained that he did not fully believe in the Bible, though he confessed that he "envied" those who were able to easily believe. His personal diaries indicate that he had made several important mathematical discoveries years or decades before his contemporaries published them. Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to the implicit use of the Jordan curve theorem. Abington, United Kingdom: Helicon. He then married Minna Waldeck (1788–1831)[41][42] on 4 August 1810,[41] and had three more children. [18], In 1840, Gauss published his influential Dioptrische Untersuchungen,[19] in which he gave the first systematic analysis on the formation of images under a paraxial approximation (Gaussian optics). Most of his work was about number theory and astronomy . Gauss's intellectual abilities attracted the attention of the Duke of Brunswick,[10][5] who sent him to the Collegium Carolinum (now Braunschweig University of Technology),[10] which he attended from 1792 to 1795,[14] and to the University of Göttingen from 1795 to 1798. [citation needed] The reverse featured the approach for Hanover. [9] Many versions of this story have been retold since that time with various details regarding what the series was – the most frequent being the classical problem of adding all the integers from 1 to 100. Though he did take in a few students, Gauss was known to dislike teaching. 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. However, he subsequently produced three other proofs, the last one in 1849 being generally rigorous. [3] Sometimes referred to as the Princeps mathematicorum[4] (Latin for '"the foremost of mathematicians"') and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians. sein. [42] Minna Waldeck died on 12 September 1831. Man braucht nun nur mehr die Anzahl Die Gaußsche Summenformel (nicht zu verwechseln mit einer Gaußschen Summe), auch kleiner Gauß genannt, ist eine Formel für die Summe der ersten [69], In 2007 a bust of Gauss was placed in the Walhalla temple.[70]. 1 [61], Letters from Gauss years before 1829 reveal him obscurely discussing the problem of parallel lines. "Gauss, Carl Friedrich (1777–1855)." Februar 1855 in Göttingen) war ein deutscher Mathematiker, Statistiker, Astronom, Geodät und Physiker. aufeinanderfolgenden geraden Zahlen: Die Formel für die Summe der ersten 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), and some authors, such as Joseph J. Rotman in his book A First Course in Abstract Algebra(2000), question whether it ever happened. , Gauss was so pleased with this result that he requested that a regular heptadecagon be inscribed on his tombstone. A discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, and 50 Hz. Gauss Was Born to Poor, Working-Class Parents & Was a Child Prodigy Who Figured … 725) appeared in 1955 on the hundredth anniversary of his death; two others, nos. Darunter schreibt man die Zahlen in umgekehrter Reihenfolge: Die Summe jeder Spalte ist [42] Gauss was never quite the same without his first wife, and he, just like his father, grew to dominate his children. der grünen Kästchen führt. His paper, Theoria Interpolationis Methodo Nova Tractata,[56] was published only posthumously in Volume 3 of his collected works. n Carl Friedrich Gauss; (1777-1855), German mathematician and scientist acknowledged to be one of the three leading mathematicians of all time, the others being Archimedes and Newton. The year 1796 was productive for both Gauss and number theory. 1 1965). Gauss was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1822.[65]. Neben dem oben vorgeführten Beweis der Vorwärts- und Rückwärts-Summation ist noch das folgende allgemeine Prinzip interessant:[3], Um zu beweisen, dass für alle natürlichen In the process, he so streamlined the cumbersome mathematics of 18th-century orbital prediction that his work remains a cornerstone of astronomical computation. Carl Friedrich Gauß entdeckte diese Formel als neunjähriger Schüler wieder. Prepared By : Aditya Kumar Pathak 2. His mother lived in his house from 1817 until her death in 1839.[5]. Gauss eventually had conflicts with his sons. Media in category "Carl Friedrich Gauß" The following 41 files are in this category, out of 41 total. [30], Apart from his correspondence, there are not many known details about Gauss's personal creed. bis zu info), Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a famous mathematician from Göttingen, Germany. Born Johann Carl Friedrich Gauss to poor parents, Gauss displayed his prodigious calculating skills before he was even three years old. und. The method had been described earlier by Adrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since 1794 or 1795. n Gauss, Carl Friedrich (1777-1855). His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). [48], Before she died, Sophie Germain was recommended by Gauss to receive an honorary degree; she never received it.[49]. Carl Friedrich Gauß signature.svg 847 × 756; 68 KB. 1 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 100. {\displaystyle n} Da es [41] Gauss plunged into a depression from which he never fully recovered. [72], Carl Friedrich Gauss, who also introduced the so-called Gaussian logarithms, sometimes gets confused with Friedrich Gustav Gauss [de] (1829–1915), a German geologist, who also published some well-known logarithm tables used up into the early 1980s. [71], On 30 April 2018, Google honoured Gauss in his would-be 241st birthday with a Google Doodle showcased in Europe, Russia, Israel, Japan, Taiwan, parts of Southern and Central America and the United States. [citation needed], Another story has it that in primary school after the young Gauss misbehaved, his teacher, J.G. Johann Carl Friedrich Gauss, also known as the Prince of Math, but most commonly called Carl Friedrich Gauss, was born on April 30, 1777, in Braunschweig, Germany (named Holy Roman Empire at the time). At an early age his intellectual abilities attracted the attention of the Duke of Brunswick, who secured his education first at the Collegium Carolinum (1792-1795) in his native city and then at the University of Göttingen … Gauss usually declined to present the intuition behind his often very elegant proofs—he preferred them to appear "out of thin air" and erased all traces of how he discovered them. Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean. [18] For example, at the age of 62, he taught himself Russian. Johann Carl Friedrich Gauss is one of the most influential mathematicians in history. The stonemason declined, stating that the difficult construction would essentially look like a circle.[16]. Early Life 2. Later, he moved to Missouri and became a successful businessman. Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work. 7 benefits of working from home; Jan. 26, 2021. Die genaue Aufgabenstellung ist nicht überliefert. [41][42], Gauss had six children. Eine Verallgemeinerung auf eine beliebige positive ganze Zahl als Exponenten ist die Faulhabersche Formel. Quoted in Waltershausen, Wolfgang Sartorius von (1856, repr. Royal Netherlands Academy of Arts and Sciences, the letter from Robert Gauss to Felix Klein, Learn how and when to remove this template message, constructed with straightedge and compass, List of things named after Carl Friedrich Gauss, "General Investigations of Curved Surfaces", "The Sesquicentennial of the Birth of Gauss", "Mind Over Mathematics: How Gauss Determined The Date of His Birth", "Letter:WORTHINGTON, Helen to Carl F. Gauss – 26 July 1911", "Anatomical Observations on the Brain and Several Sense-Organs of the Blind Deaf-Mute, Laura Dewey Bridgman", "Person:GAUSS, Carl Friedrich (1777–1855) – Gauss's Children", "Johanna Elizabeth Osthoff 1780–1809 – Ancestry", "Letter: Charles Henry Gauss to Florian Cajori – 21 December 1898", "Did Gauss know Dirichlet's class number formula in 1801? That is, curvature does not depend on how the surface might be embedded in 3-dimensional space or 2-dimensional space. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. Gauss says more than once that, for brevity, he gives only the synthesis, and suppresses the analysis of his propositions. In 1818 Gauss, putting his calculation skills to practical use, carried out a geodetic survey of the Kingdom of Hanover, linking up with previous Danish surveys. [46] Around that time, the two men engaged in a correspondence. Toward the end of his life, it brought him confidence. ⋅ 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. Many biographers of Gauss disagree about his religious stance, with Bühler and others considering him a deist with very unorthodox views,[31][32][33] while Dunnington (though admitting that Gauss did not believe literally in all Christian dogmas and that it is unknown what he believed on most doctrinal and confessional questions) points out that he was, at least, a nominal Lutheran. Bolyai's son, János Bolyai, discovered non-Euclidean geometry in 1829; his work was published in 1832. {\displaystyle 50\cdot 101} Wegen seiner überragenden wissenschaftlichen Leistungen galt er bereits zu seinen Lebzeiten als Princeps Mathematicorum („Fürst der Mathematiker“; „Erster unter den Mathematikern“). 50 He discovered a construction of the heptadecagon on 30 March. Various principles which he advocated became an integral part of statistics and his theory of errors remained a major focus of probability theory up to the 1930s. The son of peasant parents (both were illiterate), he developed a staggering number of important ideas and had many more named after him. Für diese Summenformel gibt es zahlreiche Beweise. Karl Friedrich Gauss was born in Brunswick on April 30, 1777. 1246 and 1811, in 1977, the 200th anniversary of his birth. 2 Sie wurde von dem deutschen Mathematiker Carl Friedrich Gauß (1777–1855) um das Jahr 1800 herum aufgestellt. His work is astronomy and physics is nearly as significant as that in mathematics. (2014). Like many of the great mathematicians, Gauss showed amazing mathematical skill from an … They had an argument over a party Eugene held, for which Gauss refused to pay. n Hayes, 2006 There are discrepancies about the exact story and his age at the time ... Carl Friedrich Gauss: 1777-1855. Die einfache Halbierung des Quadrats entlang einer seiner Diagonalen würde die genau auf der Diagonale liegenden Kästchen ebenfalls teilen, was unerwünscht ist. "Sophie Germain, or, Was Gauss a feminist?". After three months of intense work, he predicted a position for Ceres in December 1801—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 was born on April 30, 1777 in Brunswick (now it is Western Germany). Many biographists think that he got his… Diese Summenformel wird als der "Der kleine Gauss" bezeichnet. Gauss shaped the treatment of observations into a practical tool. Wikimedia Commons German mathematician Carl Friedrich Gauss, here in his early 60s. The Prince of Math (as he is commonly known) made contributions to the fields of Algebra, Geometry, Astronomy and many more. n Here's why", "An algorithm for the machine calculation of complex Fourier series", "Gauss and the history of the fast fourier transform", "Die Vermessung der Welt (2012) – Internet Movie Database", "Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst: Startseite", "Johann Carl Friedrich Gauß's 241st Birthday", English translation of Waltershausen's 1862 biography, Carl Friedrich Gauss on the 10 Deutsche Mark banknote, List of scientists whose names are used as units, Scientists whose names are used in physical constants, People whose names are used in chemical element names, https://en.wikipedia.org/w/index.php?title=Carl_Friedrich_Gauss&oldid=1015714693, Technical University of Braunschweig alumni, Corresponding Members of the St Petersburg Academy of Sciences, Fellows of the American Academy of Arts and Sciences, Honorary Members of the St Petersburg Academy of Sciences, Members of the Bavarian Maximilian Order for Science and Art, Members of the Royal Netherlands Academy of Arts and Sciences, Members of the Royal Swedish Academy of Sciences, Recipients of the Pour le Mérite (civil class), CS1 maint: bot: original URL status unknown, Short description is different from Wikidata, Wikipedia pending changes protected pages, Pages using infobox scientist with unknown parameters, Articles with unsourced statements from July 2007, Articles needing additional references from July 2012, All articles needing additional references, Articles with unsourced statements from March 2021, Articles with unsourced statements from December 2019, Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference, Wikipedia articles with BIBSYS identifiers, Wikipedia articles with CANTIC identifiers, Wikipedia articles with CINII identifiers, Wikipedia articles with PLWABN identifiers, Wikipedia articles with RKDartists identifiers, Wikipedia articles with SELIBR identifiers, Wikipedia articles with SUDOC identifiers, Wikipedia articles with Trove identifiers, Wikipedia articles with WORLDCATID identifiers, Wikipedia articles with multiple identifiers, Creative Commons Attribution-ShareAlike License, developed an algorithm for determining the, This page was last edited on 3 April 2021, at 02:44. Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. [23], In 1854, Gauss selected the topic for Bernhard Riemann's inaugural lecture "Über die Hypothesen, welche der Geometrie zu Grunde liegen" (About the hypotheses that underlie Geometry). [28], Gauss declared he firmly believed in the afterlife, and saw spirituality as something essentially important for human beings. [41][42] Johanna died on 11 October 1809,[41][42][43] and her youngest child, Louis, died the following year. He is most famous for his groundbreaking work in the fields of algebra, statistics, differential geometry, number theory, electrostatics and optics. … [15] His breakthrough occurred in 1796 when he showed that a regular polygon can be constructed by compass and straightedge if the number of its sides is the product of distinct Fermat primes and a power of 2. While this method is attributed to a 1965 paper by James Cooley and John Tukey,[55] Gauss developed it as a trigonometric interpolation method. He has had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. erweitert wird. aufeinanderfolgenden natürlichen Zahlen: Diese Reihe ist ein Spezialfall der arithmetischen Reihe, und ihre Summen

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