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113-522: Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous adjective Gaussian is pronounced / ˈ ɡ aʊ s i ən / . Terrestrial Celestial Gauss Monuments were erected in Brunswick and Göttingen (the last together with Weber). Busts of Gauss were placed in
226-603: A Prussian province ; after 1919 Brunswick became a free state). Historically a close tie existed between the royal house of Hanover ( Electorate of Hanover ) and the United Kingdom of Great Britain and Ireland as a result of their personal union in the 18th century (the personal union was dissolved when Victoria became the Queen of the United Kingdom in 1837 because Hanover did not allow female rulers). West of
339-492: A heliometer from Fraunhofer . The scientific activity of Gauss, besides pure mathematics, can be roughly divided into three periods: astronomy was the main focus in the first two decades of the 19th century, geodesy in the third decade, and physics, mainly magnetism, in the fourth decade. Gauss made no secret of his aversion to giving academic lectures. But from the start of his academic career at Göttingen, he continuously gave lectures until 1854. He often complained about
452-423: A magnetometer in 1833 and – alongside Wilhelm Eduard Weber – the first electromagnetic telegraph in 1833. Gauss was the first to discover and study non-Euclidean geometry , coining the term as well. He further developed a fast Fourier transform some 160 years before John Tukey and James Cooley . Gauss refused to publish incomplete work and left several works to be edited posthumously . He believed that
565-522: A Lower Saxon Constituency Association ( Wahlkreisverband IX (Niedersachsen) ). This indicates that at that time the western administrations of the Prussian Province of Hanover and the state of Oldenburg were perceived as being "Lower Saxon". The forerunners of today's state of Lower Saxony were lands that were geographically and, to some extent, institutionally interrelated from very early on. The County of Schaumburg (not to be confused with
678-406: A butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate. He had one elder brother from his father's first marriage. Gauss was a child prodigy in mathematics. When
791-569: A collection of short remarks about his results from the years 1796 until 1814, shows that many ideas for his mathematical magnum opus Disquisitiones Arithmeticae (1801) date from this time. Gauss graduated as a Doctor of Philosophy in 1799, not in Göttingen, as is sometimes stated, but at the Duke of Brunswick's special request from the University of Helmstedt, the only state university of
904-491: A considerable literary estate, too. Gauss referred to mathematics as "the queen of sciences" and arithmetics as "the queen of mathematics", 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. On certain occasions, Gauss claimed that the ideas of another scholar had already been in his possession previously. Thus his concept of priority as "the first to discover, not
1017-672: A critique of d'Alembert's work. He subsequently produced three other proofs, the last one in 1849 being generally rigorous. His attempts clarified the concept of complex numbers considerably along the way. In the preface to the Disquisitiones , Gauss dates the beginning of his work on number theory to 1795. By studying the works of previous mathematicians like Fermat, Euler, Lagrange, and Legendre, he realized that these scholars had already found much of what he had discovered by himself. The Disquisitiones Arithmeticae , written since 1798 and published in 1801, consolidated number theory as
1130-431: A curious feature of his working style that he carried out calculations with a high degree of precision much more than required, and prepared tables with more decimal places than ever requested for practical purposes. Very likely, this method gave him a lot of material which he used in finding theorems in number theory. Gauss refused to publish work that he did not consider complete and above criticism. This perfectionism
1243-474: A decade. Therese then took over the household and cared for Gauss for the rest of his life; after her father's death, she married actor Constantin Staufenau. Her sister Wilhelmina married the orientalist Heinrich Ewald . Gauss's mother Dorothea lived in his house from 1817 until she died in 1839. The eldest son Joseph, while still a schoolboy, helped his father as an assistant during the survey campaign in
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#17327663083961356-483: A discipline and covered both elementary and algebraic number theory . Therein he introduces the triple bar symbol ( ≡ ) for congruence and uses it for a clean presentation of modular arithmetic . It deals with the unique factorization theorem and primitive roots modulo n . In the main sections, Gauss presents the first two proofs of the law of quadratic reciprocity and develops the theories of binary and ternary quadratic forms . The Disquisitiones include
1469-682: A habit in his later years, for example, the number of paths from his home to certain places in Göttingen, or the number of living days of persons; he congratulated Humboldt in December 1851 for having reached the same age as Isaac Newton at his death, calculated in days. Similar to his excellent knowledge of Latin he was also acquainted with modern languages. At the age of 62, he began to teach himself Russian , very likely to understand scientific writings from Russia, among them those of Lobachevsky on non-Euclidean geometry. Gauss read both classical and modern literature, and English and French works in
1582-555: A heart attack in Göttingen; and was interred in the Albani Cemetery there. Heinrich Ewald , Gauss's son-in-law, and Wolfgang Sartorius von Waltershausen , Gauss's close friend and biographer, gave eulogies at his funeral. Gauss was a successful investor and accumulated considerable wealth with stocks and securities, finally a value of more than 150 thousand Thaler; after his death, about 18 thousand Thaler were found hidden in his rooms. The day after Gauss's death his brain
1695-465: A number of areas to the east, for example, in what is now west and north Saxony-Anhalt. The land of the Saxons was divided into about 60 Gaue . The Frisians had not moved into this region; for centuries they preserved their independence in the most northwesterly region of the present-day Lower Saxon territory. The original language of the folk in the area of Old Saxony was West Low German , one of
1808-474: A private scholar. He gave the second and third complete proofs of the fundamental theorem of algebra , made contributions to number theory , and developed the theories of binary and ternary quadratic forms. Gauss was instrumental in the identification of Ceres as a dwarf planet. His work on the motion of planetoids disturbed by large planets led to the introduction of the Gaussian gravitational constant and
1921-702: A scandal in public, Eugen suddenly left Göttingen under dramatic circumstances in September 1830 and emigrated via Bremen to the United States. He wasted the little money he had taken to start, after which his father refused further financial support. The youngest son Wilhelm wanted to qualify for agricultural administration, but had difficulties getting an appropriate education, and eventually emigrated as well. Only Gauss's youngest daughter Therese accompanied him in his last years of life. Collecting numerical data on very different things, useful or useless, became
2034-415: A strong calculus as the sole tasks of astronomy. At university, he was accompanied by a staff of other lecturers in his disciplines, who completed the educational program; these included the mathematician Thibaut with his lectures, the physicist Mayer , known for his textbooks, his successor Weber since 1831, and in the observatory Harding , who took the main part of lectures in practical astronomy. When
2147-445: A university chair in Göttingen, "because he was always involved in some polemic." Gauss's life was overshadowed by severe problems in his family. When his first wife Johanna suddenly died shortly after the birth of their third child, he revealed the grief in a last letter to his dead wife in the style of an ancient threnody , the most personal surviving document of Gauss. The situation worsened when tuberculosis ultimately destroyed
2260-561: Is the only Bundesland that encompasses both maritime and mountainous areas. The northwestern area of the state, on the coast of the North Sea, is called East Frisia and the seven East Frisian Islands offshore are popular with tourists. In the extreme west of Lower Saxony is the Emsland , an economically emerging but rather sparsely populated area, once dominated by inaccessible swamps. The northern half of Lower Saxony, also known as
2373-667: Is well-developed agriculturally . In the west lie the County of Bentheim , Osnabrück Land , Emsland , Oldenburg Land , Ammerland , Oldenburg Münsterland , and on the coast East Frisia . The state is dominated by several large northwards-flowing rivers, including the Ems , Weser , Aller , and the Elbe. The highest point in Lower Saxony is the Wurmberg (971 metres or 3,186 feet) in
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#17327663083962486-759: The British Zone of Occupation . On 23 August 1946, the British Military Government issued Ordinance No. 46 "Concerning the dissolution of the provinces of the former state of Prussia in the British Zone and their reconstitution as independent states" , which initially established the State of Hanover on the territory of the former Prussian Province of Hanover. Its minister president, Hinrich Wilhelm Kopf , had already suggested in June 1945
2599-592: The Celestial police . One of their aims was the discovery of further planets. They assembled data on asteroids and comets as a basis for Gauss's research on their orbits, which he later published in his astronomical magnum opus Theoria motus corporum coelestium (1809). In November 1807, Gauss followed a call to the University of Göttingen , then an institution of the newly founded Kingdom of Westphalia under Jérôme Bonaparte , as full professor and director of
2712-502: The Gauss composition law for binary quadratic forms, as well as the enumeration of the number of representations of an integer as the sum of three squares. As an almost immediate corollary of his theorem on three squares , he proves the triangular case of the Fermat polygonal number theorem for n = 3. From several analytic results on class numbers that Gauss gives without proof towards
2825-461: The Nazi Party seized power in 1933, they quickly transformed Germany into a highly centralized state and divided the entire Third Reich into Gaue which largely superseded (but did not outright replace) Germany's traditional federal system. Nevertheless, some changes to the old state and provincial borders were made in 1937, notably including the city of Cuxhaven being fully integrated into
2938-625: The Netherlands . Furthermore, the state of Bremen forms two enclaves within Lower Saxony, one being the city of Bremen , the other its seaport , Bremerhaven (which is a semi-exclave , as it has a coastline). Lower Saxony thus borders more neighbours than any other single Bundesland . The state's largest cities are the state capital Hanover , Braunschweig (Brunswick), Oldenburg , Osnabrück , Wolfsburg , Göttingen , Salzgitter , Hildesheim , mainly situated in its central and southern parts, except Oldenburg and Lüneburg. Lower Saxony
3051-871: The North German Plain , is almost invariably flat except for the gentle hills around the Bremen geestland . Towards the south and southwest lie the northern parts of the Central Uplands : the Weser Uplands and the Harz Mountains. Between these two lie the Lower Saxon Hills , a range of low ridges. The region in the northeast, the Lüneburg Heath ( Lüneburger Heide ), is the largest heathland area of Germany. In
3164-810: The Walhalla hall of fame near Regensburg and in the German Research Centre for Geosciences in Potsdam . Several places where Gauss has stayed in Germany are marked with plaques. Germany issued three postage stamps honoring Gauss, one in 1955 on the hundredth anniversary of his death and two others in 1977, the 200th anniversary of his birth. Carl Friedrich Gauss Johann Carl Friedrich Gauss (German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ; Latin : Carolus Fridericus Gauss ; 30 April 1777 – 23 February 1855)
3277-493: The astronomical observatory , and kept the chair until his death in 1855. He was soon confronted with the demand for two thousand francs from the Westphalian government as a war contribution, which he could not afford to pay. Both Olbers and Laplace wanted to help him with the payment, but Gauss refused their assistance. Finally, an anonymous person from Frankfurt , later discovered to be Prince-primate Dalberg , paid
3390-545: The district of Tecklenburg and the state of Lippe . Kopf's plan was ultimately based on a draft for the reform of the German Empire from the late 1920s by Georg Schnath and Kurt Brüning. The strong Welf connotations of this draft, according to Thomas Vogtherr, did not simplify the development of a Lower Saxon identity after 1946. An alternative model, proposed by politicians in Oldenburg and Brunswick, envisaged
3503-472: The method of least squares , which he had discovered before Adrien-Marie Legendre published it. Gauss was in charge of the extensive geodetic survey of the Kingdom of Hanover together with an arc measurement project from 1820 to 1844; he was one of the founders of geophysics and formulated the fundamental principles of magnetism . Fruits of his practical work were the inventions of the heliotrope in 1821,
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3616-428: The north temperate zone of central Europe that is affected by prevailing Westerlies and is located in a transition zone between the maritime climate of Western Europe and the continental climate of Eastern Europe . This transition is clearly noticeable within the state: whilst the northwest experiences an Atlantic (North Sea coastal) to Sub-Atlantic climate, with comparatively low variations in temperature during
3729-550: The popularization of scientific matters. His only attempts at popularization were his works on the date of Easter (1800/1802) and the essay Erdmagnetismus und Magnetometer of 1836. Gauss published his papers and books exclusively in Latin or German . He wrote Latin in a classical style but used some customary modifications set by contemporary mathematicians. In his inaugural lecture at Göttingen University from 1808, Gauss claimed reliable observations and results attained only by
3842-432: The "Constituency Association of Lower Saxony" in 1920. In a lecture on 14 September 2007, Dietmar von Reeken described the emergence of a "Lower Saxony consciousness" in the 19th century, the geographical basis of which was used to invent a territorial construct: the resulting local heritage societies ( Heimatvereine ) and their associated magazines routinely used the terms "Lower Saxony" or "Lower Saxon" in their names. At
3955-531: The 16 Länder of the Federal Republic of Germany . In rural areas, Northern Low Saxon and Saterland Frisian are still spoken, though by declining numbers of people. Lower Saxony borders on (from north and clockwise) the North Sea , the states of Schleswig-Holstein , Hamburg , Mecklenburg-Vorpommern , Brandenburg , Saxony-Anhalt , Thuringia , Hesse and North Rhine-Westphalia , and
4068-469: The 1930s, a real Lower Saxony did not yet exist, but there were a plethora of institutions that would have called themselves "Lower Saxon". The motives and arguments in the disputes between "Lower Saxony" and "Westphalia" were very similar on both sides: economic interests, political aims, cultural interests and historical aspects. After the Second World War most of Northwest Germany lay within
4181-441: The Duke was killed in the battle of Jena in 1806. The duchy was abolished in the following year, and Gauss's financial support stopped. When Gauss was calculating asteroid orbits in the first years of the century, he established contact with the astronomical community of Bremen and Lilienthal , especially Wilhelm Olbers , Karl Ludwig Harding , and Friedrich Wilhelm Bessel , as part of the informal group of astronomers known as
4294-494: The French language. Gauss was "in front of the new development" with documented research since 1799, his wealth of new ideas, and his rigour of demonstration. Whereas previous mathematicians like Leonhard Euler let the readers take part in their reasoning for new ideas, including certain erroneous deviations from the correct path, Gauss however introduced a new style of direct and complete explanation that did not attempt to show
4407-597: The Harz. Most of the significant hills and mountains are found in the southeastern part of the state. The lowest point in the state, at about 2.5 metres or 8 feet 2 inches below sea level, is a depression near Freepsum in East Frisia. The state's economy, population, and infrastructure are centred on the cities and towns of Hanover, Stadthagen, Celle, Braunschweig, Wolfsburg , Hildesheim, and Salzgitter. Together with Göttingen in southern Lower Saxony, they form
4520-625: The Middle Ages, the town of Lüneburg was wealthy due to salt-mining and the salt trade. To the north the Elbe valley separates Lower Saxony from Hamburg, Schleswig-Holstein, Mecklenburg-Vorpommern , and Brandenburg. The left banks of the Elbe downstream Hamburg are known as the Altes Land (Old Country). Due to its gentle local climate and fertile soil, it is the state's largest area of fruit farming, its chief produce being apples . Most of
4633-643: The North German Plain, while the south is in the Lower Saxon Hills , including the Weser Uplands , Leine Uplands , Schaumburg Land , Brunswick Land , Untereichsfeld , Elm , and Lappwald . In the northeast of Lower Saxony is the Lüneburg Heath. The heath is dominated by the poor, sandy soils of the geest , whilst in the central-east and southeast in the loess börde zone , productive soils with high natural fertility occur. Under these conditions—with loam and sand -containing soils—the land
List of things named after Carl Friedrich Gauss - Misplaced Pages Continue
4746-640: The Principality of Schaumburg-Lippe) around the towns of Rinteln and Hessisch Oldendorf did indeed belong to the Prussian province of Hesse-Nassau until 1932, a province that also included large parts of the present state of Hesse, including the cities of Kassel , Wiesbaden and Frankfurt am Main ; but in 1932 the County of Schaumburg became part of the Prussian Province of Hanover. When
4859-637: The Prussian Province of Hanover under the Greater Hamburg Act . The effect of this Nazi-era change was that in 1946, after the Third Reich had collapsed and when state of Lower Saxony was founded, only four states needed to be merged. With the exception of Bremen and the areas that were ceded to the Soviet Occupation Zone in 1945, all those areas allocated to the new state of Lower Saxony in 1946, had already been merged into
4972-614: The River Hunte a "de-Westphalianising process" began in 1815. After the Congress of Vienna the territories of the later administrative regions ( Regierungsbezirke ) of Osnabrück and Aurich transferred to the Kingdom of Hanover. The Grand Duchy of Oldenburg and the Principality of Schaumburg-Lippe retained state autonomy. Nevertheless, the entire Weser-Ems region (including the city of Bremen ) were grouped in 1920 into
5085-549: The Saxon peoples left their homeland in Holstein about the 3rd century and pushed southwards over the Elbe , where they expanded into the sparsely populated regions in the rest of the lowlands, in present-day Northwest Germany and the northeastern part of what is now the Netherlands . From about the 7th century the Saxons had occupied a settlement area that roughly corresponds to the present state of Lower Saxony, of Westphalia and
5198-535: The Weser-Ems region was placed under the rule of Brunswick-Lüneburg. The word Niedersachsen was first used before 1300 in a Dutch rhyming chronicle ( Reimchronik ). From the 14th century it referred to the Duchy of Saxe-Lauenburg (as opposed to Saxe-Wittenberg ). On the creation of the imperial circles in 1500, a Lower Saxon Circle was distinguished from a Lower Rhenish–Westphalian Circle . The latter included
5311-475: The act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. The posthumous papers, his scientific diary , and short glosses in his own textbooks show that he worked to a great extent in an empirical way. He was a lifelong busy and enthusiastic calculator, who made his calculations with extraordinary rapidity, mostly without precise controlling, but checked
5424-591: The act of learning, not possession of knowledge, provided the greatest enjoyment. Gauss confessed to disliking teaching, but some of his students became influential mathematicians, such as Richard Dedekind and Bernhard Riemann . Gauss was born on 30 April 1777 in Brunswick in the Duchy of Brunswick-Wolfenbüttel (now in the German state of Lower Saxony ). His family was of relatively low social status. His father Gebhard Dietrich Gauss (1744–1808) worked variously as
5537-680: The area of Helmstedt. The highest levels of precipitation are experienced in the Harz because the Lower Saxon part forms the windward side of this mountain range against which orographic rain falls. The average annual temperature is 8 °C (46 °F); 7.5 °C (45.5 °F) in the Altes Land and 8.5 °C (47.3 °F) in the district of Cloppenburg . Lower Saxony is divided into 37 districts ( Landkreise or simply Kreise ): Furthermore, there are eight urban districts and two cities with special status: Between 1946 and 2004,
5650-711: The areas surrounding the Hanseatic cities of Bremen and Hamburg are much more oriented towards those centres. Sometimes, overlaps and transition areas happen between the various regions of Lower Saxony. Several of the regions listed here are part of other, larger regions, that are also included in the list. Just under 20% of the land area of Lower Saxony is designated as nature parks, i.e.: Dümmer , Elbhöhen-Wendland , Elm-Lappwald , Harz , Lüneburger Heide , Münden , Terra.vita , Solling-Vogler , Lake Steinhude , Südheide , Weser Uplands , Wildeshausen Geest , Bourtanger Moor-Bargerveen . Lower Saxony falls climatically into
5763-637: The best-paid professors of the university. When Gauss was asked for help by his colleague and friend Friedrich Wilhelm Bessel in 1810, who was in trouble at Königsberg University because of his lack of an academic title, Gauss provided a doctorate honoris causa for Bessel from the Philosophy Faculty of Göttingen in March 1811. Gauss gave another recommendation for an honorary degree for Sophie Germain but only shortly before her death, so she never received it. He also gave successful support to
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#17327663083965876-517: The birth of Louis, who himself died a few months later. Gauss chose the first names of his children in honour of Giuseppe Piazzi , Wilhelm Olbers, and Karl Ludwig Harding, the discoverers of the first asteroids. On 4 August 1810, Gauss married Wilhelmine (Minna) Waldeck, a friend of his first wife, with whom he had three more children: Eugen (later Eugene) (1811–1896), Wilhelm (later William) (1813–1879), and Therese (1816–1864). Minna Gauss died on 12 September 1831 after being seriously ill for more than
5989-701: The burdens of teaching, feeling that it was a waste of his time. On the other hand, he occasionally described some students as talented. Most of his lectures dealt with astronomy, geodesy, and applied mathematics , and only three lectures on subjects of pure mathematics. Some of Gauss's students went on to become renowned mathematicians, physicists, and astronomers: Moritz Cantor , Dedekind , Dirksen , Encke , Gould , Heine , Klinkerfues , Kupffer , Listing , Möbius , Nicolai , Riemann , Ritter , Schering , Scherk , Schumacher , von Staudt , Stern , Ursin ; as geoscientists Sartorius von Waltershausen , and Wappäus . Gauss did not write any textbook and disliked
6102-504: The city of Hamburg lie south of the Elbe. The state and city of Bremen is an enclave entirely surrounded by Lower Saxony. The Bremen/Oldenburg Metropolitan Region is a cooperative body for the enclave area. To the southeast, the state border runs through the Harz, low mountains that are part of the German Central Uplands . The northeast and west of the state, which form roughly three-quarters of its land area, belong to
6215-496: The contemporary school of Naturphilosophie . Gauss had an "aristocratic and through and through conservative nature", with little respect for people's intelligence and morals, following the motto " mundus vult decipi ". He disliked Napoleon and his system, and all kinds of violence and revolution caused horror to him. Thus he condemned the methods of the Revolutions of 1848 , though he agreed with some of their aims, such as
6328-517: The core of the Hannover–Braunschweig–Göttingen–Wolfsburg Metropolitan Region . Lower Saxony has clear regional divisions that manifest themselves geographically, as well as historically and culturally. In the regions that used to be independent, especially the heartlands of the former states of Brunswick , Hanover , Oldenburg and Schaumburg-Lippe , a marked local regional awareness exists. By contrast,
6441-598: The course of the year and a surplus water budget, the climate towards the southeast is increasingly affected by the Continent. This is clearly shown by greater temperature variations between the summer and winter halves of the year and in lower and more variable amounts of precipitation across the year. This sub-continental effect is most sharply seen in the Wendland, in the Weser Uplands (Hamelin to Göttingen) and in
6554-597: The division of the British occupation zone into three large states proved to be capable of gaining a majority. Because this division of their occupation zone into relatively large states also met the interests of the British, on 8 November 1946 Regulation No. 55 of the British military government was issued, by which the State of Lower Saxony with its capital Hanover were founded, backdated to 1 November 1946. The state
6667-645: The duchy. Johann Friedrich Pfaff assessed his doctoral thesis, and Gauss got the degree in absentia without further oral examination. The Duke then granted him the cost of living as a private scholar in Brunswick. Gauss subsequently refused calls from the Russian Academy of Sciences in St. Peterburg and Landshut University . Later, the Duke promised him the foundation of an observatory in Brunswick in 1804. Architect Peter Joseph Krahe made preliminary designs, but one of Napoleon's wars cancelled those plans:
6780-514: The elementary teachers noticed his intellectual abilities, they brought him to the attention of the Duke of Brunswick who sent him to the local Collegium Carolinum , which he attended from 1792 to 1795 with Eberhard August Wilhelm von Zimmermann as one of his teachers. Thereafter the Duke granted him the resources for studies of mathematics, sciences, and classical languages at the University of Göttingen until 1798. His professor in mathematics
6893-457: The end of the 1920s in the context of discussions about a reform of the Reich, and promoted by the expanding local heritage movement ( Heimatbewegung ), a 25-year conflict started between "Lower Saxony" and "Westphalia". The supporters of this dispute were administrative officials and politicians, but regionally focussed scientists of various disciplines were supposed to have fuelled the arguments. In
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#17327663083967006-412: The end of the fifth section, it appears that Gauss already knew the class number formula in 1801. In the last section, Gauss gives proof for the constructibility of a regular heptadecagon (17-sided polygon) with straightedge and compass by reducing this geometrical problem to an algebraic one. He shows that a regular polygon is constructible if the number of its sides is either a power of 2 or
7119-669: The first investigations, due to mislabelling, with that of the physician Conrad Heinrich Fuchs , who died in Göttingen a few months after Gauss. A further investigation showed no remarkable anomalies in the brains of both persons. Thus, all investigations on Gauss's brain until 1998, except the first ones of Rudolf and Hermann Wagner, actually refer to the brain of Fuchs. Gauss married Johanna Osthoff on 9 October 1805 in St. Catherine's church in Brunswick. They had two sons and one daughter: Joseph (1806–1873), Wilhelmina (1808–1840), and Louis (1809–1810). Johanna died on 11 October 1809, one month after
7232-440: The first to publish" differed from that of his scientific contemporaries. In contrast to his perfectionism in presenting mathematical ideas, he was criticized for a negligent way of quoting. He justified himself with a very special view of correct quoting: if he gave references, then only in a quite complete way, with respect to the previous authors of importance, which no one should ignore; but quoting in this way needed knowledge of
7345-466: The following territories that, in whole or in part, belong today to the state of Lower Saxony: the Bishopric of Osnabrück , the Bishopric of Münster , the County of Bentheim , the County of Hoya , the Principality of East Frisia , the Principality of Verden , the County of Diepholz , the County of Oldenburg , the County of Schaumburg and the County of Spiegelberg . At the same time a distinction
7458-459: The formation of a state of Lower Saxony, that was to include the largest possible region in the middle of the British Zone. In addition to the regions that actually became Lower Saxony subsequently, Kopf asked, in a memorandum dated April 1946, for the inclusion of the former Prussian district of Minden-Ravensberg (i.e. the Westphalian city of Bielefeld as well as the Westphalian districts of Minden , Lübbecke , Bielefeld , Herford and Halle ),
7571-404: The former Hanoverian president ( Regierungspräsident ) as their first minister-president. Kopf led a five-party coalition, whose basic task was to rebuild a state afflicted by the war's rigours. Kopf's cabinet had to organise an improvement of food supplies and the reconstruction of the cities and towns destroyed by Allied air raids during the war years. Hinrich Wilhelm Kopf remained – interrupted by
7684-560: The foundation of the independent state of "Weser-Ems", that would be formed from the state of Oldenburg, the Hanseatic City of Bremen and the administrative regions of Aurich and Osnabrück. Several representatives of the state of Oldenburg even demanded the inclusion of the Hanoverian districts of Diepholz , Syke , Osterholz-Scharmbeck and Wesermünde in the proposed state of "Weser-Ems". Likewise an enlarged State of Brunswick
7797-529: The four administrative regions or governorates ( Regierungsbezirke ), into which Lower Saxony had been hitherto divided, were dissolved. These were the governorates of Braunschweig, Hanover, Lüneburg and Weser-Ems. The largest towns in Lower Saxony as of 31 December 2017: The name of Saxony derives from that of the Germanic confederation of tribes called the Saxons . Before the late medieval period, there
7910-474: The health of his second wife Minna over 13 years; both his daughters later suffered from the same disease. Gauss himself gave only slight hints of his distress: in a letter to Bessel dated December 1831 he described himself as "the victim of the worst domestic sufferings". By reason of his wife's illness, both younger sons were educated for some years in Celle , far from Göttingen. The military career of his elder son Joseph ended after more than two decades with
8023-460: The history of science and more time than he wished to spend. Soon after Gauss's death, his friend Sartorius published the first biography (1856), written in a rather enthusiastic style. Sartorius saw him as a serene and forward-striving man with childlike modesty, but also of "iron character" with an unshakeable strength of mind. Apart from his closer circle, others regarded him as reserved and unapproachable "like an Olympian sitting enthroned on
8136-467: The idea of a unified Germany. As far as the political system is concerned, he had a low estimation of the constitutional system; he criticized parliamentarians of his time for a lack of knowledge and logical errors. Some Gauss biographers have speculated on his religious beliefs. He sometimes said "God arithmetizes" and "I succeeded – not on account of my hard efforts, but by the grace of the Lord." Gauss
8249-545: The main transport artery to West Berlin and, from 1945 to 1990 was the busiest European border crossing point. Of economic significance for the state was the Volkswagen concern, that restarted the production of civilian vehicles in 1945, initially under British management, and in 1949 transferred into the ownership of the newly founded country of West Germany and state of Lower Saxony. Overall, Lower Saxony, with its large tracts of rural countryside and few urban centres,
8362-598: The mathematician Gotthold Eisenstein in Berlin. Gauss was loyal to the House of Hanover . After King William IV died in 1837, the new Hanoverian King Ernest Augustus annulled the 1833 constitution. Seven professors, later known as the " Göttingen Seven ", protested against this, among them his friend and collaborator Wilhelm Weber and Gauss's son-in-law Heinrich Ewald. All of them were dismissed, and three of them were expelled, but Ewald and Weber could stay in Göttingen. Gauss
8475-649: The medieval, Welf estates of the Duchy of Brunswick-Lüneburg . All the Welf princes called themselves dukes "of Brunswick and Lüneburg" despite often ruling parts of a duchy that was forever being divided and reunited as various Welf lines multiplied or died out. Two major principalities survived east of the Weser after the Napoleonic Wars: the Kingdom of Hanover and the Duchy of Brunswick (after 1866 Hanover became
8588-439: The new Lower Saxon constitution entered force, replacing the "Provisional Lower Saxon Constitution" of 1951. It enables referendums and plebiscites and establishes environmental protection as a fundamental state principle. The former Hanoverian Amt Neuhaus with its parishes of Dellien, Haar, Kaarßen, Neuhaus (Elbe), Stapel, Sückau, Sumte and Tripkau as well as the villages of Neu Bleckede, Neu Wendischthun and Stiepelse in
8701-696: The northern and eastern border of North Rhine-Westphalia has largely been identical with that of the Prussian Province of Westphalia . Only the Free State of Lippe was not incorporated into North Rhine-Westphalia until January 1947. With that the majority of the regions left of the Upper Weser became North Rhine-Westphalian. In the end, at the meeting of the Zone Advisory Board on 20 September 1946, Kopf's proposal with regard to
8814-590: The observatory was completed, Gauss took his living accommodation in the western wing of the new observatory and Harding in the eastern one. They had once been on friendly terms, but over time they became alienated, possibly – as some biographers presume – because Gauss had wished the equal-ranked Harding to be no more than his assistant or observer. Gauss used the new meridian circles nearly exclusively, and kept them away from Harding, except for some very seldom joint observations. Brendel subdivides Gauss's astronomic activity chronologically into seven periods, of which
8927-411: The original languages. His favorite English author was Walter Scott , his favorite German Jean Paul . Gauss liked singing and went to concerts. He was a busy newspaper reader; in his last years, he used to visit an academic press salon of the university every noon. Gauss did not care much for philosophy, and mocked the "splitting hairs of the so-called metaphysicians", by which he meant proponents of
9040-508: The parish of Teldau and the historic Hanoverian region in the forest district of Bohldamm in the parish of Garlitz transferred with effect from 30 June 1993 from Mecklenburg-Vorpommern to Lower Saxony ( Lüneburg district ). From these parishes the new municipality of Amt Neuhaus was created on 1 October 1993. In 1998 Gerhard Glogowski succeeded Gerhard Schröder who became Federal Chancellor. Because he had been linked with various scandals in his home city of Brunswick, he resigned in 1999 and
9153-475: The problem by accepting offers from Berlin in 1810 and 1825 to become a full member of the Prussian Academy without burdening lecturing duties, as well as from Leipzig University in 1810 and from Vienna University in 1842, perhaps because of the family's difficult situation. Gauss's salary was raised from 1000 Reichsthaler in 1810 to 2400 Reichsthaler in 1824, and in his later years he was one of
9266-425: The product of a power of 2 and any number of distinct Fermat primes . In the same section, he gives a result on the number of solutions of certain cubic polynomials with coefficients in finite fields , which amounts to counting integral points on an elliptic curve . An unfinished eighth chapter was found among left papers only after his death, consisting of work done during 1797–1799. One of Gauss's first results
9379-592: The railroad system in the US for some months. Eugen left Göttingen in September 1830 and emigrated to the United States, where he joined the army for five years. He then worked for the American Fur Company in the Midwest. Later, he moved to Missouri and became a successful businessman. Wilhelm married a niece of the astronomer Bessel ; he then moved to Missouri, started as a farmer and became wealthy in
9492-437: The rank of a poorly paid first lieutenant , although he had acquired a considerable knowledge of geodesy. He needed financial support from his father even after he was married. The second son Eugen shared a good measure of his father's talent in computation and languages, but had a vivacious and sometimes rebellious character. He wanted to study philology, whereas Gauss wanted him to become a lawyer. Having run up debts and caused
9605-435: The reader the author's train of thought. Gauss was the first to restore that rigor of demonstration which we admire in the ancients and which had been forced unduly into the background by the exclusive interest of the preceding period in new developments. But for himself, he propagated a quite different ideal, given in a letter to Farkas Bolyai as follows: It is not knowledge, but the act of learning, not possession but
9718-411: The results by masterly estimation. Nevertheless, his calculations were not always free from mistakes. He coped with the enormous workload by using skillful tools. Gauss used a lot of mathematical tables , examined their exactness, and constructed new tables on various matters for personal use. He developed new tools for effective calculation, for example the Gaussian elimination . It has been taken as
9831-558: The shoe business in St. Louis in later years. Eugene and William have numerous descendants in America, but the Gauss descendants left in Germany all derive from Joseph, as the daughters had no children. In the first two decades of the 19th century, Gauss was the only important mathematician in Germany, comparable to the leading French ones; his Disquisitiones Arithmeticae was the first mathematical book from Germany to be translated into
9944-495: The state's districts and independent towns were grouped into eight regions, with a different status for two regions ( Verwaltungsbezirke ), comprising the formerly free states of Brunswick and Oldenburg. In 1978 these regions were merged into four governorates ( Regierungsbezirke ). In 2005 the Bezirksregierungen (regional governments) were again split into separate bodies. 1946–1978: 1978–2004: On 1 January 2005
10057-469: The state's territory was part of the historic Kingdom of Hanover , and the state of Lower Saxony has adopted the coat of arms and other symbols of the former kingdom. It was created by the merger of the State of Hanover with three smaller states on 1 November 1946. Lower Saxony has a natural boundary in the north in the North Sea and the lower and middle reaches of the River Elbe , although parts of
10170-494: The successor to Hinrich Wilhelm Kopf. He was replaced in 1970 by Alfred Kubel . The arguments about the Gorleben Nuclear Waste Repository , that began during the time in office of minister president Ernst Albrecht (1976–1990), have played an important role in state and federal politics since the end of the 1970s. In 1990 Gerhard Schröder entered the office of minister-president. On 1 June 1993,
10283-567: The sum. Gauss took on the directorate of the 60-year-old observatory, founded in 1748 by Prince-elector George II and built on a converted fortification tower, with usable, but partly out-of-date instruments. The construction of a new observatory had been approved by Prince-elector George III in principle since 1802, and the Westphalian government continued the planning, but Gauss could not move to his new place of work until September 1816. He got new up-to-date instruments, including two meridian circles from Repsold and Reichenbach , and
10396-577: The summer of 1821. After a short time at university, in 1824 Joseph joined the Hanoverian army and assisted in surveying again in 1829. In the 1830s he was responsible for the enlargement of the survey network to the western parts of the kingdom. With his geodetical qualifications, he left the service and engaged in the construction of the railway network as director of the Royal Hanoverian State Railways . In 1836 he studied
10509-421: The summit of science". His close contemporaries agreed that Gauss was a man of difficult character. He often refused to accept compliments. His visitors were occasionally irritated by his grumpy behaviour, but a short time later his mood could change, and he would become a charming, open-minded host. Gauss abominated polemic natures; together with his colleague Hausmann he opposed to a call for Justus Liebig on
10622-485: The time in office of Heinrich Hellwege (1955–1959) – as the head of government in Lower Saxony until 1961. The greatest problem facing the first state government in the immediate post-war years was the challenge of integrating hundreds of thousands of refugees from Germany's former territories in the east (such as Silesia and East Prussia ), which had been annexed by Poland and the Soviet Union . Lower Saxony
10735-558: The varieties of language in the Low German dialect group. The establishment of permanent boundaries between what later became Lower Saxony and Westphalia began in the 12th century. In 1260, in a treaty between the Archbishopric of Cologne and the Duchy of Brunswick-Lüneburg the lands claimed by the two territories were separated from each other. The border ran along the Weser to a point north of Nienburg. The northern part of
10848-421: The years since 1820 are taken as a "period of lower astronomical activity". The new, well-equipped observatory did not work as effectively as other ones; Gauss's astronomical research had the character of a one-man enterprise without a long-time observation program, and the university established a place for an assistant only after Harding died in 1834. Nevertheless, Gauss twice refused the opportunity to solve
10961-630: Was Abraham Gotthelf Kästner , whom Gauss called "the leading mathematician among poets, and the leading poet among mathematicians" because of his epigrams . Astronomy was taught by Karl Felix Seyffer , with whom Gauss stayed in correspondence after graduation; Olbers and Gauss mocked him in their correspondence. On the other hand, he thought highly of Georg Christoph Lichtenberg , his teacher of physics, and of Christian Gottlob Heyne , whose lectures in classics Gauss attended with pleasure. Fellow students of this time were Johann Friedrich Benzenberg , Farkas Bolyai , and Heinrich Wilhelm Brandes . He
11074-585: Was a German mathematician , astronomer , geodesist , and physicist who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. He is widely considered one of the greatest mathematicians ever. While studying at the University of Göttingen , he propounded several mathematical theorems . Gauss completed his masterpieces Disquisitiones Arithmeticae and Theoria motus corporum coelestium as
11187-792: Was a member of the Lutheran church , like most of the population in northern Germany. It seems that he did not believe all dogmas or understand the Holy Bible quite literally. Sartorius mentioned Gauss's religious tolerance , and estimated his "insatiable thirst for truth" and his sense of justice as motivated by religious convictions. In his doctoral thesis from 1799, 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 . Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains
11300-551: Was a single Duchy of Saxony . The term "Lower Saxony" was used after the dissolution of the stem duchy in the late 13th century to distinguish the parts of the former duchy ruled by the House of Welf from the Electorate of Saxony on one hand, and from the Duchy of Westphalia on the other. The name and coat of arms of the present state go back to the Germanic tribe of Saxons . During the Migration Period some of
11413-478: Was at the western end of the direct escape route from East Prussia and had the longest border with the Soviet Zone. On 3 October 1950 Lower Saxony took over the sponsorship of the very large number of refugees from Silesia . In 1950 there was still a shortage of 730,000 homes according to official figures. During the period when Germany was divided, the Lower Saxon border crossing at Helmstedt found itself on
11526-701: Was deeply affected by this quarrel but saw no possibility to help them. Gauss took part in academic administration: three times he was elected as dean of the Faculty of Philosophy. Being entrusted with the widow's pension fund of the university, he dealt with actuarial science and wrote a report on the strategy for stabilizing the benefits. He was appointed director of the Royal Academy of Sciences in Göttingen for nine years. Gauss remained mentally active into his old age, even while suffering from gout and general unhappiness. On 23 February 1855, he died of
11639-704: Was formed by a merger of the Free States of Brunswick , of Oldenburg and of Schaumburg-Lippe with the previously formed State of Hanover. But there were exceptions: The demands of Dutch politicians that the Netherlands should be given the German regions east of the Dutch-German border as war reparations , were roundly rejected at the London Conference of 26 March 1949. In fact only about 1.3 km (0.50 sq mi) of west Lower Saxony
11752-517: Was in keeping with the motto of his personal seal Pauca sed Matura ("Few, but Ripe"). Many colleagues encouraged him to publicize new ideas and sometimes rebuked him if he hesitated too long, in their opinion. Gauss defended himself, claiming that the initial discovery of ideas was easy, but preparing a presentable elaboration was a demanding matter for him, for either lack of time or "serenity of mind". Nevertheless, he published many short communications of urgent content in various journals, but left
11865-484: Was likely a self-taught student in mathematics since he independently rediscovered several theorems. He solved a geometrical problem that had occupied mathematicians since the Ancient Greeks , when he determined in 1796 which regular polygons can be constructed by compass and straightedge . This discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss's mathematical diary,
11978-485: Was made with the eastern part of the old Saxon lands from the central German principalities later called Upper Saxony for dynastic reasons. The close historical links between the domains of the Lower Saxon Circle now in modern Lower Saxony survived for centuries especially from a dynastic point of view. The majority of historic territories whose land now lies within Lower Saxony were sub-principalities of
12091-411: Was one of the industrially weaker regions of the federal republic for a long time. In 1960, 20% of the working population worked on the land. In the rest of the federal territory the figure was just 14%. Even in economically prosperous times the jobless totals in Lower Saxony are constantly higher than the federal average. In 1961 Georg Diederichs took office as the minister president of Lower Saxony as
12204-485: Was proposed in the southeast to include the Regierungsbezirk of Hildesheim and the district of Gifhorn . Had this plan come to fruition, the territory of the present Lower Saxony would have consisted of three states of roughly equal size. The district council of Vechta protested on 12 June 1946 against being incorporated into the metropolitan area of Hanover ( Großraum Hannover ). If the State of Oldenburg
12317-512: Was removed, preserved, and studied by Rudolf Wagner , who found its mass to be slightly above average, at 1,492 grams (3.29 lb). Wagner's son Hermann , a geographer, estimated the cerebral area to be 219,588 square millimetres (340.362 sq in) in his doctoral thesis. In 2013, a neurobiologist at the Max Planck Institute for Biophysical Chemistry in Göttingen discovered that Gauss's brain had been mixed up soon after
12430-457: Was replaced by Sigmar Gabriel . From 2003 to his election as Federal President in 2010 Christian Wulff was minister president in Lower Saxony. The Osnabrücker headed a CDU-led coalition with the FDP as does his successor, David McAllister . After the elections on 20 January 2013 McAllister was deselected . At the end of 2014, there were almost 571,000 non-German citizens in Lower Saxony. At
12543-432: Was the empirically found conjecture of 1792 – the later called prime number theorem – giving an estimation of the number of prime numbers by using the integral logarithm . Lower Saxony Lower Saxony is a German state ( Land ) in northwestern Germany . It is the second-largest state by land area, with 47,614 km (18,384 sq mi), and fourth-largest in population (8 million in 2021) among
12656-475: Was to be dissolved, Vechta District would much rather be included in the Westphalian region. Particularly in the districts where there was a political Catholicism the notion was widespread, that Oldenburg Münsterland and the Regierungsbezirk of Osnabrück should be part of a newly formed State of Westphalia. Since the foundation of the states of North Rhine-Westphalia and Hanover on 23 August 1946
12769-561: Was transferred to the Netherlands, in 1949. → see main article Dutch annexation of German territory after World War II The first Lower Saxon parliament or Landtag met on 9 December 1946. It was not elected; rather it was established by the British Occupation Administration (a so-called "appointed parliament"). That same day the parliament elected the Social Democrat , Hinrich Wilhelm Kopf ,
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