Carl Friedrich Gauss

Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Carolus Fridericus Gauss latinisiert; * 30. April 1777 in Braunschweig; † 23. February 1855 in Goettingen) was a German mathematician, astronomer, a Geodät and a physicist alsoa broadly varied field at interests. He is regarded as one of the most important mathematicians and called prince of mathematics or princeps mathematicorum.

Table of contents

lives

Gauss' birth house, William route 30, in the Second World War completely destroys

Carl Friedrich was the only child of the married people Gerhard Dietrich and Dorothea Gauss, geb. Benze. The nut/mother an almost analphabetische,however to a high degree intelligent daughter of a poor stone-cutter, worked first as a housemaid, before she became the second Mrs. Gerhard Dietrich Gauss'. This had many occupations, it was and. A. Gardner, butcher, bricklayer, buyer assistant and Treasurer of a small insurance company. Anecdotes mean that already three-year Carl Friedrich corrected his father during the pay slip. Later he said of itself, he a counting before speaking learned. Its life long it kept the gift,to accomplish the most complicated arithmetic problems in the head.

With seven years Gauss came into the elementary school. There its teacher Büttner placed the task to it to sum up the numbers from 1 to 100. It had solved it after short time, by itFormed 50 pairs of the sum 101 (1 + 100, 2 + 99,…, 50 + 51) and 5050 as result received. The formula developed from it is called occasionally also „the small Gauss “.

This event left Gauss' teacherits unusual mathematical gift recognize, whereupon it organized a special computing book from Hamburg for it and for it provided, supported from its assistant Martin Bartels that Gauss could visit the High School Catharineum. When the miracle child was years old Gauss fourteen, becameit duke Carl William Ferdinand of Braunschweig admits made. This supported Gauss financially and provided for his living costs. So Gauss from 1792 to 1795 at the Collegium Carolinum could, to settle between higher school and university, which the predecessor of the today's technical ones University in Braunschweig is, study. There it was a professor Eberhard August William of Carpenter, who recognized its mathematical talent, promoted him and became him a paternal friend.

In October 1795 it changed to the University of Goettingen. Therehe heard with professor Heyne lectures on classical philology, which interested him at that time exactly the same as mathematics. That one was rather badly represented by Abraham Gotthelf Kästner, which was a poet at the same time. The only one, with which it itself in thatMathematics to measure could, was the twelve years before the deceased Leonhard Euler, whose discoveries it found according to own statement everything, independently of it a second time. With George Christoph Lichtenberg he very probably heard in the summer semester 1796 experimental physics andin the following winter semester astronomy. In Goettingen it closed friendship with Wolfgang Bolyai.

Gauß'sches 17-Eck
Gauss' 17-Eck

at the age of nineteen years succeeded it to Gauss as first, the regular seventeen-hits a corner only with circle and ruler to design. A sensational discovery - sincethe antique one gave it in this area hardly still progress. This was also a reason to decide against languages and philosophy and for the study of mathematics which it 1799 with its doctor work to the Academia Julia (university in Helmstedt) locked. Contrary to Goettingen mathematics was by Johann Friedrich Pfaff well represented on the fact and not least put here Gauss' sponsor, the duke of Braunschweig, Wert that it at one „do not attain a doctorate to foreign “university.

After its graduationGauss in Braunschweig of the small content, which the duke paid him, lived and worked on its work Disquisitiones arithmeticae.

Gauss rejected a call to the Peter citizens Academy of Sciences: indeed from gratitude against his sponsor, the dukeby Braunschweig, and probably in hope that this would build an observatory in Braunschweig for him. After the sudden death of the duke after the battle with Jena and Auerstedt Gauss became in November 1807 professor in Goettingen and director thatthere observatory. There it had to hold training meetings, against which it developed however a dislike. Nevertheless several of its students became influential mathematicians, under it smelling pool of broadcasting corporations Dedekind and Bernhard Riemann.

In November 1803 he got engaged with Johanna Elizabeth Rosina easthopes himself(* 1780, † 1809), the daughter of a Weissgerbers from Braunschweig, which it to 9. October 1805 married. To 21. August 1806 was born still in Braunschweig the first child, Joseph, designated after the discoverer that of cerium, Giuseppe Piazzi. InGoettingen followed 1808 the daughter Wilhelmine, to 12. August 1840 died, and at the 11. October 1809 Louis, with its birth his Mrs. Johanna died and it at the 1. March 1810 followed. One year after, to 4. August 1810took place the marriage with Friederica „Minna “Wilhelmine, geb. Forest-hit a corner (* 1788, † 1831). The marriage was very lucky, and the two had three children: Eugen (* 29. July 1811, † 1896), which the rights studied and later to America emigrated, over thereto live as a buyer; William (* October 1813, † 1883), who followed 1837 Eugen and likewise emigrated to America, in order to operate agriculture there; and Therese (* June 1816, † 1864). In the summer 1818 Minna began to be ailing, which itself later thanTuberkulose to put out should and to 12. September 1831 deceased it. From then on daughter Therese led the household.

Gauss' father died to 14. April 1808 in Braunschweig. To 18. April 1839 deceased the nut/mother at the age of 95 years inGoettingen. Gauss died to 23. February 1855 in the morning at 1 o'clock 5 minutes in Goettingen. Today it lies there on the Albanifriedhof (Cheltenham park) buried. Many of its discoveries it communicated or noted in letters to friends it in itsDiaries, which only 1898 were discovered.

When at the age its work strength decreased, it in addition, employed increasingly with literature, led themselves still lists across the monthly incomes of the Hannover railway and the life expectancy of famous men (counted in days). Thus wroteit to 7. December 1853 at Alexander of Humboldt: „It is the day after tomorrow the day, where you, my dear friend, change into an area, in which still none the Koryphäen of the exacten sciences penetrated, the day, where it the sameOlder reach, in which Newton his by 30766 days measured terrestrial career closed. “

Gauss was deeply religious and conservative. Besides it was very monarchistic adjusted and could not not understand the revolution about 1848.

distrusted

to achievements Gaussalready with twelve years of the proof in elementary geometry and it suspected with sixteen years that there must be non-Euclidean geometry beside Euclidean still another another.

With eighteen years he discovered some characteristics of the prime number distribution and found the methodthe smallest squares. After it the most probable result for a new measurement from a sufficient large number of previous measurements can be determined. On this basis it examined late theories for the computation of areas under curves, it to Gauss bath tub curve to arrive left. The associated function is well-known as the standard normal distribution and with many tasks for probability calculation is used.

As 19jähriger it led 1796, with views across the length of curve on a Lemniskate as a function of the distance of the point of curveto the origin, with the lemniskatischen sine functions those historically first, today elliptical functions so mentioned . It however never published its notes over it.

Gauss seized early the use of complex numbers, so also in his doctor work of 1799, the onestricter proof of the fundamental principle of algebra contained. This sentence means that each algebraic equation of nth degree possesses exactly n real or complex roots. The old proof of d'Alembert criticized Gauss as insufficient.

To 29. March 1796, thus with nineteen years,designed it the regular seventeen-hits a corner only with circle and ruler and supplied thereby the first considerable addition of Euclidean constructions for 2000 years. This was however only one subsidiary result with the work for its pay-theoretically much longer-range work Disquisitiones arithmeticae.A first announcement of this work was at the 1. June 1796 in the intelligence sheet of the general literature newspaper in Jena. The Disquisitiones became fundamental for the further development of the number theory, to which one of its main contributions was the proof of the square reciprocity law.This work is with difficulty readable like all its different, since Gauss enjoyed obviously to communicate only the results and to smear all ways there.

After the completion of the Disquisitiones Gauss turned to the astronomy. Cause for this was thoseDiscovery of the Planetoiden of cerium by Giuseppe Piazzi at the 1. January 1801, whose course one had again lost briefly after its discovery. The 24-jährige Gauss created it, the course of the Planetoiden with the help of its compensation calculations on basis of the method of the smallestTo compute squares in such a way that Heinrich Olbers it exactly one year later, at the 1. January 1802, to regain could. Gauss busy itself thereafter also still with the course of the Planetoiden Pallas, on its computation those Paris academy a prize money suspended, could the solution had however not find. Its experiences with the planet course movement flowed in its work Theoria motus corporum coelestium into sectionibus conicis Solem ambientium (theory of the movement of the heavenly bodies, which circle the sun in conic sections), the 1809appeared.

In order to be able to determine the Osterdatum for any year computationally, it developed a closed formula. For the first time this computation was published in the monthly Correspondenz published by baron von Zach for the transport of the ground connection and the astronomy, volume II,August 1800. It reprinted in the collected works, volume VI. In the article some more over the determination of Easter, publishes to 12. September 1807 in the Braunschweigi magazine, still proceeded Gauss from a Epaktensprung every 300 years.In the magazine for astronomy and related sciences 1816 became the article correction the essay: Computation of the Easter publishes, in which Gauss makes an addition of his Gauss Osterformel, which plan the Epaktensprung every 312.5 years.

In the area that Geodesy collected Gauss between 1797 and 1801 the first experiences, when it stood for the quartermaster general Lecoq during its land surveying of the duchy of Westphalia as an advisor to the side. For the second time he came 1816 thereby into contact, as him the king ofDenmark with the execution of a degree of latitude and a degree of longitude measurement in Danish area assigned. After locking negotiations Gauss led the land surveying of the Kingdom of Hanover then between 1818 and 1826 („Gauss land survey “). By the method of the smallest squares invented by itand the systematic solution of extensive linear sets of equations (Gauss Eliminationsverfahren) succeeded to it a substantial increase of the accuracy. Also for practical execution it was interested; it invented the Heliotrop lit up over sun mirrors as measuring instrument.

In these years busyit also with the theory of the surfaces and the illustrations and put important bases for the Differentialgeometrie. Independently of Bolyai and Lobaschweski he noticed that the Euclidean parallel axiom is not think necessary. Its it published thoughts on non-Euclidean geometryhowever not, probably from fear of the lack of understanding of the contemporaries. According to general relativity theory the area on astronomical scales is actually non-Euclidean; the considerations of Gauss turned out thus after nearly one hundred years as physically relevant. Perhaps developed onlyat that time the legend, Gauss has on occasion the Hannover land surveying empirically after a deviation of the Winkelsumme of particularly large triangles (as for instance the triangle, that of breaking into in the resin, the island mountain in the Thüringer forest and the high Hagen with Dransfeldformed) by the Euclidean value of 180° one searches; historically this is not occupied.

Together with William Eduard weber he worked starting from 1831 in the area of the magnetism. Gauss invented the magnetometer and connected in such a way to 1833 its observatory with thatphysical Institut. It exchanged over electromagnetically affected compass needles messages with weber; the first (electromagnetic) Telegrafenverbindung in the world. With him together it developed also the cgs system of units, the 1881 on an international congress in Paris to the basis thatelectrotechnical unit one determined.

Gauss worked in many areas, published its results however only if a theory were complete according to its opinion. This led to the fact that he referred colleagues occasionally to it, this or that result to have for a long time proven,it because of the incompleteness of the underlying theory or it to fast work which is missing necessary amusement only not to have presented. Critics accused to him that this expression of an exaggerated validity craze was. Characteristically it possessed a Petschaft, thatone of few fruits behangenen tree and the slogan Pauca sed matura (Weniges, but hoar frost) showed.

Fact is that he was an intensive diary writer and noted there also many of its results. After its death became over twenty thisVolumes found. So it could be occupied that he actually furnished a majority of his maintained achievements. It is accepted that not all of its diaries are received. The state and university library of Lower Saxony Goettingen digitized the collected works of Gauss andin Internet posed.

name givers

methods or ideas developed by Gauss, which carry his name, are:

methods and ideas, which are based partly on its work are:

to its honours are designated:

its honours the Braunschweigi

writings

  • 1799: Doctor work over the fundamental principle of algebra
  • 1801: Disquisitiones Arithmeticae
  • 1809: Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium (theory thatMovement of the heavenly bodies, which circle the sun in conic sections)
  • 1827: Disquisitiones of general about superficies curvas (general investigation on curved surfaces)
  • 1843/44: Investigations on thes subject of higher geodesy, part of 1
  • 1846/47: Investigations on thes subject of higher geodesy, part of 2
work on []

Thinking marks

fixed image in Braunschweig (at the Gauss mountain)

literature

  • Erich cutter: Mathematics seriously and cheerfully. Chapter. 14, brothers white publishing house, BerlinBeautiful mountain 1968

literature with purchases to Carl Friedrich Gauss

Web on the left of

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