NationMaster - Encyclopedia: Carl Friedrich Gauss

Johann Carl Friedrich Gauss (pronounced /ˈɡaʊs/, listen (help· info); in German usually Gauß, Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as "the prince of mathematicians" and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.^[1] Image File history File links Download high resolution version (576x738, 235 KB) Description: Ausschnitt aus einem GemÃ¤lde von C. F. Gauss Source: evtl. ... Christian Albrecht Jensen (June 26, 1792â€”July 13, 1870) was a Danish painter, born in Bredstedt, Nordfriesland. ... is the 120th day of the year (121st in leap years) in the Gregorian calendar. ... Year 1777 (MDCCLXXVII) was a common year starting on Wednesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Sunday of the 11-day slower Julian calendar). ... Coordinates: Time zone: CET/CEST (UTC+1/+2) Administration Country: Germany State: Lower Saxony District: Urban district City subdivisions: 20 Boroughs Lord Mayor: Gert Hoffmann (CDU) Governing parties: CDU / FDP Basic Statistics Area: 192. ... is the 54th day of the year in the Gregorian calendar. ... Year 1855 (MDCCCLV) was a common year starting on Monday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Saturday of the 12-day slower Julian calendar). ... GÃ¶ttingen marketplace with old city hall, GÃ¤nseliesel fountain and pedestrian zone GÃ¶ttingen ( ) is a city in Lower Saxony, Germany. ... Map of Germany showing Hanover Hanover (in German: Hannover [haˈnoːfɐ]), on the river Leine, is the capital of the state of Lower Saxony (Niedersachsen), Germany. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... The Georg-August University of GÃ¶ttingen (Georg-August-UniversitÃ¤t GÃ¶ttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... University of Helmstedt in the 17th century The University of Helmstedt, official Latin name: Academia Julia (Julius University), was a university in Helmstedt, Brunswick-LÃ¼neburg, Holy Roman Empire, that existed from 1576 until 1810. ... Johann Friedrich Pfaff (December 22, 1765- April 21, 1825) was a German mathematician. ... Friedrich Wilhelm Bessel (July 22, 1784 â€“ March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli). ... Christoph Gudermann (March 25, 1798 - September 25, 1852) was born in Vienenburg, Germany. ... Christian Ludwig Gerling (1788-1864) studied under Carl Friedrich Gauss, obtaining his doctorate in 1812 for a thesis entitled: Methodi proiectionis orthographicae usum ad calculos parallacticos facilitandos explicavit simulque eclipsin solarem die, at the University of Gottingen. ... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 â€“ February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Johann Franz Encke (September 23, 1791 – August 26, 1865) was a German astronomer, born in Hamburg. ... Johann Benedict Listing born July 25, 1808, died December 24, 1882 was a German mathematician, born in Frankfurt, Germany, and died in GÃ¶ttingen, Germany. ... Bernhard Riemann. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... GAUSSIAN is a computational chemistry software program, first written by John Pople. ... For other senses of this word, see magnetism (disambiguation). ... The Copley Medal is a scientific award for work in any field of science, the highest award granted by the Royal Society of London. ... Image File history File links De-carlfriedrichgauss. ... For other uses, see Latin (disambiguation). ... is the 120th day of the year (121st in leap years) in the Gregorian calendar. ... Year 1777 (MDCCLXXVII) was a common year starting on Wednesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Sunday of the 11-day slower Julian calendar). ... is the 54th day of the year in the Gregorian calendar. ... Year 1855 (MDCCCLV) was a common year starting on Monday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Saturday of the 12-day slower Julian calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... This article is about the profession. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... This article is about the field of statistics. ... Analysis has its beginnings in the rigorous formulation of calculus. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... An old geodetic pillar (1855) at Ostend, Belgium A Munich archive with lithography plates of maps of Bavaria Geodesy (pronounced [1]), also called geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three... Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. ... For other uses, see Astronomy (disambiguation). ... For the book by Sir Isaac Newton, see Opticks. ...

Gauss was a child prodigy, of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, at the age of 21 (1798), though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day. Wunderkind redirects here. ... An anecdote is a short tale narrating an interesting or amusing biographical incident. ... The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ... Magnum opus (sometimes Opus magnum, plural magna opera), from the Latin meaning great work,[1] refers to the best, most popular, or most renowned achievement of an author, artist, or composer, and most commonly one who has contributed a very large amount of material. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...

Early years

Gauss was born in Brunswick, in the Duchy of Brunswick-Lüneburg (now part of Lower Saxony, Germany), as the only son of poor working-class parents.^[2] There are several stories of his early genius, all of them open to doubt; according to one, his gifts became very apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances. Image File history File links Metadata Size of this preview: 800 Ã— 600 pixelsFull resolution (1024 Ã— 768 pixels, file size: 382 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 800 Ã— 600 pixelsFull resolution (1024 Ã— 768 pixels, file size: 382 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Coordinates: Time zone: CET/CEST (UTC+1/+2) Administration Country: Germany State: Lower Saxony District: Urban district City subdivisions: 20 Boroughs Lord Mayor: Gert Hoffmann (CDU) Governing parties: CDU / FDP Basic Statistics Area: 192. ... A duchy is a territory, fief, or domain ruled by a duke or duchess. ... Brunswick-LÃ¼neburg was an historical state within the Holy Roman Empire. ... With an area of 47,618 km and nearly eight million inhabitants, Lower Saxony (German Niedersachsen) lies in north-western Germany and is second in area and fourth in population among the countrys sixteen Bundesl nder (federal states). ...

Another famous story, and one that has evolved in the telling, has it that in primary school his teacher, J.G. Büttner, tried to occupy pupils by making them add up the integers from 1 to 100. The young Gauss produced the correct answer within seconds by a flash of mathematical insight, to the astonishment of his teacher and his assistant Martin Bartels. Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050 (see arithmetic series and summation).^[3] J. Rotman states in his book A first course in Abstract Algebra that he believes this incident never happened. A primary school in ÄŒeskÃ½ TÄ›Å¡Ãn, Czech Republic. ... The integers are commonly denoted by the above symbol. ... JCM Bartels Johann Christian Martin Bartels (b. ... // Definition In mathematics, an arithmetic series is the sum of the components of an arithmetic progression. ... Sum redirects here. ...

His father had wanted him to follow in his footsteps and become a mason. He was not supportive of Gauss's schooling in mathematics and science. Gauss was primarily supported by his mother in this effort and by the Duke of Brunswick,^[1] who awarded Gauss a fellowship to the Collegium Carolinum (now Technische Universität Braunschweig), which he attended from 1792 to 1795, from where he moved to the University of Göttingen from 1795 to 1798. While in university, Gauss independently rediscovered several important theorems;^{[citation needed]} his breakthrough occurred in 1796 when he was able to show that any regular polygon with a number of sides which is a Fermat prime (and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2) can be constructed by compass and straightedge. 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. Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone. The stonemason declined, stating that the difficult construction would essentially look like a circle. Look up mason in Wiktionary, the free dictionary. ... Charles William Ferdinand, Duke of Brunswick-LÃ¼neburg, (Karl Wilhelm Ferdinand, Herzog zu Braunschweig-LÃ¼neburg, FÃ¼rst von Braunschweig-WolfenbÃ¼ttel-Bevern) (October 9, 1735 - 1806) was a German military general born in WolfenbÃ¼ttel, Germany. ... The Technical University at Brunswick, Lower Saxony, is the oldest of Germanys technical universities. ... 1792 was a leap year starting on Sunday (see link for calendar). ... 1795 was a common year starting on Thursday (see link for calendar). ... The Georg-August University of GÃ¶ttingen (Georg-August-UniversitÃ¤t GÃ¶ttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... 1795 was a common year starting on Thursday (see link for calendar). ... Year 1798 (MDCCXCVIII) was a common year starting on Monday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 11-day slower Julian calendar). ... Look up polygon in Wiktionary, the free dictionary. ... In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer. ... â€œExponentâ€ redirects here. ... This article does not cite any references or sources. ... Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ... The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. ... Erchingers heptadecagon In geometry, a heptadecagon (or 17-gon) is a seventeen-sided polygon. ... Headstones in the Japanese Cemetry in Broome, Western Australia A cemetery in rural Spain A typical late 20th century headstone in the United States A headstone, tombstone or gravestone is a marker, normally carved from stone, placed over or next to the site of a burial. ...

1796 was a most productive year for both Gauss and number theory. The construction of the heptadecagon was discovered on March 30. He invented modular arithmetic, greatly simplifying manipulations in number theory. He became the first to prove the quadratic reciprocity law on April 8. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on May 31, gives a good understanding of how the prime numbers are distributed among the integers. Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on July 10 and then jotted down in his diary the famous words, "Heureka! num=

Δ + Δ + Δ

." On October 1 he published a result on the number of solutions of polynomials with coefficients in finite fields (this ultimately led to the Weil conjectures 150 years later). is the 89th day of the year (90th in leap years) in the Gregorian calendar. ... Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value â€” the modulus. ... In number theory, the law of quadratic reciprocity connects the solvability of two related quadratic equations in modular arithmetic. ... April 8 is the 98th day of the year (99th in leap years) in the Gregorian calendar. ... In number theory, the prime number theorem (PNT) describes the approximate, asymptotic distribution of the prime numbers. ... is the 151st day of the year (152nd in leap years) in the Gregorian calendar. ... In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are 1 and itself. ... A triangular number is a number that can be arranged in the shape of an equilateral triangle. ... is the 191st day of the year (192nd in leap years) in the Gregorian calendar. ... Eureka (Eureka!, or Heureka; Greek (later ); IPA: (modern Greek), (ancient Greek, both former and later forms), Anglicised as ) is a famous exclamation attributed to Archimedes. ... is the 274th day of the year (275th in leap years) in the Gregorian calendar. ... In mathematics, the Weil conjectures, which had become theorems by 1974, were some highly-influential proposals from the late 1940s by AndrÃ© Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. ...

Middle years

In his 1799 dissertation, A New Proof That Every Rational Integer Function of One Variable Can Be Resolved into Real Factors of the First or Second Degree, Gauss gave a proof of the fundamental theorem of algebra. This important theorem states that every polynomial over the complex numbers must have at least one root. Other mathematicians had tried to prove this before him, e.g. Jean le Rond d'Alembert. Gauss's dissertation contained a critique of d'Alembert's proof, but his own attempt would not be accepted owing to implicit use of the Jordan curve theorem. Gauss over his lifetime produced three more proofs, probably due in part to this rejection of his dissertation; his last proof in 1849 is generally considered rigorous by today's standard. His attempts clarified the concept of complex numbers considerably along the way. In mathematics, the fundamental theorem of algebra states that every complex polynomial in one variable and of degree â‰¥ has some complex root. ... In mathematics, a polynomial is an expression that is constructed from one variable or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ... In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that f(x) = 0. ... Jean le Rond dAlembert, pastel by Maurice Quentin de La Tour Jean le Rond dAlembert (November 16, 1717 â€“ October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ... In topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane divides the plane into an inside and an outside. It was proved by Oswald Veblen in 1905. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ...

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae, which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity. In that same year, Italian astronomer Giuseppe Piazzi discovered the dwarf planet Ceres, but could only watch it for a few days. Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ... Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value â€” the modulus. ... In number theory, the law of quadratic reciprocity connects the solvability of two related quadratic equations in modular arithmetic. ... Giuseppe Piazzi. ... Artists impression of Pluto (background) and Charon (foreground). ... 1 Ceres (IPA , Latin: ) is a dwarf planet in the asteroid belt. ...

Gauss predicted correctly the position at which it could be found again, and it was rediscovered by Franz Xaver von Zach on December 31, 1801 in Gotha, and one day later by Heinrich Olbers in Bremen. Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again." Though Gauss had up to this point been supported by the 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. 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. Image File history File links Download high resolution version (478x800, 34 KB) Summary Title page from the first edition of Carl Friedrich Gauss Disquisitiones Arithmeticae. ... Image File history File links Download high resolution version (478x800, 34 KB) Summary Title page from the first edition of Carl Friedrich Gauss Disquisitiones Arithmeticae. ... The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ... Franz Xaver, Baron Von Zach Baron Franz Xaver von Zach (Franz Xaver Freiherr von Zach) (June 4, 1754 - September 2, 1832) was an Austrian astronomer born at Bratislava. ... is the 365th day of the year (366th in leap years) in the Gregorian calendar. ... The Union Jack, flag of the newly formed United Kingdom of Great Britain and Ireland. ... Gotha is a town in Thuringia, in Germany. ... Heinrich Wilhelm Olbers. ... This article is about the city in Germany. ... GÃ¶ttingen marketplace with old city hall, GÃ¤nseliesel fountain and pedestrian zone GÃ¶ttingen ( ) is a city in Lower Saxony, Germany. ...

The discovery of Ceres by Piazzi on January 1, 1801 led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in 1809 under the name Theoria motus corporum coelestium in sectionibus conicis solem ambientum (theory of motion of the celestial bodies moving in conic sections around the sun). Piazzi had only been able to track Ceres for a couple of months, following it for three degrees across the night sky. Then it disappeared temporarily behind the glare of the Sun. 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. 1 Ceres (IPA , Latin: ) is a dwarf planet in the asteroid belt. ... is the 1st day of the year in the Gregorian calendar. ... The Union Jack, flag of the newly formed United Kingdom of Great Britain and Ireland. ...

Gauss, who was 23 at the time, heard about the problem and tackled it. 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. In the process, he so streamlined the cumbersome mathematics of 18th century orbital prediction that his work—- published a few years later as Theory of Celestial Movement—- remains a cornerstone of astronomical computation.^{[citation needed]} It introduced the Gaussian gravitational constant, and contained an influential treatment of the method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error. Gauss was able to prove the method in 1809 under the assumption of normally distributed errors (see Gauss-Markov theorem; see also Gaussian). The method had been described earlier by Adrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since 1795.^{[citation needed]} Carl Friedrich Gauss expressed the gravitational constant in units of the solar system rather than SI units. ... Least squares is a mathematical optimization technique that attempts to find a best fit to a set of data by attempting to minimize the sum of the squares of the differences (called residuals) between the fitted function and the data. ... Measurement is the determination of the size or magnitude of something. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... This article is not about Gauss-Markov processes. ... GAUSSIAN is a computational chemistry software program, first written by John Pople. ... Adrien-Marie Legendre (September 18, 1752 â€“ January 10, 1833) was a French mathematician. ...

Gauss was a prodigious mental calculator. Reputedly, when asked how he had been able to predict the trajectory of Ceres with such accuracy he replied, "I used logarithms." The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. "Look them up?" Gauss responded. "Who needs to look them up? I just calculate them in my head!" Image File history File links Size of this preview: 508 Ã— 600 pixelsFull resolution (655 Ã— 773 pixel, file size: 250 KB, MIME type: image/jpeg) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Size of this preview: 508 Ã— 600 pixelsFull resolution (655 Ã— 773 pixel, file size: 250 KB, MIME type: image/jpeg) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... This article does not cite any references or sources. ... In mathematics, if two variables of bn = x are known, the third can be found. ...

In 1818 Gauss, putting his calculation skills to practical use, carried out a geodesic survey of the state of Hanover, linking up with previous Danish surveys. To aid in the survey, Gauss invented the heliotrope, an instrument that uses a mirror to reflect sunlight over great distances, to measure positions. Surveyor at work with a leveling instrument. ... Capital Hanover Head of State King of Hanover Hanover (German: ) was a historical territory in todays Germany, at various times a principality, an electorate of the Holy Roman Empire, a kingdom and a province of Prussia and of Germany. ... The heliotrope is an instrument that reflects sunlight over great distances to mark the positions of participants in a land survey. ...

Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory. Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean. 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. Bolyai's son, János Bolyai, discovered non-Euclidean geometry in 1829; his work was published in 1832. After seeing it, Gauss wrote to Farkas Bolyai: "To praise it would amount to praising myself. For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." This unproved statement put a strain on his relationship with János Bolyai (who thought that Gauss was "stealing" his idea), but it is now generally taken at face value.^{[citation needed]} Letters by Gauss years before 1829 reveal him obscurely discussing the problem of parallel lines. Waldo Dunnington, in "Gauss, Titan of Science", successfully proves, however, that Gauss was in fact in full possession of non-Euclidian geometry long before it was published by János, but that he refused to publish any of it because of his fear of controversy. Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry describes hyperbolic, elliptic and absolute geometry, which are contrasted with Euclidean geometry. ... â€œEinsteinâ€ redirects here. ... Farkas Bolyai (February 9, 1775 - November 20, 1856, also known as Wolfgang Bolyai in Germany) was a Hungarian mathematician, mainly known for his work in Geometry. ... János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician. ...

The survey of Hanover later led to the development of the Gaussian distribution, also known as the normal distribution, for describing measurement errors. Moreover, it fuelled Gauss's interest in differential geometry, a field of mathematics dealing with curves and surfaces. In this field, he came up in 1828 with an important theorem, the theorema egregium (remarkable theorem in Latin) establishing an important property of the notion of curvature. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface; that is, curvature does not depend on how the surface might be embedded in (3-dimensional) space. Download high resolution version (1300x975, 135 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (1300x975, 135 KB) Wikipedia does not have an article with this exact name. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... This article is about the field of statistics. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... An open surface with X-, Y-, and Z-contours shown. ... The Theorema Egregium (Remarkable Theorem) is an important theorem of Carl Friedrich Gauss concerning the curvature of surfaces. ... For other uses, see Latin (disambiguation). ... In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. ... This article is about angles in geometry. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... In mathematics, an embedding (or imbedding) is one instance of some mathematical object contained within another instance, such as a group that is a subgroup. ...

Later years, death, and afterwards

In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber; it led to new knowledge in the field of magnetism (including finding a representation for the unit of magnetism in terms of mass, length and time) and the discovery of Kirchhoff's circuit laws in electricity. Gauss and Weber constructed the first electromagnetic telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic observatory to be built in the garden of the observatory and with Weber founded the magnetischer Verein ("magnetic club"), which supported measurements of earth's magnetic field in many regions of the world. He developed a method of measuring the horizontal intensity of the magnetic field which has been in use well into the second half of the 20th century and worked out the mathematical theory for separating the inner (core and crust) and outer (magnetospheric) sources of Earth's magnetic field. Wilhelm Eduard Weber (October 24, 1804 - June 23, 1891) was a noted physicist. ... For other senses of this word, see magnetism (disambiguation). ... Not to be confused with Kerckhoffs principle. ... The electrical telegraph is a telegraph that uses electric signals. ... The planetary core consists of the innermost layer(s) of a planet. ... Look up Crust in Wiktionary, the free dictionary. ... A magnetosphere is the region around an astronomical object in which phenomena are dominated or organized by its magnetic field. ...

Gauss died in Göttingen, Hanover (now part of Lower Saxony, Germany) in 1855 and is interred in the cemetery Albanifriedhof there. Two individuals 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. His brain was preserved and was studied by Rudolf Wagner who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square centimeters. Highly developed convolutions were also found, which in the early 20th century was suggested as the explanation of his genius.^[4] GÃ¶ttingen marketplace with old city hall, GÃ¤nseliesel fountain and pedestrian zone GÃ¶ttingen ( ) is a city in Lower Saxony, Germany. ... Capital Hanover Head of State King of Hanover Hanover (German: ) was a historical territory in todays Germany, at various times a principality, an electorate of the Holy Roman Empire, a kingdom and a province of Prussia and of Germany. ... With an area of 47,618 km and nearly eight million inhabitants, Lower Saxony (German Niedersachsen) lies in north-western Germany and is second in area and fourth in population among the countrys sixteen Bundesl nder (federal states). ... Albanifriedhof a cemetery in Germany just outside the city wall to the southeast. ... Georg Heinrich August von Ewald (November 16, 1803 - May 4, 1875) was a German orientalist and theologian. ... Baron Wolfgang Sartorius von Waltershausen (1809-1876), German geologist, was born at GÃ¶ttingen, on the 17th of December 1809, and educated at the university in that city. ... This article is about Rudolf Wagner. ...

Family

Gauss's personal life was overshadowed by the early death of his first wife, Johanna Osthoff, in 1809, soon followed by the death of one child, Louis. Gauss plunged into a depression from which he never fully recovered. He married again, to a friend of his first wife named Friederica Wilhelmine Waldeck (Minna), but this second marriage does not seem to have been very happy as it was plagued by Minna's continuous illness.^{[citation needed]} When his second wife died in 1831 after a long illness, one of his daughters, Therese, took over the household and cared for Gauss until the end of his life. His mother lived in his house from 1817 until her death in 1839.^[1] On the Threshold of Eternity. ...

Gauss had six children. With Johanna (1780–1809), his children were Joseph (1806–1873), Wilhelmina (1808–1846) and Louis (1809–1810). Of all of Gauss's children, Wilhelmina was said to have come closest to his talent, but she died young. With Minna Waldeck he also had three children: Eugene (1811–1896), Wilhelm (1813–1879) and Therese (1816–1864). Eugene emigrated to the United States about 1832 after a falling out with his father, eventually settling in St. Charles, Missouri, where he became a well-respected member of the community.^{[citation needed]} Wilhelm also settled in Missouri, starting as a farmer and later becoming wealthy in the shoe business in St. Louis. Therese kept house for Gauss until his death, after which she married. St. ... This article is about the U.S. state. ... For other uses, see Farmer (disambiguation). ... Nickname: Location in the state of Missouri Coordinates: , Country State County Independent City Government - Mayor Francis G. Slay (D) Area - City 66. ...

Gauss eventually had conflicts with his sons, two of whom migrated to the United States. He did not want any of his sons to enter mathematics or science for "fear of sullying the family name". His conflict with Eugene was particularly bitter.^{[citation needed]} Gauss wanted Eugene to become a lawyer, but Eugene wanted to study languages. They had an argument over a party Eugene held, which Gauss refused to pay for. The son left in anger and immigrated to the United States, where he was quite successful. It took many years for Eugene's success to counteract his reputation among Gauss's friends and colleagues. See also the letter from Robert Gauss to Felix Klein on September 3, 1912. For the fish called lawyer, see Burbot. ... is the 246th day of the year (247th in leap years) in the Gregorian calendar. ... 1912 (MCMXII) was a leap year starting on Monday in the Gregorian calendar (or a leap year starting on Tuesday in the 13-day-slower Julian calendar). ...

Personality

Gauss was an ardent perfectionist and a hard worker. According to Isaac Asimov, Gauss was once interrupted in the middle of a problem and told that his wife was dying. He is purported to have said, "Tell her to wait a moment till I'm done."^[5] This anecdote is briefly discussed in W. Dunnington's "Gauss, Titan of Science" where it is suggested that it is an apocryphal story. Perfectionism, in psychology, is a belief that perfection should be strived for. ... Isaac Asimov (January 2?, 1920?[1] â€“ April 6, 1992), pronounced , originally Ð˜ÑÐ°Ð°Ðº ÐžÐ·Ð¸Ð¼Ð¾Ð² but now transcribed into Russian as ÐÐ¹Ð·ÐµÐº ÐÐ·Ð¸Ð¼Ð¾Ð² [1], was a Russian-born American author and professor of biochemistry, a highly successful writer, best known for his works of science fiction and for his popular science books. ...

He was never a prolific writer, refusing to publish works which he did not consider complete and above criticism. This was in keeping with his personal motto "pauca sed matura" (few, but ripe). A study of his personal diaries reveals that he had in fact discovered several important mathematical concepts years or decades before they were published by his contemporaries. Prominent mathematical historian Eric Temple Bell estimated that had Gauss made known all of his discoveries, mathematics would have been advanced by 50 years.^[6] For other persons named Eric Bell, see Eric Bell (disambiguation). ...

A criticism of Gauss is that he did not support the younger mathematicians who followed him. He rarely, if ever, collaborated with other mathematicians and was considered aloof and austere by many.^{[citation needed]} Though he did take in a few students, Gauss was known to dislike teaching. It is said that he attended only a single scientific conference, which was in Berlin in 1828. However, several of his students became influential mathematicians, among them Richard Dedekind, Bernhard Riemann, and Friedrich Bessel. Before she died, Sophie Germain was recommended by Gauss to receive her honorary degree. This article is about the capital of Germany. ... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 â€“ February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Bernhard Riemann. ... Friedrich Wilhelm Bessel (July 22, 1784 â€“ March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli). ... Sophie Germain Marie-Sophie Germain (April 1, 1776 â€“ June 27, 1831), born to a middle-class merchant family in Paris, France, was a French mathematician. ...

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.^{[citation needed]} This is fully, however briefly, explained by Gauss himself in his "Disquisitiones Arithmeticae", where he states that all analysis (i.e. the paths one travelled to reach the solution of a problem) must be suppressed for sake of brevity.

Gauss was deeply religious and conservative.^{[citation needed]} He supported monarchy and opposed Napoleon, whom he saw as an outgrowth of revolution. NapolÃ©on I, Emperor of the French (born Napoleone di Buonaparte, changed his name to NapolÃ©on Bonaparte)[1] (15 August 1769; Ajaccio, Corsica â€“ 5 May 1821; Saint Helena) was a general during the French Revolution, the ruler of France as First Consul (Premier Consul) of the French Republic from... For other uses, see Revolution (disambiguation). ...

Commemorations

The cgs unit for magnetic induction was named gauss in his honour. This article or section is in need of attention from an expert on the subject. ... The former Weights and Measures office in Middlesex, England. ... Electromagnetic induction is the production of an electrical potential difference (or voltage) across a conductor situated in a changing magnetic field. ... The gauss, abbreviated as G, is the cgs unit of magnetic flux density (B), named after the German mathematician and physicist Carl Friedrich Gauss. ...

From 1989 until the end of 2001, his portrait and a normal distribution curve as well as some prominent buildings of Göttingen were featured on the German ten-mark banknote. The other side of the note features the heliotrope and a triangulation approach for Hannover. Germany has issued three stamps honouring Gauss, as well. A righteous stamp (no. 725), was issued in 1955 on the hundredth anniversary of his death; two other stamps, no. 1246 and 1811, were issued in 1977, the 200th anniversary of his birth. Image File history File links Gauss-10DM.jpg Summary http://GermanNotes. ... Image File history File links Gauss-10DM.jpg Summary http://GermanNotes. ... The Deutsche Mark (DM, DEM) was the official currency of West and, from 1990, unified Germany. ... GÃ¶ttingen marketplace with old city hall, GÃ¤nseliesel fountain and pedestrian zone GÃ¶ttingen ( ) is a city in Lower Saxony, Germany. ... The heliotrope is an instrument that reflects sunlight over great distances to mark the positions of participants in a land survey. ... Triangulation can be used to find the distance from the shore to the ship. ... Map of Germany showing Hanover Hanover (in German: Hannover [haˈnoːfɐ]), on the river Leine, is the capital of the state of Lower Saxony (Niedersachsen), Germany. ...

In 2007, his bust was introduced to the Walhalla. Bust of Richard Bently by Roubiliac A bust is a sculpture depicting a persons chest, shoulders, and head, usually supported by a stand. ... View of the Walhalla from the Danube View of the Walhalla main hall The Walhalla, Hall of Fame and Honor is a hall of fame located on the Danube River 10 km from Regensburg, in Bavaria, Germany. ...

Gauss is a large lunar crater, named after Carl Friedrich Gauss, that is located near the northeastern limb of the Moons near side. ... This article is about Earths moon. ... For other uses, see Asteroid (disambiguation). ... MR MARK EVANS IS COOL ... First German Antarctica Expedition (1901-1903), was an Antarctica expedition led by Arctic veteran and geology professor Erich von Drygalski in the ship Gauss. ... Gauss was a ship used for the First German Antarctica Expedition (1901-1903). ... Gaussberg (or Mount Gauss) is an extinct volcanic cone, 370 metres high, fronting on Davis Sea immediately west of Posadowsky Glacier in Antarctica. ... The Gauss Tower is an observation tower built of reinforced concrete on the summit of the High Hagens in Dransfeld. ... The Centre for Education in Mathematics and Computing, hosted at the University of Waterloo, administers mathematics and computing contests for Canadian high school students. ... Crown College is one of the residential colleges that makes up the University of California, Santa Cruz, USA. Located on the upper northern side of campus by Merrill College, Crown also borders the newly constructed Colleges Nine and Ten. ... NMR may refer to: Nuclear magnetic resonance, a phenomenon involving the interaction of atomic nuclei and external magnetic fields Nielsen Media Research, a U.S. company which measures TV, radio and newspaper audiences This is a disambiguation page — a navigational aid which lists other pages that might otherwise share... The University of Utah (also The U or the U of U or the UU), located in Salt Lake City, is the flagship public research university in the state of Utah, and one of 10 institutions that make up the Utah System of Higher Education. ...

Encyclopedia > Carl Friedrich Gauss

Contents

Early years

Middle years

Later years, death, and afterwards

Family

Personality

Commemorations

See also

References

Notes

Further Reading

External links

Further reading