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Gauss' Diary
Gauss's diary was a record of the mathematical discoveries of German mathematician Carl Friedrich Gauss from 1796 to 1814. It was rediscovered in 1897 and published by , and reprinted in volume X1 of his collected works and in . There is an English translation with commentary given by , reprinted in the second edition of . Sample entries Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin. Entry 1, dated 1796, March 30, states "", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass. Entry 18, dated 1796, July 10, states " ΕΥΡΗΚΑ! " and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem. Entry 43, dated 1796, October 21, states "Vicimus GEGAN" (We have conquered GEGAN). The meaning of this was a mystery for many years. found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eureka Gauss
Eureka (often abbreviated as E!, or Σ!) is an intergovernmental organisation for research and development funding and coordination. Eureka is an open platform for international cooperation in innovation. Organisations and companies applying through Eureka programmes can access funding and support from national and regional ministries or agencies for their international R&D projects. , Eureka has 43 full members, including the European Union (represented by the European Commission) and four associated members (Argentina, Chile, South Africa, and Singapore). All 27 EU Member States are also members of Eureka. Eureka is not an EU research programme, but rather an intergovernmental organisation of national ministries or agencies, of which the EU is a member. Cooperation and synergy are sought between Eureka and the research activities of the EU proper, such as with European Union's Horizon 2020 and the European Research Area. History Founded in 1985 by prominent European politic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptadecagon
In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon. Regular heptadecagon A '' regular heptadecagon'' is represented by the Schläfli symbol . Construction As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19.Arthur Jones, Sidney A. Morris, Kenneth R. Pearson, ''Abstract Algebra and Famous Impossibilities'', Springer, 1991, p. 178./ref> This proof represented the first progress in regular polygon construction in over 2000 years. Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions, and secondly on his proof that this can be done if the odd prime factors of N, the number of sides of the regular polygon, are distinct Fermat prime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eureka (word)
Archimedes exclaiming ''Eureka''. In his excitement, he forgets to dress and runs nude in the streets straight out of his bath ''Eureka'' ( grc, εὕρηκα) is an interjection used to celebrate a discovery or invention. It is a transliteration of an exclamation attributed to Ancient Greek mathematician and inventor Archimedes. Etymology "Eureka" comes from the Ancient Greek word εὕρηκα ''heúrēka'', meaning "I have found (it)", which is the first person singular perfect indicative active of the verb εὑρίσκω ''heurískō'' "I find". It is closely related to ''heuristic'', which refers to experience-based techniques for problem-solving, learning, and discovery. Pronunciation The accent of the English word is on the second syllable, following Latin rules of accent, which require that a penult (next-to-last syllable) must be accented if it contains a long vowel. In the Greek pronunciation, the first syllable has a high pitch accent, because the Ancient Gree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Polygonal Number Theorem
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers. That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on. That is, the -gonal numbers form an additive basis of order . Examples Three such representations of the number 17, for example, are shown below: *17 = 10 + 6 + 1 (''triangular numbers'') *17 = 16 + 1 (''square numbers'') *17 = 12 + 5 (''pentagonal numbers''). History The theorem is named after Pierre de Fermat, who stated it, in 1638, without proof, promising to write it in a separate work that never appeared.. Joseph Louis Lagrange proved the square case in 1770, which states that every positive number can be represented as a sum of four squares, for example, . Gauss proved the triangular case in 1796, commemorating the occasion by writing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GEGAN Gauss
Gauss's diary was a record of the mathematical discoveries of German mathematician Carl Friedrich Gauss from 1796 to 1814. It was rediscovered in 1897 and published by , and reprinted in volume X1 of his collected works and in . There is an English translation with commentary given by , reprinted in the second edition of . Sample entries Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin. Entry 1, dated 1796, March 30, states "", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass. Entry 18, dated 1796, July 10, states " ΕΥΡΗΚΑ! " and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem. Entry 43, dated 1796, October 21, states "Vicimus GEGAN" (We have conquered GEGAN). The meaning of this was a mystery for many years. found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemniscatic Elliptic Function
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Carlo de' Toschi di Fagnano, Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols and (sometimes the symbols and or and are used instead) are analogous to the trigonometric functions sine and cosine. While the trigonometric sine relates the arc length to the chord length in a unit-diameter circle x^2+y^2 = x, the lemniscate sine relates the arc length to the chord length of a lemniscate \bigl(x^2+y^2\bigr)^2=x^2-y^2. The lemniscate functions have periods related to a number called the lemniscate constant, the ratio of a lemniscate's perimeter to its diameter. This number is a Quartic plane curve, quartic analog of the (Conic section, quadratic) , pi, ratio of perimeter to diameter of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
