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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] |
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] |
Proceedings Of The National Academy Of Sciences
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2021 impact factor of 12.779. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the mass media, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open access journal, with an embargo period of six months that can be bypassed for an author fee ( hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verlag Harri Deutsch
The (VHD, HD) with headquarters in Frankfurt am Main, Germany, as well as in Zürich and Thun, Switzerland, was a German publishing house founded in 1961 and closed in 2013. Overview The ' with headquarters in Frankfurt am Main, Germany, was a German publishing house founded by Harri Deutsch in 1961 as a spin-off of the scientific bookstore Fachbuchhandlung Harri Deutsch (FHD), which had existed for about a decade earlier. Both were situated near Goethe-Universität Frankfurt am Main. Between 1963 and about 1979 the publisher also had an office in Zürich. Around 1974 another branch was opened in Thun. The company's activities focussed mostly on textbooks and encyclopedic works in the areas of mathematics, physics, chemistry and other sciences and technologies, in the first three decades in particular titles licensed from publishers of the former Eastern Bloc including the East-German publishers Edition Leipzig, , Akademie Verlag, VEB Bibliographisches Institut, VEB Verlag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ostwalds Klassiker Der Exakten Wissenschaften
Ostwalds Klassiker der exakten Wissenschaften (English: Ostwald's classics of the exact sciences) is a German book series that contains important original works from all areas of natural sciences. It was founded in 1889 by the physical chemist Wilhelm Ostwald and is now published by Europa-Lehrmittel. History The series was first published by Wilhelm Engelmann in Leipzig and then by Akademische Verlagsgesellschaft in Leipzig and more recently in reprints and new editions by Verlag Harri Deutsch in Frankfurt. Ostwald's aim was to remedy the "" (Lack of knowledge of those great works on which the edifice of science rests). The first volume in 1889 was (On the conservation of power) (first 1847) by Hermann von Helmholtz. In 1894, the physicist Arthur von Oettingen von Ostwald took over the editing (and remained editor until 1920, when Ostwald's son, Wolfgang Ostwald, took over the task). However, Ostwald initially continued to publish the chemistry volumes until he was replaced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expositiones Mathematicae
''Expositiones Mathematicae'' is a peer-reviewed mathematics, mathematical scientific journal, journal. The journal was established in 1983. It has been published by Elsevier since 2001. It is published 4 times a year and is edited by Robert C. Dalang. Abstracting and indexing The journal is abstracted and indexed in the following bibliographic databases: References External links * {{mathematics-journal-stub Mathematics journals Elsevier academic journals Publications established in 1983 Quarterly journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
