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Ruth Moufang
Ruth Moufang (10 January 1905 – 26 November 1977) was a German mathematician. Biography She was born to German chemist Eduard Moufang and Else Fecht Moufang. Eduard Moufang was the son of Friedrich Carl Moufang (1848-1885) from Mainz, and Elisabeth von Moers from Mainz. Ruth Moufang's mother was Else Fecht, who was the daughter of Alexander Fecht (1848-1913) from Kehl and Ella Scholtz (1847-1921). Ruth was the younger of her parents' two daughters, having an elder sister named Erica. Education and career She studied mathematics at the University of Frankfurt. In 1931 she received her Ph.D. on projective geometry under the direction of Max Dehn, and in 1932 spent a fellowship year in Rome. After her year in Rome, she returned to Germany to lecture at the University of Königsberg and the University of Frankfurt. Denied permission to teach by the minister of education of Nazi Germany, she worked at Research and Development of Krupp (battleships, U-boats, tanks, howitzers, g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darmstadt
Darmstadt () is a city in the States of Germany, state of Hesse in Germany, located in the southern part of the Frankfurt Rhine Main Area, Rhine-Main-Area (Frankfurt Metropolitan Region). Darmstadt has around 160,000 inhabitants, making it the fourth largest city in the state of Hesse after Frankfurt am Main, Wiesbaden, and Kassel. Darmstadt holds the official title "City of Science" () as it is a major centre of scientific institutions, universities, and high-technology companies. The European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) and the European Space Agency's European Space Operations Centre (ESA ESOC) are located in Darmstadt, as well as Gesellschaft für Schwerionenforschung, GSI Centre for Heavy Ion Research, where several chemical elements such as bohrium (1981), meitnerium (1982), hassium (1984), darmstadtium (1994), roentgenium (1994), and copernicium (1996) were discovered. The existence of the following elements was also confirmed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazi Germany
Nazi Germany, officially known as the German Reich and later the Greater German Reich, was the German Reich, German state between 1933 and 1945, when Adolf Hitler and the Nazi Party controlled the country, transforming it into a Totalitarianism, totalitarian dictatorship. The Third Reich, meaning "Third Realm" or "Third Empire", referred to the Nazi claim that Nazi Germany was the successor to the earlier Holy Roman Empire (800–1806) and German Empire (1871–1918). The Third Reich, which the Nazis referred to as the Thousand-Year Reich, ended in May 1945, after 12 years, when the Allies of World War II, Allies defeated Germany and entered the capital, Berlin, End of World War II in Europe, ending World War II in Europe. After Hitler was appointed Chancellor of Germany in 1933, the Nazi Party began to eliminate political opposition and consolidate power. A 1934 German referendum confirmed Hitler as sole ''Führer'' (leader). Power was centralised in Hitler's person, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Intelligencer
''The Mathematical Intelligencer'' is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released quarterly with a subset of open access articles. Some articles have been cross-published in the ''Scientific American''. Karen Parshall and Sergei Tabachnikov are currently the co-editors-in-chief. History The journal was started informally in 1971 by Walter Kaufmann-Buehler and Alice and Klaus Peters. "Intelligencer" was chosen by Kaufmann-Buehler as a word that would appear slightly old-fashioned. An exploration of mathematically themed stamps, written by Robin Wilson, became one of its earliest columns. Prior to 1977, articles of the ''Intelligencer'' were not contained in regular volumes and were sent out sporadically to those on a mailing list. To gauge interest, the inaugural mailing included twelve thousand people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agnes Scott College
Agnes Scott College is a Private university, private Women's Colleges in the Southern United States, women's Liberal arts colleges in the United States, liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church (USA), Presbyterian Church and is considered one of the Seven Sisters of the South. It also offers co-educational graduate programs. History The college was founded in 1889 as Decatur Female Seminary by Presbyterian minister Frank Henry Gaines. In 1890, the name was changed to Agnes Scott Institute to honor the mother of the college's primary benefactor, Col. George Washington Scott. The name was changed again to Agnes Scott College in 1906 and remains today a Women's Colleges in the Southern United States, women's college. Agnes Scott is considered the first higher education institution in the state of Georgia to receive regional accreditation. The ninth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Von Staudt
Karl Georg Christian von Staudt (24 January 1798 – 1 June 1867) was a German mathematician who used synthetic geometry to provide a foundation for arithmetic. Life and influence Karl was born in the Free Imperial City of Rothenburg, which is now called Rothenburg ob der Tauber in Germany. From 1814 he studied in Gymnasium in Ausbach. He attended the University of Göttingen from 1818 to 1822 where he studied with Gauss who was director of the observatory. Staudt provided an ephemeris for the orbits of Mars and the asteroid Pallas. When in 1821 Comet Nicollet-Pons was observed, he provided the elements of its orbit. These accomplishments in astronomy earned him his doctorate from University of Erlangen in 1822. Staudt's professional career began as a secondary school instructor in Würzburg until 1827 and then Nuremberg until 1835. He married Jeanette Dreschler in 1832. They had a son Eduard and daughter Mathilda, but Jeanette died in 1848. The book ''Geometrie der Lage'' (184 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associative Law
In mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: \begin (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24 . \end Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of Hypercomplex number, hypercomplex Number#Classification, number system. The octonions are usually represented by the capital letter O, using boldface or blackboard bold \mathbb O. Octonions have eight dimension (vector space), dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are commutative property, noncommutative and associative property, nonassociative, but satisfy a weaker form of associativity; namely, they are alternative algebra, alternative. They are also Power associativity, power associative. Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Octonions are related to exceptional structures in mathematics, among them the Simple Lie group#Exceptional cases, exceptional Lie groups. Octonions have applications in fields such as string theory, special relativity and qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley Plane
In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions.Baez (2002). The Cayley plane was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley for his 1845 paper describing the octonions. Properties In the Cayley plane, lines and points may be defined in a natural way so that it becomes a 2-dimensional projective space, that is, a projective plane. It is a non-Desarguesian plane, where Desargues' theorem does not hold. More precisely, as of 2005, there are two objects called Cayley planes, namely the real and the complex Cayley plane. The real Cayley plane is the symmetric space F4/Spin(9), where F4 is a compact form of an exceptional Lie group and Spin(9) is the spin group of nine-dimensional Euclidean space (realized in F4). It admits a cell decomposition into three cells, of dimensions 0, 8 and 16.Iliev and Manivel (2005). The complex Cayley plane is a homogeneous space under the complexification o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues's Theorem
In projective geometry, Desargues's theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and those of the other by and . ''Axial perspectivity'' means that lines and meet in a point, lines and meet in a second point, and lines and meet in a third point, and that these three points all lie on a common line called the ''axis of perspectivity''. ''Central perspectivity'' means that the three lines and are concurrent, at a point called the ''center of perspectivity''. This intersection theorem is true in the usual Euclidean plane but special care needs to be taken in exceptional cases, as when a pair of sides are parallel, so that their "point of intersection" recedes to infinity. Commonly, to remove these exceptions, mathematicians "complete" the Euclidean plane by adding points at infinity, following Jean-Victor Poncelet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Structure
In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set of identities (known as ''axioms'') that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called ''scalar multiplication'' between elements of the field (called '' scalars''), and elements of the vector space (called '' vectors''). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-associative Algebra
A non-associative algebra (or distributive algebra) is an algebra over a field where the binary operation, binary multiplication operation is not assumed to be associative operation, associative. That is, an algebraic structure ''A'' is a non-associative algebra over a field (mathematics), field ''K'' if it is a vector space over ''K'' and is equipped with a ''K''-bilinear map, bilinear binary multiplication operation ''A'' × ''A'' → ''A'' which may or may not be associative. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidean space equipped with the cross product operation. Since it is not assumed that the multiplication is associative, using parentheses to indicate the order of multiplications is necessary. For example, the expressions (''ab'')(''cd''), (''a''(''bc''))''d'' and ''a''(''b''(''cd'')) may all yield different answers. While this use of ''non-associative'' means that associativity is not assumed, it does not mean that ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
