|
Reuschle's Theorem
In elementary geometry, Reuschle's theorem describes a property of the cevians of a triangle intersecting in a common point and is named after the German mathematician Karl Gustav Reuschle (1812–1875). It is also known as Terquem's theorem after the French mathematician Olry Terquem (1782–1862), who published it in 1842. In a triangle ABC with its three cevians intersecting in a common point other than the vertices A, B or C let P_a, P_b and P_c denote the intersections of the (extended) triangle sides and the cevians. The circle defined by the three points P_a, P_b and P_c intersects the (extended) triangle sides in the (additional) points P'_a, P'_b and P'_c. Reuschle's theorem now states that the three new cevians AP'_a, BP'_b and CP'_c intersect in a common point as well. References *Friedrich Riecke (ed.): ''Mathematische Unterhaltungen''. Volume I, Stuttgart 1867, (reprint Wiesbaden 1973), , p. 125 (German) *M. D. Fox, J. R. Goggins: "Cevian Axes and Related Curves." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satz Von Reuschle3
' (German for ''sentence'', ''movement'', ''set'', ''setting'') is any single member of a musical piece, which in and of itself displays a complete sense, (Hugo Riemann, Riemann 1976: 841) such as a sentence (music), sentence, phrase (music), phrase, or movement (music), movement. Notes Sources *Riemann (1976). Cited in Jean-Jacques Nattiez, Nattiez, Jean-Jacques (1990). ''Music and Discourse: Toward a Semiology of Music'' (''Musicologie générale et sémiologue'', 1987). Translated by Carolyn Abbate (1990). . Formal sections in music analysis German words and phrases {{music-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cevian
In geometry, a cevian is a line that intersects both a triangle's vertex, and also the side that is opposite to that vertex. Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name. Length Stewart's theorem The length of a cevian can be determined by Stewart's theorem: in the diagram, the cevian length is given by the formula :\,b^2m + c^2n = a(d^2 + mn). Less commonly, this is also represented (with some rearrangement) by the following mnemonic: :\underset = \!\!\!\!\!\! \underset Median If the cevian happens to be a median (thus bisecting a side), its length can be determined from the formula :\,m(b^2 + c^2) = a(d^2 + m^2) or :\,2(b^2 + c^2) = 4d^2 + a^2 since :\,a = 2m. Hence in this case :d= \frac\sqrt2 . Angle bisector If the cevian happens to be an angle bisector, its length obeys the formulas :\,(b + c)^2 = a^2 \le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Gustav Reuschle
Karl Gustav Reuschle (26 December 1812 – 22 May 1875) was a German mathematician, geographer and educator. Reuschle was born in Mehrstetten in Württemberg and studied math and theology at the University of Tübingen. After his graduation he continued his studies in mathematics for a year in Paris and for a year in Berlin. From 1837 onwards Reuschle worked as a teacher, first in Schöntal then in Tübingen (1938) and finally since 1840 at a gymnasium in Stuttgart, where he taught as professor for mathematics and geography. Reuschle authored a number of science books, mostly on geography and mathematics. Particularly well received at the time was his biography of Johannes Kepler (1871). His son Karl Reuschle (1847–1909) was a mathematician as well, he became the cofounder of the mathematical seminar at the University of Stuttgart. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Olry Terquem
Olry Terquem (16 June 1782 – 6 May 1862) was a French people, French mathematician. He is known for his works in geometry and for founding two scientific journals, one of which was the first journal about the history of mathematics. He was also the pseudonymous author (as Tsarphati) of a sequence of letters advocating radical reform in Judaism.. He was History of the Jews in France, French Jewish. Education and career Terquem grew up speaking Yiddish, and studying only the Hebrew language and the Talmud.. Biographical appendix, pp. 385–386. However, after the French revolution his family came into contact with a wider society, and his studies broadened. Despite his poor French he was admitted to study mathematics at the École Polytechnique in Paris, beginning in 1801, as only the second Jew to study there.. See in particulapp. 60–61 He became an assistant there in 1803, and earned his doctorate in 1804. After finishing his studies he moved to Mainz (at that time know ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Riecke
Friedrich may refer to: Names *Friedrich (surname), people with the surname ''Friedrich'' *Friedrich (given name), people with the given name ''Friedrich'' Other *Friedrich (board game), a board game about Frederick the Great and the Seven Years' War * ''Friedrich'' (novel), a novel about anti-semitism written by Hans Peter Richter *Friedrich Air Conditioning, a company manufacturing air conditioning and purifying products *, a German cargo ship in service 1941-45 See also *Friedrichs (other) *Frederick (other) *Nikolaus Friedreich Nikolaus Friedreich (1 July 1825 in Würzburg – 6 July 1882 in Heidelberg) was a German pathologist and neurologist, and a third generation physician in the Friedreich family. His father was psychiatrist Johann Baptist Friedreich (1796–1862) ... {{disambig ja:フリードリヒ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
