|
Marden's Theorem
In mathematics, Marden's theorem, named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative. See also geometrical properties of polynomial roots. Statement A cubic polynomial has three zeroes in the complex number plane, which in general form a triangle, and the Gauss–Lucas theorem states that the roots of its derivative lie within this triangle. Marden's theorem states their location within this triangle more precisely: :Suppose the zeroes , , and of a third-degree polynomial are non-collinear. There is a unique ellipse inscribed in the triangle with vertices , , and tangent to the sides at their midpoints: the Steiner inellipse. The foci of that ellipse are the zeroes of the derivative . Proof This proof comes from an exercise in Fritz Carlson's book “Geometri” (in Swedish, 1943). Additional relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marden Theorem
Marden may refer to: Places Australia * Marden, South Australia, a suburb of Adelaide England * Marden, Herefordshire * Marden, Kent ** Marden Airfield ** Marden railway station * Marden, Tyne and Wear * Marden, West Sussex ** East Marden ** North Marden * Marden, Wiltshire ** Marden Henge * Up Marden, Compton, West Sussex * Marden Park, Surrey Other uses * Marden (surname) * Marden's theorem, in complex geometry * River Marden The River Marden is a small tributary of the River Avon, Bristol, River Avon in England. It flows from the hills surrounding Calne and meets the Avon about a mile upstream of Chippenham. The river has a mean flow of . Course The Marden rises j ..., Wiltshire, England See also * Marsden (other) * Madsen (other) {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the figure. The same definition extends to any object in n-dimensional Euclidean space. In geometry, one often assumes uniform mass density, in which case the '' barycenter'' or ''center of mass'' coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin. In physics, if variations in gravity are considered, then a '' center of gravity'' can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center. History The term "centroid" was coined in 1814. It is used as a substitute for the older terms "center of grav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorems About Polynomials
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reason ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorems About Triangles
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasonin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Für Die Reine Und Angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Daniel Huybrechts (Rheinische Friedrich-Wilhelms-Universität Bonn). Past editors * 1826–1856: August Leopold Crelle * 1856–1880: Carl Wilhelm Borchardt * 1881–1888: Leopold Kronecker, Karl Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over concerns about competing with the '' American Journal of Mathematics''. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *'' Memoirs of the American Mathematical Society'' *'' Notices of the American Mathematical Society'' *'' Proceedings of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bôcher's Theorem
In mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher. Bôcher's theorem in complex analysis In complex analysis, the theorem states that the finite zero of a function, zeros of the derivative r'(z) of a non-constant function, constant rational function r(z) that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of r(z) and particles of negative mass at the zeros and poles, poles of r(z), with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance. Furthermore, if ''C''1 and ''C''2 are two disjoint circular regions which contain respectively all the zeros and all the poles of r(z) , then ''C''1 and ''C''2 also contain all the critical points of r(z) . Bôcher's theorem for harmonic functions In the theory of harmonic functions, Bôcher's theorem states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The editor-in-chief heads all departments of the organization and is held accoun ... is Vadim Ponomarenko ( San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly ..., college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 11 Dupont in the Dupont Circle, Washington, D.C., Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lester R
Lester is an ancient Anglo-Saxon surname and given name. People Given name * Lester Bangs (1948–1982), American music critic * Lester Oliver Bankhead (1912–1997), American architect * Lester W. Bentley (1908–1972), American artist from Wisconsin * Lester Bird (1938–2021), second prime minister of Antigua and Barbuda (1994–2004) * Lester D. Boronda (1886–1953), American painter, furniture designer, sculptor * Lester Cotton (born 1996), American football player * Lester del Rey (1915–1993), American science fiction author and editor * Lester Ellis (born 1965), Australian former professional boxer * Lester Flatt (1914–1979), American bluegrass musician * Lester Gillis (1908–1934), better known as Baby Face Nelson, American gangster * Les Gold (born 1950), American pawnbroker and reality TV star * Lester Holt (born 1959), American television journalist * Lester Charles King (1907–1989), English geomorphologist * Lester Lanin (1907–2004), American j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dan Kalman
Daniel "Dan" Simon Kalman (born March 21, 1952, in Oakland, California) is an American mathematician and winner of nine awards for expository writing in mathematics. (Several article titles have links to online pdf's.) Education and career After graduating from Oakland High School in 1970, Kalman matriculated at Harvey Mudd College, where he graduated in 1974. From 1974 to 1980 he was a graduate student at the University of Wisconsin–Madison, where he received his PhD in 1980. He was from 1978 to 1979 an instructor at Lawrence University in Appleton, Wisconsin, and from 1979 to 1983 an assistant professor at the University of Wisconsin–Green Bay. After teaching as a visiting lecturer from 1983 to 1985 at Augustana College in Sioux Falls, South Dakota, Kalman worked from 1985 to 1993 as a member of the technical staff of The Aerospace Corporation in Los Angeles. At Washington, D.C.'s American University he was from 1993 to 1998 an assistant professor, from 1998 to 2003 an ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
