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Hudde's Rules
In mathematics, Hudde's rules are two properties of polynomial roots described by Johann Hudde. 1. If ''r'' is a double root of the polynomial equation ::a_0x^n + a_1x^ + \cdots + a_x + a_n = 0 :and if b_0, b_1, \dots, b_, b_n are numbers in arithmetic progression, then ''r'' is also a root of ::a_0b_0x^n + a_1b_1x^ + \cdots + a_b_x + a_nb_n = 0. :This definition is a form of the modern theorem that if ''r'' is a double root of ''ƒ''(''x'') = 0, then ''r'' is a root of ''ƒ'' '(''x'') = 0. 2. If for ''x'' = ''a'' the polynomial ::a_0x^n + a_1x^ + \cdots + a_x + a_n :takes on a relative maximum or minimum value, then ''a'' is a root of the equation ::na_0x^n + (n-1)a_1x^ + \cdots + 2a_x^2 + a_x = 0. :This definition is a modification of Fermat's theorem in the form that if ''ƒ''(''a'') is a relative maximum or minimum value of a polynomial ''ƒ''(''x''), then ''ƒ'' '(''a'') = 0, where ''ƒ'' ' is the derivative of ''ƒ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
La Géométrie
''La Géométrie'' was published in 1637 as an appendix to ''Discours de la méthode'' (''Discourse on the Method''), written by René Descartes. In the ''Discourse'', he presents his method for obtaining clarity on any subject. ''La Géométrie'' and two other appendices, also by Descartes, ''La Dioptrique'' (''Optics'') and ''Les Météores'' (''Meteorology''), were published with the ''Discourse'' to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience). The work was the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking. It also contributed to the mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorems In Algebra
In mathematics, a theorem is a statement that has been proved, or can be proved. 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 the mainstream of 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, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. 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'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules
Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule that is part of school discipline * Sport rule, a rule that defines how a sport is played * Game rule, a rule that defines how a game is played * Moral, a rule or element of a moral code for guiding choices in human behavior * Norm (philosophy), a kind of sentence or a reason to act, feel or believe * Rule of thumb, a principle with broad application that is not intended to be strictly accurate or reliable for every situation * Unspoken rule, an assumed rule of human behavior that is not voiced or written down * Slide rule, a mechanical analog computer Science * Rule of inference or transformation rule, a term in logic for a function which takes premises and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duckworth Overlook
Duckworth Books, originally Gerald Duckworth and Company, founded in 1898 by Gerald Duckworth, is a British publisher.Our History duckworthbooks.co.uk. Retrieved 29 November 2020. History 
Gerald Duckworth founded the company in 1898, setting up its office at 3 . Staff included
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Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics. He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission on the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirsti Pedersen
Kirsti Andersen (born December 9, 1941, Copenhagen), published under the name Kirsti Pedersen, is a Danish historian of mathematics. She is an Associate Professor of the History of Science at Aarhus University, where she had her Candidate examination in 1967. Work Andersen has written on the early history of mathematical analysis (for example, Cavalieri and Roberval). She has also written extensively on the history of graphical perspective. In a 1985 article she related the science of perspective as described by Simon Stevin, Frans van Schooten, Willem 's Gravesande, Brook Taylor, and Johann Heinrich Lambert. In a 1987 article she examined the ancient roots of linear perspective as found in Euclid's Optics and Ptolemy ( Geography and Planisphaerium). In 1991 she recalled Desargues’ method of perspective. In 1992 her book on Brook Taylor appeared, and she wrote on the alternative "plan and elevation technique". In 2007 her '' The Geometry of an Art'' provided a comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ProQuest
ProQuest LLC is an Ann Arbor, Michigan-based global information-content and technology company, founded in 1938 as University Microfilms by Eugene B. Power. ProQuest is known for its applications and information services for libraries, providing access to dissertations, theses, ebooks, newspapers, periodicals, historical collections, governmental archives, cultural archives,"Jisc and ProQuest Enable Access to Essential Digital Content" retrieved May 21, 2014 and other aggregated databases. This content was estimated to be around 125 billion digital pages, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Louis University
Saint Louis University (SLU) is a private Jesuit research university with campuses in St. Louis, Missouri, United States, and Madrid, Spain. Founded in 1818 by Louis William Valentine DuBourg, it is the oldest university west of the Mississippi River and the second-oldest Jesuit university in the United States. It is one of 27 member institutions of the Association of Jesuit Colleges and Universities. The university is accredited by the North Central Association of Colleges and Secondary Schools. In the 2021–2022 academic year, SLU had an enrollment of 12,883 students. The student body included 8,138 undergraduate students and 4,745 graduate students that represents all 50 states and 82 countries. The university is classified as a Research II university by the Carnegie Classification of Institutions of Higher Education. For more than 50 years, the university has maintained a campus in Madrid, Spain. The Madrid campus was the first freestanding campus operated by an Ameri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl B
Carl may refer to: *Carl, Georgia, city in USA *Carl, West Virginia, an unincorporated community *Carl (name), includes info about the name, variations of the name, and a list of people with the name *Carl², a TV series * "Carl", an episode of television series ''Aqua Teen Hunger Force'' * An informal nickname for a student or alum of Carleton College CARL may refer to: *Canadian Association of Research Libraries *Colorado Alliance of Research Libraries See also *Carle (other) *Charles *Carle, a surname *Karl (other) *Karle (other) Karle may refer to: Places * Karle (Svitavy District), a municipality and village in the Czech Republic * Karli, India, a town in Maharashtra, India ** Karla Caves, a complex of Buddhist cave shrines * Karle, Belgaum, a settlement in Belgaum d ... {{disambig ja:カール zh:卡尔 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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