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Rhetorical Algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property). This article describes the history of the theory of equations, referred to in this article as "algebra", from the origins to the emergence of algebra as a separate area of mathematics. Etymology The word "algebra" is derived from the Arabic word , and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, ''Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala'', can be translated as ''The Compendious Book on Calculation by Completion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication. Elementary algebra is the main form of algebra taught in schools. It examines mathematical statements using variables for unspecified values and seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called '' systems of linear equations''. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions. Abstract algebra studies algebraic structures, which consist of a set of mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantus
Diophantus of Alexandria () (; ) was a Greek mathematician who was the author of the '' Arithmetica'' in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic equations. Although Joseph-Louis Lagrange called Diophantus "the inventor of algebra" he did not invent it; however, his exposition became the standard within the Neoplatonic schools of Late antiquity, and its translation into Arabic in the 9th century AD and had influence in the development of later algebra: Diophantus' method of solution matches medieval Arabic algebra in its concepts and overall procedure. The 1621 edition of ''Arithmetica'' by Bachet gained fame after Pierre de Fermat wrote his famous " Last Theorem" in the margins of his copy. In modern use, Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations are two other subareas of number theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Mathematics
Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during Classical antiquity, classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Ancient Greek, Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in Mathematical proof, proofs is an important difference between Greek mathematics and those of preceding civilizations. The early history of Greek mathematics is obscure, and traditional narratives of Theorem, mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero Of A Function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) ''vanishes'' at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x) = 0. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by f(x)=x^2-5x+6=(x-2)(x-3) has the two roots (or zeros) that are 2 and 3. f(2)=2^2-5\times 2+6= 0\textf(3)=3^2-5\times 3+6=0. If the function maps real numbers to real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equations
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. 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. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Symbol X
''The'' is a grammatical article in English, denoting nouns that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the most frequently used word in the English language; studies and analyses of texts have found it to account for seven percent of all printed English-language words. It is derived from gendered articles in Old English which combined in Middle English and now has a single form used with nouns of any gender. The word can be used with both singular and plural nouns, and with a noun that starts with any letter. This is different from many other languages, which have different forms of the definite article for different genders or numbers. Pronunciation In most dialects, "the" is pronounced as (with the voiced dental fricative followed by a schwa) when followed by a consonant sound, and as (homophone of the archaic pronoun ''thee' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Descartes
René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, and later becoming a central intellectual of the Dutch Golden Age. Although he served a Dutch Reformed Church, Protestant state and was later counted as a Deism, deist by critics, Descartes was Roman Catholicism, Roman Catholic. Many elements of Descartes's philosophy have precedents in late Aristotelianism, the Neostoicism, revived Stoicism of the 16th century, or in earlier philosophers like Augustine of Hippo, Augustine. In his natural philosophy, he differed from the Scholasticism, schools on two major point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
François Viète
François Viète (; 1540 – 23 February 1603), known in Latin as Franciscus Vieta, was a French people, French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a Conseil du Roi, privy councillor to both Henry III of France, Henry III and Henry IV of France, Henry IV of France. Biography Early life and education Viète was born at Fontenay-le-Comte in present-day Vendée. His grandfather was a merchant from La Rochelle. His father, Etienne Viète, was an attorney in Fontenay-le-Comte and a notary in Le Busseau. His mother was the aunt of Barnabé Brisson, a magistrate and the first president of parliament during the ascendancy of the Ligue, Catholic League of France. Viète went to a Franciscan school and in 1558 studied law at Poitiers, graduating as a Bachelor of Laws in 1559. A year later, he began his career as an attorney in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abū Al-Hasan Ibn Alī Al-Qalasādī
Abū'l-Ḥasan ʿAlī ibn Muḥammad ibn ʿAlī al-Qurashī al-Qalaṣādī (; 1412–1486) was a Muslim Arab Islamic mathematics, mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence. Franz Woepcke stated that al-Qalaṣādī was known as one of the most influential voices in Mathematical notation, algebraic notation for taking "the first steps toward the introduction of algebraic symbolism''. He wrote numerous books on arithmetic and algebra, including ''al-Tabsira fi'lm al-hisab'' ( "''Clarification of the science of arithmetic''"). Early life Al-Qalaṣādī was born in Baza, Granada, Baza, an outpost of the Emirate of Granada. He received education in Granada, but continued to support his family in Baza. He published many works and eventually retired to his native Baza. His works dealt with Algebra and contained the precise mathematical answers to problems in everyday life, such as the composition of medicaments, the calculation of the drop of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ibn Al-Banna Al-Marrakushi
Ibn al‐Bannāʾ al‐Marrākushī (), full name: Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi al-Marrakushi () (29 December 1256 – 31 July 1321), was an Arab Muslim polymath who was active as a mathematician, astronomer, Islamic scholar, Sufi and astrologer. Biography Ahmad ibn Muhammad ibn Uthman was born in the ''Qa'at Ibn Nahid'' Quarter of Marrakesh on 29 or 30 December 1256. His '' nisba'' al-Marrakushi is in relation to his birth and death in his hometown Marrakesh and al azdi means he was from the big arab tribe Azd. His father was a mason thus the '' kunya'' Ibn al-Banna' (lit. the son of the mason). Ibn al-Banna' studied a variety of subjects under at least 17 masters: Quran under the '' Qari's'' Muhammad ibn al-bashir and shaykh al-Ahdab. '' ʻilm al-ḥadīth'' under ''qadi al-Jama'a'' (chief judge) of Fez َAbu al-Hajjaj Yusuf ibn Ahmad ibn Hakam al-Tujibi, Abu Yusuf Ya'qub ibn Abd al-Rahman al-Jazuli and Abu abd allah ibn. ''Fiqh and Usul al-Fiqh'' under A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
