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  • Literature - 8 | Britannica.com
    by the characters but also a shot by shot outline of the film s action Screenplays may be adapted from novels or stage plays or developed Scriblerus Club 18th century British literary club whose founding members were the brilliant Tory wits Alexander Pope Jonathan Swift John Gay Thomas Parnell and John Arbuthnot Its purpose was to ridicule pretentious erudition and scholarly jargon through the person script in motion pictures the written text of a film The nature of scripts varies from those that give only a brief outline of the action to detailed shooting scripts in which every action gesture and implication is explicitly stated Frequently scripts sea serpent mythological and legendary marine animal that traditionally resembles an enormous snake The belief in huge creatures that inhabited the deep was widespread throughout the ancient world In the Old Testament there are several allusions to a primordial Seifert Jaroslav poet and journalist who in 1984 became the first Czech to win the Nobel Prize for Literature Seifert made a living as a journalist until 1950 but his first book of poetry Město v slzách Town in Tears was published in 1920 His early proletarian Senecan tragedy body of nine closet dramas i e plays intended to be read rather than performed written in blank verse by the Roman Stoic philosopher Seneca in the 1st century ad Rediscovered by Italian humanists in the mid 16th century they became the models senryū a three line unrhymed Japanese poem structurally similar to a haiku but treating human nature usually in an ironic or satiric vein It is also unlike haiku in that it usually does not have any references to the seasons Senryū developed from haiku and sentimental comedy a dramatic genre of the 18th century denoting plays in which middle class protagonists triumphantly overcome a series of moral trials Such comedy aimed at producing tears rather than laughter Sentimental comedies reflected contemporary philosophical sentimental novel broadly any novel that exploits the reader s capacity for tenderness compassion or sympathy to a disproportionate degree by presenting a beclouded or unrealistic view of its subject In a restricted sense the term refers to a widespread European novelistic Serbian literature the literature of the Serbs a Balkan people speaking the Serbian language still referred to by linguists as Serbo Croatian Serbian literature developed primarily from the 12th century producing such religious works as the illuminated Miroslav Gospel serial a novel or other work appearing as in a magazine in parts at intervals Novels written in the 19th century were commonly published as serials Many works by Charles Dickens George Eliot William Makepeace Thackeray Anthony Trollope and others first setting in literature the location and time frame in which the action of a narrative takes place The makeup and behaviour of fictional characters often depend on their environment quite as much as on their personal characteristics Setting is of great importance shāʿir Arabic poet in Arabic literature poet who in pre Islāmic times was a tribal dignitary whose poetic utterances were deemed supernaturally inspired by such spirits as jinn and shaitans As such his word was needed to insure the success of certain shangam literature the earliest writings in the Tamil language thought to have been produced in three chankam s or literary academies in Madurai India from the 1st to the 4th century ce The Tolkappiyam a book of grammar and rhetoric and eight anthologies Ettuttokai shanshu Chinese morality books literally good books in Chinese religion popular texts devoted to a moral accounting of actions leading to positive and negative merit These works often combine traditional Confucian notions of filial piety xiao and reciprocity Shaw George Bernard Irish comic dramatist literary critic and socialist propagandist winner of the Nobel Prize for Literature in 1925 Shaw s article on socialism appeared in the 13th edition of the Encyclopædia Britannica Early life and career George Bernard Shaw was shilling shocker a novel of crime or violence especially popular in late Victorian England and originally costing one shilling Shilling shockers were usually characterized by sensational incidents and lurid writing Compare dime novel penny dreadful Shklovsky Viktor Borisovich Russian literary critic and novelist He was a major voice of Formalism a critical school that had great influence in Russian literature in the 1920s Educated at the University of St Petersburg Shklovsky helped found OPOYAZ the Society for the Study Sholokhov Mikhail Aleksandrovich Russian novelist winner of the 1965 Nobel Prize for Literature for his novels and stories about the Cossacks of southern Russia After joining the Red Army in 1920 and spending two years in Moscow he returned in 1924 to his native Cossack village in short story brief fictional prose narrative that is shorter than a novel and that usually deals with only a few characters The short story is usually concerned with a single effect conveyed in only one or a few significant episodes or scenes The form encourages Showalter Elaine American literary critic and teacher and founder of gynocritics a school of feminist criticism concerned with woman as writer with the history themes genres and structures of literature by women Showalter studied English at Bryn Mawr College Sicilian octave an Italian stanza or poem having eight lines of 11 syllables hendecasyllables rhyming abababab The form may have originated in Tuscany about the 13th century though little is known about its origins The Sicilian octave was in use until the 16th Sicilian school group of Sicilian southern Italian and Tuscan poets centred in the courts of Emperor Frederick II 1194 1250 and his son Manfred d 1266 they established the vernacular as opposed to Provençal as the standard language for Italian love poetry sídh in Irish folklore a hill or mound under which fairies live The phrase aos sídhe or the plural sídhe on its own sometimes anglicized as shee can denote fairy folk collectively See also banshee Sidney Sir Philip Elizabethan courtier statesman soldier poet and patron of scholars and poets considered the ideal gentleman of his

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  • Literature - 9 | Britannica.com
    literature body of largely religious and occult writings that has developed since the 7th century when Tibetan became a written language Until the 13th century most Tibetan literary works were skillfully methodical translations from Sanskrit of Buddhist texts tongue twister word or group of words made difficult to articulate by a close sequence of similar consonantal sounds Tongue twisters are often passed on for generations becoming a rich part of folklore Two widely known English language twisters are She sells sea topographical poetry verse genre characterized by the description of a particular landscape A subgenre the prospect poem details the view from a height The form was established by John Denham in 1642 with the publication of his poem Cooper s Hill Topographical poems Torres Bodet Jaime Mexican poet novelist educator and statesman Torres Bodet studied law and literature at the National University of Mexico He later became secretary to the National Preparatory School then chief of the department of public libraries in the Ministry tragedy branch of drama that treats in a serious and dignified style the sorrowful or terrible events encountered or caused by a heroic individual By extension the term may be applied to other literary works such as the novel Although the word tragedy is tragicomedy dramatic work incorporating both tragic and comic elements When coined by the Roman dramatist Plautus in the 2nd century bc the word denoted a play in which gods and men masters and slaves reverse the roles traditionally assigned to them gods and Tranströmer Tomas Swedish lyrical poet noted for his spare but resonant language particularly his unusual metaphors more transformative than substitutive which have been associated with a literary surrealism His verse was at once revelatory and mysterious Tranströmer Trilling Lionel American literary critic and teacher whose criticism was informed by psychological sociological and philosophical methods and insights Educated at Columbia University M A 1926 Ph D 1938 Trilling taught briefly at the University of Wisconsin trilogy a series of three dramas or literary or musical compositions that although each is in one sense complete have a close mutual relation and form one theme or develop aspects of one basic concept The term originally referred specifically to a group of triolet Middle French clover leaf medieval French verse form that consists of eight short lines rhyming ABaAabAB the capital letters indicate lines that are repeated The name triolet is taken from the three repetitions of the first line The great art of troubadour lyric poet of southern France northern Spain and northern Italy writing in the langue d oc of Provence the troubadours flourished from the late 11th to the late 13th century Their social influence was unprecedented in the history of medieval poetry trouvère any of a school of poets that flourished in northern France from the 11th to the 14th century The trouvère was the counterpart in the language of northern France the langue d oïl to the Provençal troubadour from whom the trouvères derived their highly Turkish literature the body of written works in the Turkish language The earliest Turkish literature was produced in Mongol controlled Anatolia during the later 13th century Among the numerous Turkic dynasties of Central Asia South Asia the Middle East and the Caucasus Turkmen literature the body of written works produced by the Turkmen people of Central Asia Reconstructing a literary history of the Turkmen is extremely difficult They did not possess their own educational or literary institutions but instead lived at various times type name in dramatic practice name given to a character to ensure that the personality may be instantly ascertained In England the allegorical morality plays of the late Middle Ages presented characters personifying for example the seven deadly sins being ubi sunt a verse form in which the poem or its stanzas begin with the Latin words ubi sunt where are or their equivalent in another language and which has as a principal theme the transitory nature of all things A well known example is François Villon s Ukrainian literature the body of writings in the Ukrainian language The earliest writings of the Ukrainians works produced in Kievan Rus from the 11th to the 13th century were composed in Church Slavonic and are thus the common literary heritage of the Russians and Belarusians Ulster cycle in ancient Irish literature a group of legends and tales dealing with the heroic age of the Ulaids a people of northeast Ireland from whom the modern name Ulster derives The stories set in the 1st century bc were recorded from oral tradition between Undset Sigrid Norwegian novelist who received the Nobel Prize for Literature in 1928 Her father was an archaeologist and her home life was steeped in legend folklore and the history of Norway Both this influence and her own life story are constantly present in unicorn mythological animal resembling a horse or a kid with a single horn on its forehead The unicorn appeared in early Mesopotamian artworks and it also was referred to in the ancient myths of India and China The earliest description in Greek literature unities in drama the three principles derived by French classicists from Aristotle s Poetics they require a play to have a single action represented as occurring in a single place and within the course of a day These principles were called respectively Urdu literature writings in the Urdu language of the Muslims of Pakistan and northern India It is written in the Perso Arabic script and with a few major exceptions the literature is the work of Muslim writers who take their themes from the life of the Indian subcontinent utopian poetry poetry that describes a utopia or any sort of utopian ideal Sir Thomas More s Utopia 1516 the first printed work to use the term utopia derived from the Greek words for not ou and place topos is for many specialists the major starting point Uzbek literature the body of written works produced by the Uzbek people of Central Asia

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  • Algebra | Britannica.com
    10th century Indian mathematician of the same name He flourished Atiyah Sir Michael Francis British mathematician who was awarded the Fields Medal in 1966 primarily for his work in topology Atiyah received a knighthood in 1983 and the Order of Merit in 1992 He also served as president of the Royal Society 1990 95 Atiyah s father was Lebanese Bhāskara II the leading mathematician of the 12th century who wrote the first work with full and systematic use of the decimal number system Bhāskara II was the lineal successor of the noted Indian mathematician Brahmagupta 598 c 665 as head of an astronomical binomial theorem statement that for any positive integer n the n th power of the sum of two numbers a and b may be expressed as the sum of n 1 terms of the form in the sequence of terms the index r takes on the successive values 0 1 2 n The coefficients Borcherds Richard Ewen British mathematician who won the Fields Medal in 1998 for his work in algebra Borcherds studied undergraduate mathematics at the University of Cambridge and went on to finish his doctorate there in 1983 Afterward he held teaching and research positions Bourbaki Nicolas pseudonym chosen by eight or nine young mathematicians in France in the mid 1930s to represent the essence of a contemporary mathematician The surname selected in jest was that of a French general who fought in the Franco German War 1870 71 The Brauer Richard Dagobert German born American mathematician and educator a pioneer in the development of modern algebra Brauer graduated from the University of Königsberg and received his Ph D in 1925 from the University of Berlin He accepted a teaching position at Königsberg Burnside s problem in group theory a branch of modern algebra problem of determining if a finitely generated periodic group with each element of finite order must necessarily be a finite group The problem was formulated by the English mathematician William Burnside Cardano Girolamo Italian physician mathematician and astrologer who gave the first clinical description of typhus fever and whose book Ars magna The Great Art or The Rules of Algebra is one of the cornerstones in the history of algebra Educated at the universities Cartan Henri French mathematician who made fundamental advances in the theory of analytic functions Son of the distinguished mathematician Élie Cartan Henri Cartan began his academic career as professor of mathematics at the Lycée Caen 1928 29 He was appointed Deligne Pierre René Belgian mathematician who was awarded the Fields Medal 1978 the Crafoord Prize 1988 and the Abel Prize 2013 for his work in algebraic geometry Deligne received a bachelor s degree in mathematics 1966 and a doctorate 1968 from the Free University Descartes s rule of signs in algebra rule for determining the maximum number of positive real number solutions roots of a polynomial equation in one variable based on the number of times that the signs of its real number coefficients change when the

    Original URL path: http://www.britannica.com/topic-browse/Mathematics/Algebra (2016-02-13)
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  • Analysis | Britannica.com
    essence of a contemporary mathematician The surname selected in jest was that of a French general who fought in the Franco German War 1870 71 The Bourgain Jean Belgian mathematician who was awarded the Fields Medal in 1994 for his work in analysis Bourgain received a Ph D from the Free University of Brussels 1977 He held appointments at the Free University 1981 85 jointly at the University of Illinois calculus branch of mathematics concerned with the calculation of instantaneous rates of change differential calculus and the summation of infinitely many small factors to determine some whole integral calculus Two mathematicians Isaac Newton of England calculus of variations branch of mathematics concerned with the problem of finding a function for which the value of a certain integral is either the largest or the smallest possible Many problems of this kind are easy to state but their solutions commonly involve difficult Cauchy Augustin Louis Baron French mathematician who pioneered in analysis and the theory of substitution groups groups whose elements are ordered sequences of a set of things He was one of the greatest of modern mathematicians At the onset of the Reign of Terror 1793 94 Copson Edward Thomas mathematician known for his contributions to analysis and partial differential equations especially as they apply to mathematical physics Copson studied at St John s College Oxford and then was a lecturer of mathematics first at the University of Darboux s theorem in analysis a branch of mathematics statement that for a function f x that is differentiable has derivatives on the closed interval a b then for every x with f a x f b there exists some point c in the open interval a b such Euler Leonhard Swiss mathematician and physicist one of the founders of pure mathematics He not only made decisive and formative contributions to the subjects of geometry calculus mechanics and number theory but also developed methods for solving problems in observational Fefferman Charles Louis American mathematician who was awarded the Fields Medal in 1978 for his work in classical analysis Fefferman attended the University of Maryland B S 1966 and Princeton N J University After receiving his Ph D in 1969 he remained at Princeton Fourier Joseph Baron French mathematician known also as an Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur 1822 The Analytical Theory of Heat He showed how the conduction of heat in solid Fourier transform in mathematics a particular integral transform As a transform of an integrable complex valued function f of one real variable it is the complex valued function f ˆ of a real variable defined by the following equation In the integral equation the function Fréchet Maurice French mathematician known chiefly for his contributions to real analysis He is credited with being the founder of the theory of abstract spaces Fréchet was professor of mechanics at the University of Poitiers 1910 19 before moving to the University functional analysis

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  • Arithmetic | Britannica.com
    b c and a bc ab c that is the terms or factors may be associated in any way desired While associativity Atanasoff John V U S physicist He received his Ph D from the University of Wisconsin With Clifford Berry he developed the Atanasoff Berry Computer 1937 42 a machine capable of solving differential equations using binary arithmetic In 1941 he joined the Naval Cocker Edward reputed English author of Cocker s Arithmetic a famous textbook the popularity of which gave rise to the phrase according to Cocker meaning quite correct Cocker worked very skillfully as an engraver and is mentioned favourably in Samuel Pepys commutative law in mathematics either of two laws relating to number operations of addition and multiplication stated symbolically a b b a and ab ba From these laws it follows that any finite sum or product is unaltered by reordering its terms or distributive law in mathematics the law relating the operations of multiplication and addition stated symbolically a b c ab ac that is the monomial factor a is distributed or separately applied to each term of the binomial factor b c resulting fundamental theorem of arithmetic Fundamental principle of number theory proved by Carl Friedrich Gauss in 1801 It states that any integer greater than 1 can be expressed as the product of prime number s in only one way Karajī al mathematician and engineer who held an official position in Baghdad c 1010 1015 perhaps culminating in the position of vizier during which time he wrote his three main works al Fakhrī fīʾl jabr wa l muqābala Glorious on algebra al Badī fī l hisāb modular arithmetic in its most elementary form arithmetic done with a count that resets itself to zero every time a certain whole number N greater than

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  • Automata Theory | Britannica.com
    thesis proposed Church s thesis a principle formulated by the 20th century American logician Alonzo Church stating that the recursive functions are the only functions that can be mechanically calculated The theorem implies that the procedures of arithmetic cannot be used to decide Hopcroft John Edward American computer scientist and cowinner of the 1986 A M Turing Award the highest honour in computer science for fundamental achievements in the design and analysis of algorithms and data structures In addition Hopcroft made major contributions Rabin Michael Oser German born Israeli American mathematician and computer scientist and cowinner of the 1976 A M Turing Award the highest honour in computer science Rabin and the American mathematician and computer scientist Dana S Scott were cited for their early Scott Dana Stewart American mathematician logician and computer scientist and cowinner of the 1976 A M Turing Award the highest honour in computer science Scott and the Israeli American mathematician and computer scientist Michael O Rabin were cited in the award Stearns Richard Edwin American mathematician and computer scientist and cowinner with American computer scientist Juris Hartmanis of the 1993 A M Turing Award the highest honour in computer science Stearns and Hartmanis were cited

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  • Calculus | Britannica.com
    differentiation in mathematics process of finding the derivative or rate of change of a function In contrast to the abstract nature of the theory behind it the practical technique of differentiation can be carried out by purely algebraic manipulations using three Euler Leonhard Swiss mathematician and physicist one of the founders of pure mathematics He not only made decisive and formative contributions to the subjects of geometry calculus mechanics and number theory but also developed methods for solving problems in observational fundamental theorem of calculus Basic principle of calculus It relates the derivative to the integral and provides the principal method for evaluating definite integrals see differential calculus integral calculus In brief it states that any function that is continuous see continuity integral calculus Branch of calculus concerned with the theory and applications of integral s While differential calculus focuses on rates of change such as slopes of tangent lines and velocities integral calculus deals with total size or value such as lengths areas integration in mathematics technique of finding a function g x the derivative of which Dg x is equal to a given function f x This is indicated by the integral sign as in f x usually called the indefinite integral of the function The symbol length of a curve Geometrical concept addressed by integral calculus Methods for calculating exact lengths of line segments and arcs of circles have been known since ancient times Analytic geometry allowed them to be stated as formulas involving coordinates see coordinate Maclaurin Colin Scottish mathematician who developed and extended Sir Isaac Newton s work in calculus geometry and gravitation A child prodigy he entered the University of Glasgow at age 11 At the age of 19 he was elected a professor of mathematics at Marischal Newton Sir Isaac English physicist and

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  • Combinatorics | Britannica.com
    most prolific mathematician of the 20th century in terms of both the number of problems he solved and the number graph theory branch of mathematics concerned with networks of points connected by lines The subject of graph theory had its beginnings in recreational math problems see number game but it has grown into a significant area of mathematical research with applications Okounkov Andrei Russian mathematician awarded a Fields Medal in 2006 for his contributions bridging probability representation theory and algebraic geometry Okounkov received a doctorate in mathematics from Moscow State University 1995 and has held positions at packing in mathematics a type of problem in combinatorial geometry that involves placement of figures of a given size or shape within another given figure with greatest economy or subject to some other restriction The problem of placement of a given number permutation the various ways in which objects from a set may be selected generally without replacement to form subsets This selection of subsets is called a permutation when the order of selection is a factor a combination when order is not a factor By considering queuing theory subject in operations research that deals with the problem of providing adequate but economical

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