A Catalan is an inhabitant of Catalonia Catalan can also refer to Catalan people Catalan language Pa sos Catalans , territories where catalan is spoken Persons with the surname Catalan Eug ne Charles Catalan , a mathematician Miguel ngel Catal n 1894 1957 , Spanish spectroscopist Moses Chayyim Catalan , a rabbi of Italy Companies and organizations Catalan Communications , a publisher of graphic novels during the 1980s Catalan Company or Catalan Grand Company , a mercenary free company in 14th century Europe Catalan Ornithological Institute In mathematics Catalan number , a concept in mathematics Catalan solid , a concept in mathematics Catalan s conjecture , a theorem conjectured in 1844 and proven in 2002 Catalan s constant , mathematical constant In politics Catalan nationalism Catalan independentism Other uses Catal n crater , a lunar crater named for Miguel ngel Catal n Catalan game , a card game Catalan Atlas , a work of cartography in the 14th century Catalans Dragons , a rugby league football club Catalan forge , an early type of open hearth furnace Catalan Interpunct , an orthographic symbol Catalan Opening , a chess opening Catalan vault , an architectural feature also known as a Catalan arch or a Catalan turn Catalan wine , an alternative name used in France for wine made from the Carignan grape Catalan grape , another name for the wine grape Mourv dre disambig ca Catal desambiguaci de Catalan es Catal n ext Catal n fa fr Catalan homonymie it Catalano nl Catalaans sv Catalan tr Katalan anlam ayr m ... more details
Orphan date September 2010 Catalan charts are a subtype of the medieval period 1300 1500 portolan chart . Portolan charts are a type of map generated by using a mariner s compass and direct observation to determine the shape and location of coastlines and ports. The term portolan means pertaining to ports and harbors and should not be confused with relating to Portugal. Sometimes they are referred to as Catalan type portolans or simply Catalan portolans ref name crone Maps and their Makers, J.C.C ... exist, the Italian, and the Catalan. While both the Italian and Catalan maps derive from the same ..., both in terms of style and in content. Similarities between Italian and Catalan Portolans Image Europe Mediterranean Catalan Atlas.jpeg thumb right 300px A part of the Catalan Atlas. Copied from the Catalan Atlas Catalan Atlas Wiki Page Portolan and Catalan maps all share the characteristic rhumb ... though not to be confused with modern rhumb lines and meridian geography meridian s . Portolan and Catalan ... of latitude longitude . Differences between Italian and Catalan Portolans Scope The Catalan type ... and western Europe. In contrast, the Catalan type portolans extended as far north as Scandinavia ... sea, whereas the Catalan type map also shows other information ref name bagrow History of Cartography ... of Catalan maps which show other details, such as roads or inland cities. One such example is the Catalan Atlas, one of the most important examples of Catalan work. Evolution In general ..., whereas the medieval Catalan map continued to evolve. There are, however, some difficulties in assessing ... from the Catalan style map. Major Catalan maps in history Catalan Atlas Sites of Major Catalan Schools Majorca Majorcan cartographic school Barcelona Major Figures in the Development of Catalan Maps Angelino Dulcert Abraham Cresques See also Catalan Atlas Nautical chart Portolan chart Pa sos Catalans References references DEFAULTSORT Catalan Chart Category Map types ... more details
13178 Catalan provisional designation 1996 HF sub 18 sub is a asteroid belt main belt minor planet . It was discovered by Eric Walter Elst at the La Silla Observatory in Chile on April 18, 1996. It is named after Eug ne Charles Catalan , a French Belgian mathematician of the 19th century. See also List of minor planets 13001&ndash 14000 External links JPL Small Body Beltasteroid stub Minor planets navigator 13177 Hansschmidt 13179 Johncochrane Small Solar System bodies DEFAULTSORT Catalan Category Asteroids named for people Category Astronomical objects discovered in 1996 Category Discoveries by Eric Walter Elst fa it 13178 Catalan hu 13178 Catalan vi 13178 Catalan ... more details
Incomplete date June 2010 Unreferenced date March 2008 IPA notice Catalan Valencian cultural domain image File Catalandialects.png 220px expanded language Northern Catalan lang ca catal septentrional , IPA ca k t a s pt nt iuna IPA , also known as rossellon s is a Catalan language Catalan dialect mostly spoken in Northern Catalonia , but also extending in the northeast part of Southern Catalonia in a transition zone with Central Catalan . As this is an Eastern Catalan dialect, schwa is used in substitution of unstressed IPA a and IPA e , and IPA u substitutes unstressed IPA o . It is also the Catalan dialect with the fewest stressed vowels, only five IPA i e a o u . There are some instances of historic stressed IPA o that has change to IPA u e.g. canig canig . As in Balearic dialect s, final a s are not pronounced in those words ending with ia and containing the stress before the penultimate syllable . Some subdialects keep the typical lo article of North Western Catalan and Occitan language . There is a large body of words imported from French language French and Occitan language Occitan and some grammatical forms such as using the modifier pas , but not the no adverb, in negative sentences, the same as the Occitan language pas is used in other Catalan dialects for emphasising purposes but always with the no particle . Catalan dialects Category Catalan dialects Category Linguistic rights ie lang stub Catalonia stub ca Catal septentrional co Catalanu settentriunale fr Roussillonnais uk ... more details
Image Catalan surface.gif right thumb 600px A Catalan surface. In geometry , a Catalan surface , named after the Belgian mathematician Eug ne Charles Catalan , is a ruled surface all of whose rulings are parallel to a fixed Plane geometry plane . The vector equation of a Catalan surface is given by r s u v L u , where r s u is the space curve and L u is the unit vector of the ruling at u u . All the vectors L u are parallel to the same plane, called the directrix plane of the surface. This can be characterized by the condition the Scalar triple product mixed product L u , L u , L u 0. http books.google.com books?id K31Nzi xhoQC&pg PA279&dq catalan surface&ei 7GFySs2CN5qIlQTCsvSDAQ v onepage&q catalan 20surface&f false The parametric equations of the Catalan surface are http www.mathcurve.com surfaces catalan catalan.shtml math x f u vi u , quad y g u vj u , quad z h u vk u , math If all the rulings of a Catalan surface intersect a fixed line , then the surface is called a conoid . Catalan proved that the helicoid and the Plane geometry plane were the only Ruled surface ruled minimal surfaces . Helicoid See also Ruled surface Conoid References Vladimir Y. Rovenskii, Geometry of curves and surfaces with MAPLE http books.google.com books?id K31Nzi xhoQC&pg PA277&dq conoid maple&lr &ei B9hvSs qKYzSkASR8c3XDg ISBN 978 0 8176 4074 3 A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica , 3rd ed. Boca Raton, FL CRC Press, 2006. http www.crcpress.com ecommerce product product detail.jsf?catno C4487&isbn 0000000000000 ISBN 9781584884484 Category Surfaces Category Geometric shapes geometry stub ar ... more details
winning several shows and contests, the Catalan donkey is called the best donkey in the world , especially ... hair all over the body. Ears straight and pointy. Food grass. Habitat forests. Symbolism image Catalan Donkey 080126 02.jpg thumb right 200px Slippers with a symbol of the catalan donkey. Recently, advocats of Catalan nationalism have adopted the Catalan donkey as a symbol opposite the Toro de Osborne ... and scooters. A few people also do not regard the catalan donkey as a symbol of Catalonia, but only ... races of Catalunya http www.xtec.cat 7Ersimo projecte The Catalan donkey race http www.fuives.com Fuives world center of the Catalan donkey commonscat Catalan Donkey Burro Catal Category Donkeys Category Catalan symbols Category National symbols of Spain Category Pet mammals Category Animal breeds originating in Spain ca Ruc catal de Katalanischer Esel es Burro catal n fr ne catalan gl Burro ... more details
Image Voltacatalana.jpg thumb 240px right An example of Catalan vault in a house in Barcelona The Catalan vault , also called the Catalan turn or Catalan arch or a timbrel vault , is a type of low arch made of plain bricks often used to make a structural floor surface. It is traditionally constructed by laying bricks lengthwise over a wood form or centering , making it a much gentler curve than has generally been produced by other methods of construction. It is a traditional form in Catalonia where it is widely used , and has spread around the world through the work of Catalan architect s such as Gaud Antoni Gaud and Josep Puig i Cadafalch . A study on the stability of the Catalan vault is kept at the archive of the Institute of Catalan Studies, where it is said to have been entrusted by Puig i Cadafalch. Though it is popularly called the Catalan vault, this construction method is found throughout the Mediterranean and the invention of the term Catalan vault occurred in 1904 at an architectural congress in Madrid. The earliest known reference to this vault is from Valencia in 1382. See also Guastavino tile External links Ramage, Michael. http architecture.mit.edu class guastavino features ramage index ramage.htm Construction of a Vault . details the process of constructing a six foot by six foot vault. Category Arches and vaults Category Spanish architecture Category Catalan architecture element arch stub commonscat Volta Catalana ca Volta catalana es B veda catalana pt Ab bada catal ... more details
Unreferenced date May 2011 The Catalan rumba lang ca rumba catalana , IPA ca rumb k t an IPA is a genre of music that developed in Barcelona s Romani community beginning in the 1950s. Its rhythms are derived from the flamenco rumba , with influences from Cuban music and rock and roll . The Catalan rumba originated in the Catalan Romani communities in the Gr cia , carrer street de la Cera del Raval and Hostafrancs neighborhoods. The Romani people in Spain Romani community in those neighborhoods is long established and Catalan language Catalan speaking . The genre is based in a fusion of flamenco singing and the Afro Cuban claves . It is in 4 4 time, and consists of vocalists and handclaps, accompanied by guitar , bongos , and g iro later groups also incorporate timbales , conga drums , small percussion instruments, piano , wind instruments , electric bass , and electric keyboard . Among the most important early artists in the genre were Antonio Gonz lez musician Antonio Gonz lez El Pesca lla , Peret , Josep Maria Valent El Chacho , followed by the duo Los Amaya . In the 1970s, Gato P rez rejuvenated the Catalan rumba. In the 1980s and 1990s, the Gipsy Kings and Los Manolos brought their spirit to Catalan rumba. Recently, popular groups in the genre have included Ai, ai, ai , Sabor de Gr cia , Estopa , El Chinchilla , Melendi , Muchachito Bombo Infierno , Gertrudis , and La Troba Kung F . References Reflist External links http www.flamenco world.com magazine about rumba catalana rumba.htm Article about Catalan rumba DEFAULTSORT Catalan Rumba Category Rumba Category Catalan music Category Spanish music ca Rumba catalana es Rumba catalana oc Romba catalana ... more details
Orphan date November 2006 Infobox Bottled Water brand Vichy Catalan country Spain source Caldes de Malavella type sparkling ph 8.3 ca 14 cl 680 c2 2081 mg 6.4 ni 0.06 k 44 na 1100 s 46 tds 2900 website http www.vichycatalan.es Vichy Catalan is a Spanish brand of carbonated water. The bottler claims it can reduce cholesterol . ref http www.youtube.com watch?v 7e6xN7rsBG8&feature related Advertisement ref Sources Reflist Category Bottled water brands food product stub ar ca Grup Vichy Catalan ... more details
Image Catalan Bay.jpg 220px thumb View of Catalan Bay in the morning looking North from the Caleta Palace Hotel . Catalan Bay lang es La Caleta is a small headlands and bays bay and fishing village in Gibraltar , on the eastern side of Rock of Gibraltar The Rock away from the main city. Etymology The true origin of the name of Catalan Bay is unknown, but a couple of theories exist. The first suggests that the bay is named after a group of around 350 Catalan people Catalan from Catalonia , Spain military men believed to have settled here after having assisted the Anglo Dutch forces who won the History ... on 4 August 1704. However, no evidence exists to prove that Catalans did in fact settle in Catalan Bay ... Discovergibraltar.com Catalan Bay ref The name La Caleta meaning small bay or cove considerably pre dates that of Catalan Bay . The fishing villages of La Tunara La L nea de la Concepci n , Spain ... for much longer than it has ever been called Catalan Bay , the second theory and the most probably ... Catalan Bay ref , third theory suggests that the latter could simply be an English language English mispronounciation of Caleta . ref name DG History File Catalan Bay La Caleta in the late 1800s.jpg 220px thumb Early view of Catalan Bay looking South from the top of the access road late 19th century ... s breast when viewed from the shore. Historically, Catalan Bay had been populated by Genoa Genoese ... name DG During the nineteenth century only fishermen were permitted to live in Catalan Bay . They were ... The beach at Catalan Bay , is the second biggest sandy beach in Gibraltar. It is very popular with both .... Catalan Bay is home to the Caleta Palace Hotel , a number of restaurants specialising in fresh seafood ... Eastern Beach , Gibraltar s largest and most popular sandy beach. Beyond Catalan Bay to the south is the nearby ... of Dudley Ward Tunnel for safety reasons, only reopeing in late 2010. Further reading Catalan ... villages ang Catalan Byht ca Catalan Bay de Catalan Bay es Catalan Bay ... more details
Infobox Ethnic group group flagicon Catalonia Catalan American flagicon USA image caption population Catalan br 1,738 Americans ref http www.census.gov population socdemo ancestry ancestry q by DAC 2000.xls 2000 U.S. Census Bureau, Catalonian ref popplace California Florida Texas New York langs American English Catalan language Catalan Spanish language Spanish rels Roman Catholic Church Roman Catholic predominant Protestantism Protestant Agnosticism Agnostic or Atheism Atheist related European American s Catalan people and other groups of the Catalan diaspora Catalan Americans are citizen s or residents of the United States who acknowledge ethnic Catalan people Catalan ancestry and self identify with it. The group is formed by Catalan people Catalan born naturalized citizens or residents, their descendants and, to a lesser extent, citizens or residents of Catalan descent who still acknowledge Catalan ancestry. The Catalan or Catalonian ancestry is identified with the code 204 in the 2000 United States Census 2000 U.S. Census , with the name Catalonian . A total of 1,738 individuals who received the long form Census questionnaire which is given to 1 in 6 households self identified as Catalan Americans. In the same survey 1,660 people aged 5 or older indicated being able to speak the Catalan language , also with the name Catalonian . Because the long form is a 1 in 6 sample of the population, that figure puts the estimate of Catalan speakers in the U.S. for the year 2000 at around .... In the U.S. Census, people of Catalan ancestry are listed in a group called White american White American . List of Catalan Americans File Nombre de parlants del catal per comtat nord americ ... of Catalan Felipe Alfau , 1902 1999 novelist and poet Thaddeus Amat y Brusi , 1810 1878 Roman ... in the IndyCar Series Expand list date May 2010 See also Catalan people References reflist External ... of Catalan descent Category People of Catalan descent es Catalano estadounidense ... more details
Refimprove date August 2009 Judaeo Catalan lang he n lang ca judeocatal , IPA ca u ewk t a IPA , also called Catalanic or Qatalanit lang he n , lang ca catal nic or qatalanit , was a Jewish language spoken by the Jew ish communities in the northeastern Iberian Peninsula , especially in Catalonia and the Balearic Islands . Linguistically, it shared many features in common with early Shuadit Judaeo Proven al , although historically, ethnically and politically, the Catalanic speaking community was long distinct from the Shuadit speaking community, mostly as a result of the Moors Moorish Al Andalus occupation of Iberia . The golden age of Catalanic was in the period between the early 12th century and 1492, when the Jews were expelled from the kingdoms of Castile and Aragon see Alhambra decree . Today, except for the use of a number of Hebrew language Hebrew loanword s, there is little to distinguish the speech of the Catalan Bnei Anusim and their fellow Jews, from the Catalan language Catalan or Spanish language Spanish spoken by their non Jewish neighbors. See also Jewish languages Judaeo Romance languages Shuadit Catalan language References http www.mishkan.com jewish.lang.european.html http www.mishkan.com jewish.lang.european.html Cite GREC title judeocatal NDCHEC 0118319 Jewish languages Catalan dialects Category Catalan language Category Extinct Romance languages Category Judaeo French languages Category Judaeo Spanish languages Category Languages of Spain ie lang stub Jewish hist stub Catalonia stub an Chodigocatal n br Yuzev katalaneg ca Judeocatal de Jud o Katalanisch es Judeocatal n eu Judukatalan fr Jud o catalan it Giudeo catalano he ja lad Djudeo katalan oc Judeocatalan ru ... more details
Arnaut Catalan floruit fl. 1219&ndash 1253 was a troubadour active in the Languedoc , Catalonia , and Castile historical region Castile . He left behind five Canso song cansos , three tenso s , and one religious song. Arnaut s origins are disputed. Most Catalan people Catalan scholars, such as Mil and Fontanals, believe him to be a Catalan, hence his nickname. Others, such as Chabaneau, assign him to a prominent family from Toulouse named Catalan . If the latter is correct he is probably the same as the Dominican Order Dominican Inquisitor who persecuted Cathars with such force that he was almost killed by a mob in Albi in 1234. The troubadour was probably in Lombardy at the Este court in Caleone between 1221 and 1233. ref An Arnault and Arnaldon are recorded there in this period. ref Four of Arnaut s cansos are dedicated to Beatrice of Savoy , ref Lanquan vinc en Lombardia and Chantan cue brima feunia are examples. ref wife of Raymond Berengar IV of Provence , and one of his tensos was composed with Raymond. ref Amics N Arnautz, cent dompnas d aut paratge . ref An Arnaldus Catalanus, probably Arnaut, confirmed a donation of Raymond s at Aix en Provence on 29 August 1241. In 1252 a Don Arnaldo was in Castile at the court of Alfonso X of Castile Alfonso X , where he composed a tenso with the king, his part being Occitan and the king s Galician Portuguese . Arnaut composed one other tenso with a poet named Vaquier. Notes reflist Sources Riquer, Mart n de . Los trovadores historia literaria y textos . 3 vol. Barcelona Planeta, 1975. DEFAULTSORT Catalan, Arnaut Category People from Toulouse Category Catalan people Category Medieval poets Category Occitan poets Category Troubadours Category 13th century French people it Arnaut Catalan ... more details
notability Organizations date May 2011 primarysources date May 2011 Catalan Unity lang ca Unitat Catalana , IPA ca uni tat k t an IPA is an independence party based in southern France. It represents the Catalan minority in Northern Catalonia . References Reflist See also Republican Left of Catalonia http www.cup.cat Official site France party stub Category Political parties in Catalonia br Unitat Catalana ca Unitat Catalana es Unitat Catalana fr Unitat Catalana gl Unitat Catalana ... more details
Infobox former country native name Estat Catal conventional long name Catalan State common name Catalonia continent Europe era year start 1934 date start October 6 year end 1934 date end October 7 life span 1641 br br 1873 br br 1931 br br 1934 p1 Principality of Catalonia flag p1 Flag of Catalonia.svg s1 Kingdom of France flag s1 Royal Standard of the Kingdom of France.svg p2 First Spanish Republic flag p2 Flag of the First Spanish Republic.svg s2 First Spanish Republic flag s2 Flag of the First Spanish Republic.svg p3 Kingdom of Spain flag p3 Flag of Spain 1785 1873 and 1875 1931 .svg s3 Second Spanish Republic flag s3 Flag of Spain 1931 1939.svg p4 Second Spanish Republic flag p4 Flag of Spain 1931 1939.svg s4 Second Spanish Republic flag s4 Flag of Spain 1931 1939.svg national anthem Els Segadors image flag Flag of Catalonia.svg image map Localitzaci de la CA de Catalunya.png image map caption Map of Catalan State inside Spain common languages Catalan language Catalan capital Barcelona leader1 Pau Claris year leader1 1641 leader2 Estanislau Figueras Citation needed date February 2011 year leader2 1873 leader3 Francesc Maci year leader3 1931 leader4 Llu s Companys i Jover year leader4 1934 government type Republic The Catalan Republic lang ca Rep blica Catalana IPA ca r pub ik k t an ec , IPA ca re pub lika kata lana wc also known as the Catalan State , is an unrecognized state claimed by the Catalan independentism or nationalism. Citation needed date June 2011 The Catalan ... Figueras Estanislau Figueras Citation needed date February 2011 as Catalan State . In 1931, by Francesc Maci as Catalan Republic within Iberian Federation . ref http www.time.com time magazine ... as Catalan State within Spanish Federal Republic . Gallery gallery File Catalonia bank note ...&PGMORI E First Catalan Republic http www.racocatala.cat imat temes republica cat 20.jpeg Third Catalan Republic in The New York Times Category History of Catalonia Category Politics of Catalonia ... more details
Catalan s conjecture occasionally now referred to as Mih ilescu s theorem is a theorem in number theory that was conjectured by the mathematician Eug ne Charles Catalan in 1844 and proven in 2002 by Preda Mih ilescu . 2 sup 3 sup and 3 sup 2 sup are two perfect power power s of natural number s, whose values 8 and 9 respectively are consecutive. The conjecture states that this is the only case of two consecutive powers. That is to say, that the only Diophantine equation solution in the natural numbers of x sup a sup &minus y sup b sup 1 for x , a , y , b > 1 is x 3, a 2, y 2, b 3. History The history ..., this resolved Catalan s conjecture for all but a finite number of cases. However, the finite .... Catalan s conjecture was proved by Preda Mih ilescu in April 2002, so it is now sometimes ... n . See also Tijdeman s theorem St rmer s theorem Fermat Catalan conjecture Beal s conjecture References Catalan, Eugene. 1844 lang fr Note extraite d une lettre adress e l diteur. J. Reine Angew ... Units and a Proof of Catalan s Conjecture journal J. Reine angew. Math. volume 572 year 2004 ... issue 572 mr 2076124 cite book author Paulo Ribenboim authorlink Paulo Ribenboim title Catalan .... cite journal author Robert Tijdeman authorlink Robert Tijdeman title On the equation of Catalan journal ... Catalan s conjecture another old Diophantine problem solved journal Bulletin of the American Mathematical ... author Yuri Bilu title Catalan s conjecture after Mih ilescu journal Ast risque volume 294 year 2004 pages vii, 1&ndash 26 nopp true External links MathWorld urlname CatalansConjecture title Catalan ... Daems http www.math.leidenuniv.nl jdaems scriptie Catalan.pdf A Cyclotomic Proof of Catalan s Conjecture ... Number theory ar cs Catalanova v ta de Catalansche Vermutung es Conjetura de Catalan fr Th or me de Catalan ko it Teorema di Mih ilescu hu Catalan sejt s nl Vermoeden van Catalan ja pl Twierdzenie Mih ilescu ro Conjectura lui Catalan sl Catalanova domneva fi Catalanin ... more details
Infobox chess opening openingname Catalan Opening image Chess diagram rd nd bd qd kd bd rd pd pd pd pd pd pd pd nd pd pl pl pl pl pl pl pl bl pl rl nl bl ql kl nl rl moves 1.d4 Nf6 2.c4 e6 3.g3 d5 4.Bg2 ECO E01 E09 birth Barcelona , 1929, by Savielly Tartakower nameorigin Catalonia parentopening Indian ... The Catalan is a chess opening which can be considered to be White adopting a mixture ... ECO codes E01 E09 are for the Catalan. algebraic notation pos tocleft Black has two main approaches to choose between in the Open Catalan he plays ...dxc4 and can either try to hold onto the pawn with ...b5 or give it back for extra time to free his game. In the Closed Catalan, Black does not capture ... Kramnik , the Catalan has recently gained a good deal of attention by high level GMs. Another of its ... scored 2. The Catalan derives its name from Catalonia a region of Spain after tournament organisers ... chess transposed into an Open Catalan. In 2004, Ruben Felgaer won a tournament celebrating the 75th anniversary of Barcelona 1929 and the birth of the Catalan Opening, ahead of International ..., began with the moves 1.d4 d5 2.c4 e6 3.g3 Nf6. Open Catalan, Classical Line Chess diagram tright rd nd bd qd kd rd pd pd pd bd pd pd pd pd nd pd pl nl pl pl pl pl pl bl pl rl nl bl ql kl rl Catalan, Open, Classical line The Catalan, Open, Classical line begins 1.d4 Nf6 2.c4 e6 3.g3 d5 4.Bg2 dxc4 5.Nf3 ... stymies Black s queenside development. The Open Catalan line here has been a favorite of Anatoly ... Further reading wikibooks Chess Opening Theory 1. d4 1...Nf6 2. c4 2...e6 3. g3 Catalan Opening cite book author Neishtadt, Yakov year 1987 title Play the Catalan Open Variation publisher Pergamon isbn 0080297412 cite book author Dunnington, Angus year 1998 title Winning With the Catalan publisher ... Play the Catalan publisher Everyman Chess isbn 9781857445916 http brooklyn64.com 2010 ideas for black against the catalan 4 bb4 Ideas for Black against the Catalan 4...Bb4 Category Chess openings Category ... more details
In mathematics , Catalan s problem asks the number of ways n 1 factors can be completely parenthesized by n pairs of parentheses. For example, the following are the 14 ways that 5 factors can be parenthesized tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt tt 1 2 3 4 5 tt The numbers of ways of performing these pairings are the Catalan number s. See also Catalan number Eug ne Charles Catalan References cite book last Gardner first Martin authorlink Martin Gardner coauthors title Time Travel and Other Mathematical Bewilderments publisher W.H. Freeman and Company date 1988 location New York pages p. 256 url doi id isbn 0 7167 1924 X MathWorld title Catalan s Problem urlname CatalansProblem Category Enumerative combinatorics numtheory stub es Problema de Catalan tr Catalan problemi ... more details
The Catalan counties lang ca Comtats catalans , IPA ca kum tats k t ans IPA were the administrative divisions of the eastern Carolingian Marca Hispanica created after its Franks Frankish conquest. The various counties roughly defined what came to be known as the Principality of Catalonia . In 778, Charlemagne led his first expedition into Hispania . The territory that he subjugated to his rule was the kernel of Catalonia. In 781, he created his son Louis the Pious King of Aquitaine with the mandate to defend and extend the southern border against the Moors . In 785, Rostaing was made Count of Girona , the first of the established Catalan counties. In 797, in the greatest military triumph of his long career, the young Louis took Barcelona , the greatest city of the Catalan littoral. In 798, county of Urgell Urgell , county of Osona Osona , and county of Cerdanya Cerdanya were established under Borrell of Ausona Borrell . In 801, the greatest of the counties, Barcelona, was established under Bera, Count of Barcelona Bera . Barcelona soon overshadowed the other counties in importance, especially through the reign of Wilfred the Hairy in the late ninth century. At that time, the power of the Carolingians was waning and the neglected Hispanic march was practically independent of royal authority. In the early eleventh century, Berenguer Ramon I, Count of Barcelona , was able to submit to Sancho III of Navarre as his suzerain, even though he was still legally a vassal of Robert II ..., most of the Catalan counts had refused to do homage to the new dynasty. In the next century, most of the Catalan counties would come into the hands of the counts of Barcelona. They, in their own turn ..., creating the Crown of Aragon . Several of the later kings re created some Catalan counties ... of Rossell County of Urgell Timeline Chronology of the Catalan counties External links http www.tvcatalunya.com ... comtats catalans. Catalan . Category Medieval Catalan and Occitan history Category Counties by country ... more details
In mathematics , Catalan s constant G , which occasionally appears in estimates in combinatorics , is defined ... whether G is irrational number irrational , let alone transcendental number transcendental . Catalan s constant was named after Eug ne Charles Catalan . Integral identities Some identities include ... function, math pi 2 math and Catalan s constant these are expressible as paths on a graph. It also ... for fast evaluation of the Catalan constant is constructed by E. Karatsuba ref E.A. Karatsuba, Fast ... . Known digits The number of known digits of Catalan s constant G has increased dramatically during ... decimal digits of Catalan s constant G Date Decimal digits Computation performed by 1832 16 Thomas ... Catalan 1877 20 James Whitbread Lee Glaisher James W. L. Glaisher 1913 32 James Whitbread Lee Glaisher ... articles catalan catalan.htm 33 representations for Catalan s constant undated cite journal first1 ... associated with Catalan s constant mr 1929434 Simon Plouffe, http www.lacim.uqam.ca plouffe IntegerRelations identities3a.html A few identities III with Catalan , 1993 Provides over one hundred different ... A few identities with Catalan constant and Pi 2 , 1999 Provides a graphical interpretation of the relations MathWorld title Catalan s Constant urlname CatalansConstant http functions.wolfram.com Constants Catalan 06 01 Catalan constant Generalized power series at the Wolfram Functions Site Greg Fee, http www.gutenberg.org etext 682 Catalan s Constant Ramanujan s Formula 1996 Provides the first 300,000 digits of Catalan s constant. . Cite journal first1 David M. last1 Bradley title A class of series acceleration formulae for Catalan s constant doi 10.1023 A 1006945407723 year 1999 journal The Ramanujan ... Bradley title A class of series acceleration formulae for Catalan s constant eprint 0706.0356 year 2007 Citation first1 David M. last1 Bradley title Representations of Catalan s constant url http citeseerx.ist.psu.edu ... Combinatorics Category Mathematical constants ar ca Constant de Catalan de Catalansche ... more details
de Catalunya ref rels Roman Catholic Church Roman Catholicism , Atheism , Agnosticism langs Catalan language Catalan native Spanish language Spanish and French language French as a result of immigration ... Nord , and in France as the Pays Catalan are sometimes included in this definition. ref http www.mairie ... des Pyr n es Orientales fr ca ref Also, sometimes Catalan is used to define peoples from Catalan Countries , which include other areas where the Catalan language is spoken. Extended concept The other Catalan language Catalan speaking peoples, namely Andorran s, Valencian Community Valencians , Balearic ... as a distinct Catalan ethnic group by certain nationalists. ref http www.enciclopedia.cat fitxa v2.jsp?NDCHEC 0167848 Definition of Catalan people in GREC . Accessed 29 April 2009 ref The latter assertion is especially rooted in Catalan nationalism . Citation needed date February 2011 In the aforementioned territories often designated Pa sos Catalans , Catalan Countries , by Catalan nationalism Catalan nationalists . This extended concept is unpopular and brings eventual conflict, most of all ... merged with Roman colonists from the Italian peninsula . An early precursor to the Catalan language ... forces over most of Catalonia by the year 801. It was during this period that a Catalan national ... War . This latter conflict embroiled Spain in a larger war with France as many Catalan nobles allied ... strip of the March came under French rule, while the rest remained under Spanish hegemony . The Catalan ... Succession that started in 1705AD and ended in 1714AD. The Catalan failure to defend the perpetuation ... integrated many Catalans into French society, while in Spain a Catalan identity was increasingly ... Catalan speakers live in the pays catalan in France. An indeterminate number of Catalans emigrated ... autonomy, leading to reinforcement of a Catalan identity. Language Main Languages of Catalonia The Catalan ... language Aragonese . There are a number of linguistic varieties that are considered Catalan language ... more details
Catalan speaking world image Image Tirant lo blanc.jpg 200px caption Tirant lo Blanc , by Joanot Martorell , br the 1490 edition expanded Arts Catalan literature is the name conventionally used to refer to literature written in the Catalan language . The Catalan literary tradition is extensive, starting ... century, Renaixen a , classified Catalan literature in periods. The centuries long chapter known as Decad ncia ... of this early modern age is taking place. Catalan literature reemerged in the 19th century ... intellectuals were forced into exile and Catalan culture couldn t find its place in Catalonia until the Spanish transition to democracy restoration of democracy in Spain . Middle Ages Origins Catalan ... from Latin. Literary use of the Catalan language is generally said to have started with the religious ... the earlier Can de Santa Fe , from 1054&ndash 76, may be Catalan or Occitan . Another early Catalan poem is the mid thirteenth century Augats, sey s qui credets D u lo Payre , a planctus Mariae ... in the Catalan language is not only saluted for starting a Catalan literary tradition clearly separated ... language was the lyric poetry of the troubadours , who composed in Occitan . Since Occitan and Catalan ... composed in the Occitan poetic koin . The first Catalan troubadour trobadors may be Berenguier de ... . The most prolific Catalan troubadour during the ascendancy of Occitan as language of literature ... s earlier work. A third Catalan treatise on the language of the troubadours and composing lyric ... romance was among its time s most influential novels, and possibly the last major book in Catalan ... , has been termed La Decad ncia , the decadent period in Catalan literature because of a general falling ..., even in lands of the Catalan Aragonese Empire, which led to a cultural void. The Catalan language decadence accompanied the Catalan commercial influence in the Spanish Empire , in which the use ... Islands chose Spanish language Spanish as their language, and wouldn t resort to using the Catalan ... more details
Image Europe Mediterranean Catalan Atlas.jpeg thumb right 300px A part of the Catalan Atlas, shown in a modern orientation. The Catalan Atlas 1375 is the most important Catalonia Catalan map of the medieval period. ref name The Jewish Contribution To Civilization ref name The late medieval age of crisis and renewal, 1300 1500 It was produced by the Majorcan cartographic school and is attributed to Cresques Abraham also known as Abraham Cresques , a Jewish book Illuminated manuscript illuminator who was self described as being a master of the maps of the world as well as compasses. ref name To the Ends of the Earth 100 Maps that Change the World It has been in the royal library of France now the Biblioth que nationale de France since the time of Charles V of France Charles V . The Catalan Atlas originally consisted of 6 vellum leaves folded down the middle, painted in various colors including gold and silver. The leaves are now cut in half. Each half leaf is mounted on one side of five wooden ... cm. The overall size is therefore 65 × 300 cm. Image Compass rose from Catalan Atlas 1375 .jpg thumb right 150px Detail of Catalan Atlas, the first compass rose depicted on a map. The first two leaves contain texts in Catalan language covering cosmography , astronomy , and astrology ..., while others are indicated in black. Unlike many other nautical charts, the Catalan Atlas is read ... East to the Atlantic. The first two leaves, forming the oriental portion of the Catalan Atlas ... F W Publications Inc. ref External links commonscat Catalan Atlas http expositions.bnf.fr ciel catalan index.htm Biblioth que nationale de France L Atlas Catalan fr http web.archive.org web 20080206170425 www.bnf.fr enluminures texte atx2 07.htm The Catalan Atlas en via archive.org http www.cresquesproject.net ... balears index.php?section gallery&cid 1&pId 5 details of Catalan Atlas close up from Contemporary Balears ... Atlas catalan it Atlante catalano nl Catalaanse Wereldatlas pl Atlas Katalo ski pt Atlas Catal o ru ... more details
Image Llu s Pujals Tible.jpg 300px right In music, a Catalan shawm is one of two varieties of shawm an oboe like woodwind instrument played in Catalonia in northeastern Spain. Region, types, and uses The types of shawm commonly used in Catalonia are the tible IPA ca tib pron , Catalan language Catalan for treble and the tenora IPA ca t no pron , Catalan for tenor . The tenora is pitched about a fifth lower than the tible. These shawms are usually used with other instruments to accompany the traditional Catalan circle dance, the Sardana . Other Catalan folk shawms are the tarota IPA ca t t pron the original keyless version of the tible , and the gralla IPA ca g a pron , a short, strident instrument with a steep conical bore. Both of these resemble shawms from other parts of Spain, such as the dulzaina dol aina of Aragon and Valencia, and both employ open fingering. Difference between shawms and oboes There are several distinct differences between shawms and oboe s. Shawms normally have a larger bore, which makes them louder and more suitable than the oboe for outdoor playing. In addition, the bore is more sword shaped than that of the oboe it is more like a narrow parabola than a perfect cone . This gives the shawm a stronger, earthier, more fiery tone. Though favored in ancient times, some today find the sound harsh and irritating. The difference in bore shape also gives shawms additional problems with Intonation music intonation . It was the goals of easier fingering, better intonation, and a sound and volume level more suitable for indoor use that prompted the innovations ... the shawms very durable. Catalan shawms and other types of shawms There are many shawms throughout ... usuarios.lycos.es sdiago tibleweb.htm Tibleweb Tible web site in Catalan http www.coblasabadell.com index2 archivos eltible.htm El Tible in Catalan Video http www.sai national.org phil composers dharris.html Video of Catalan shawm band Doublereed Category Catalan musical instruments Category Single ... more details
Infobox language name Catalan, Valencian nativename catal , valenci pronunciation IPA ca k t a Eastern Catalan EC IPA ca kata la Western Catalan WC br IPA ca valensi a Valencian V states flag Andorra ... distribution of Catalan speakers 11.5 million see also sources and links in the section Number of Catalan speakers below ref ref name number of speakers ethnologue cat . ref date 2006 familycolor ... ref name alternative classification Some Iberian scholars may alternatively classify Catalan as an Iberian ... Occitano Romance ref name alternative classification stand1 Catalan orthography Catalan stand2 Valencian orthography Valencian script Latin script Latin Catalan alphabet nation Andorra br Spain Catalonia ... e map Global Catalan Countries.svg mapsize 260 notice IPA Catalan IPAc en icon k t l n , IPAc en k t l n , or IPAc en k t l n ref http dictionary.reference.com browse CatalanCatalan ... language of the department Pyr n es Orientales ref name Charte en faveur du Catalan since 2007, Catalan has no official recognition in France, as French is the only official language of that country ..., 1958 Article 2. The language of the Republic shall be French. ref History Middle Ages origin The Catalan ... and Catalan Reconquista conquests of Al Andalus to the south and to the west, the language ... century, during the ca Segle d or valenci Valencian Golden Age , Catalan literature reached ... , a royal decree by Louis XIV of France on 2 April 1700 prohibited the use of Catalan language ... against, the nonstandard languages of France patois such as Catalan, Breton, Occitan and Basque. The deliberate ... Catalan as one of the languages of the department in the Article 1 a of its Charte en faveur du Catalan ref name Charte en faveur du Catalan Cite web url http www.cg66.fr 202 charte en faveur du catalan.htm title Charte en faveur du Catalan Cite web url http www.cg66.fr 199 la catalanitat a catalunya ... with the French language, Catalan as a language of the department. lang fr Le Conseil G n ral des Pyr n es ... more details
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