/Users/andrea/_magisterarbeit/korpus/clean/testkorpus/22/file16.html NN ----------------------------------------- : mess NN . SENT function NN win VVP 1 CD file NN , , h NN , , v NN if IN v NN screen NN . SENT height NN v NN screen NN . SENT height NN 50 CD . SENT aWindow NN window NN . SENT open JJ file NN . SENT html NN , , win VV , , toolbar NP 0 CD , , status NN 0 CD , , scrollbars NNS 1 CD , , location NN 0 CD , , resizable JJ 1 CD , , menubar NP 1 CD , , screenx NN 0 CD , , screeny NN 0 CD , , width NN h NN , , height NN v NN . SENT windowstatus NN 1 CD . SENT if IN window NN . SENT focus NN aWindow NN . SENT focus NN function NN hidepic JJ if IN windowstatus NN 1 CD if IN aWindow NN . SENT location NN aWindow NN . SENT close NN . SENT windowstatus NN 0 CD . SENT End NP Leonardo NP Pisano NP Fibonacci NP Born NP . SENT 1170 CD in IN probably RB Pisa NP now RB in IN Italy NP Died VVD . SENT 1250 CD in IN possibly RB Pisa NP now RB in IN Italy NP Click NP the DT picture NN above IN to TO see VV two CD larger JJR pictures NNS Show NN birthplace NN location NN Previous JJ Chronologically RB Next JJ Biographies NNS Index NN Previous JJ Alphabetically RB Next JJ Main NP index NN Version NP for IN printing VVG Leonardo NP Pisano NP is VBZ better RBR known VVN by IN his PP$ nickname NN Fibonacci NP . SENT He PP was VBD the DT son NN of IN Guilielmo NP and CC a DT member NN of IN the DT Bonacci NP family NN . SENT Fibonacci NP himself PP sometimes RB used VVD the DT name NN Bigollo NP , , which WDT may MD mean VV good JJ for IN nothing NN or CC a DT traveller NN . SENT As IN stated VVN in IN 1 CD . SENT Did VVD his PP$ countrymen NNS wish VVP to TO express VV by IN this DT epithet NN their PP$ disdain NN for IN a DT man NN who WP concerned VVD himself PP with IN questions NNS of IN no DT practical JJ value NN , , or CC does VVZ the DT word NN in IN the DT Tuscan JJ dialect NN mean VV a DT much JJ travelled JJ man NN , , which WDT he PP was VBD . SENT Fibonacci NP was VBD born VVN in IN Italy NP but CC was VBD educated VVN in IN North NP Africa NP where WRB his PP$ father NN , , Guilielmo NP , , held VVD a DT diplomatic JJ post NN . SENT His PP$ father's NNS job NN was VBD to TO represent VV the DT merchants NNS of IN the DT Republic NP of IN Pisa NP who WP were VBD trading VVG in IN Bugia NP , , later RBR called VVN Bougie NP and CC now RB called VVN Bejaia NP . SENT Bejaia NP is VBZ a DT Mediterranean NP port NN in IN northeastern JJ Algeria NP . SENT The DT town NN lies VVZ at IN the DT mouth NN of IN the DT Wadi NN Soummam NP near IN Mount NP Gouraya NP and CC Cape NP Carbon NP . SENT Fibonacci NP was VBD taught VVN mathematics NN in IN Bugia NP and CC travelled VVD widely RB with IN his PP$ father NN and CC recognised VVD the DT enormous JJ advantages NNS of IN the DT mathematical JJ systems NNS used VVN in IN the DT countries NNS they PP visited VVD . SENT Fibonacci NP writes VVZ in IN his PP$ famous JJ book NN Liber NP abaci NNS 1202 CD . SENT When WRB my PP$ father NN , , who WP had VHD been VBN appointed VVN by IN his PP$ country NN as IN public JJ notary NN in IN the DT customs NNS at IN Bugia NP acting VVG for IN the DT Pisan NP merchants NNS going VVG there RB , , was VBD in IN charge NN , , he PP summoned VVD me PP to TO him PP while IN I PP was VBD still RB a DT child NN , , and CC having VHG an DT eye NN to TO usefulness NN and CC future JJ convenience NN , , desired VVD me PP to TO stay VV there RB and CC receive VV instruction NN in IN the DT school NN of IN accounting NN . SENT There RB , , when WRB I PP had VHD been VBN introduced VVN to TO the DT art NN of IN the DT Indians NPS nine CD symbols NNS through IN remarkable JJ teaching NN , , knowledge NN of IN the DT art NN very RB soon RB pleased VVN me PP above IN all DT else JJ and CC I PP came VVD to TO understand VV it PP , , for IN whatever WDT was VBD studied VVN by IN the DT art NN in IN Egypt NP , , Syria NP , , Greece NP , , Sicily NP and CC Provence NP , , in IN all PDT its PP$ various JJ forms NNS . SENT Fibonacci NP ended VVD his PP$ travels NNS around IN the DT year NN 1200 CD and CC at IN that DT time NN he PP returned VVD to TO Pisa NP . SENT There RB he PP wrote VVD a DT number NN of IN important JJ texts NNS which WDT played VVD an DT important JJ role NN in IN reviving VVG ancient JJ mathematical JJ skills NNS and CC he PP made VVD significant JJ contributions NNS of IN his PP$ own JJ . SENT Fibonacci NP lived VVD in IN the DT days NNS before IN printing NN , , so RB his PP$ books NNS were VBD hand RB written VVN and CC the DT only JJ way NN to TO have VH a DT copy NN of IN one CD of IN his PP$ books NNS was VBD to TO have VH another DT hand NN written JJ copy NN made VVD . SENT Of IN his PP$ books NNS we PP still RB have VHP copies NNS of IN Liber NP abaci NNS 1202 CD , , Practica NP geometriae NNS 1220 CD , , Flos NP 1225 CD , , and CC Liber NP quadratorum NN . SENT Given VVN that IN relatively RB few JJ hand NN made VVD copies NNS would MD ever RB have VH been VBN produced VVN , , we PP are VBP fortunate JJ to TO have VH access NN to TO his PP$ writing NN in IN these DT works NNS . SENT However RB , , we PP know VVP that IN he PP wrote VVD some DT other JJ texts NNS which WDT , , unfortunately RB , , are VBP lost VVN . SENT His PP$ book NN on IN commercial JJ arithmetic NN Di NP minor JJ guisa NN is VBZ lost VVN as RB is VBZ his PP$ commentary NN on IN Book NP X NP of IN Euclid's NP Elements NNS which WDT contained VVD a DT numerical JJ treatment NN of IN irrational JJ numbers NNS which WDT Euclid NP had VHD approached VVN from IN a DT geometric JJ point NN of IN view NN . SENT One PP might MD have VH thought VVN that IN at IN a DT time NN when WRB Europe NP was VBD little RB interested VVN in IN scholarship NN , , Fibonacci NP would MD have VH been VBN largely RB ignored VVN . SENT This DT , , however RB , , is VBZ not RB so RB and CC widespread JJ interest NN in IN his PP$ work NN undoubtedly RB contributed VVD strongly RB to TO his PP$ importance NN . SENT Fibonacci NP was VBD a DT contemporary JJ of IN Jordanus NP but CC he PP was VBD a DT far RB more RBR sophisticated JJ mathematician NN and CC his PP$ achievements NNS were VBD clearly RB recognised VVN , , although IN it PP was VBD the DT practical JJ applications NNS rather RB than IN the DT abstract JJ theorems NNS that WDT made VVD him PP famous JJ to TO his PP$ contemporaries NNS . SENT The DT Holy NP Roman NP emperor NN was VBD Frederick NP II NP . SENT He PP had VHD been VBN crowned VVN king NN of IN Germany NP in IN 1212 CD and CC then RB crowned VVN Holy NP Roman NP emperor NN by IN the DT Pope NP in IN St NP Peter's NP Church NP in IN Rome NP in IN November NP 1220 CD . SENT Frederick NP II NP supported VVD Pisa NP in IN its PP$ conflicts NNS with IN Genoa NP at IN sea NN and CC with IN Lucca NP and CC Florence NP on IN land NN , , and CC he PP spent VVD the DT years NNS up RB to TO 1227 CD consolidating VVG his PP$ power NN in IN Italy NP . SENT State NN control NN was VBD introduced VVN on IN trade NN and CC manufacture NN , , and CC civil JJ servants NNS to TO oversee VV this DT monopoly NN were VBD trained VVN at IN the DT University NP of IN Naples NP which WDT Frederick NP founded VVD for IN this DT purpose NN in IN 1224 CD . SENT Frederick NP became VVD aware JJ of IN Fibonacci's NP work NN through IN the DT scholars NNS at IN his PP$ court NN who WP had VHD corresponded VVD with IN Fibonacci NP since IN his PP$ return NN to TO Pisa NP around IN 1200 CD . SENT These DT scholars NNS included VVD Michael NP Scotus NN who WP was VBD the DT court NN astrologer NN , , Theodorus NP Physicus NP the DT court NN philosopher NN and CC Dominicus NP Hispanus NN who WP suggested VVD to TO Frederick NP that IN he PP meet VV Fibonacci NP when WRB Frederick's NP court NN met VVD in IN Pisa NP around IN 1225 CD . SENT Johannes NNS of IN Palermo NP , , another DT member NN of IN Frederick NP II's NP court NN , , presented VVD a DT number NN of IN problems NNS as IN challenges NNS to TO the DT great JJ mathematician NN Fibonacci NP . SENT Three CD of IN these DT problems NNS were VBD solved VVN by IN Fibonacci NP and CC he PP gives VVZ solutions NNS in IN Flos NP which WDT he PP sent VVD to TO Frederick NP II NP . SENT We PP give VVP some DT details NNS of IN one CD of IN these DT problems NNS below RB . SENT After IN 1228 CD there RB is VBZ only RB one CD known JJ document NN which WDT refers VVZ to TO Fibonacci NP . SENT This DT is VBZ a DT decree NN made VVN by IN the DT Republic NP of IN Pisa NP in IN 1240 CD in IN which WDT a DT salary NN is VBZ awarded VVN to TO . SENT . SENT . SENT . SENT the DT serious JJ and CC learned VVD Master NP Leonardo NP Bigollo NP . SENT . SENT . SENT . SENT This DT salary NN was VBD given VVN to TO Fibonacci NP in IN recognition NN for IN the DT services NNS that IN he PP had VHD given VVN to TO the DT city NN , , advising VVG on IN matters NNS of IN accounting VVG and CC teaching VVG the DT citizens NNS . SENT Liber NN abaci NNS , , published VVN in IN 1202 CD after IN Fibonacci's NP return NN to TO Italy NP , , was VBD dedicated VVN to TO Scotus NN . SENT The DT book NN was VBD based VVN on IN the DT arithmetic NN and CC algebra NN that IN Fibonacci NP had VHD accumulated VVN during IN his PP$ travels NNS . SENT The DT book NN , , which WDT went VVD on RP to TO be VB widely RB copied VVN and CC imitated VVN , , introduced VVD the DT Hindu NP Arabic NP place NN valued VVD decimal JJ system NN and CC the DT use NN of IN Arabic NP numerals NNS into IN Europe NP . SENT Indeed RB , , although IN mainly RB a DT book NN about IN the DT use NN of IN Arab JJ numerals NNS , , which WDT became VVD known VVN as IN algorism NN , , simultaneous JJ linear JJ equations NNS are VBP also RB studied VVN in IN this DT work NN . SENT Certainly RB many JJ of IN the DT problems NNS that IN Fibonacci NP considers VVZ in IN Liber NP abaci NNS were VBD similar JJ to TO those DT appearing VVG in IN Arab JJ sources NNS . SENT The DT second JJ section NN of IN Liber NP abaci NNS contains VVZ a DT large JJ collection NN of IN problems NNS aimed VVN at IN merchants NNS . SENT They PP relate VVP to TO the DT price NN of IN goods NNS , , how WRB to TO calculate VV profit NN on IN transactions NNS , , how WRB to TO convert VV between IN the DT various JJ currencies NNS in IN use NN in IN Mediterranean NP countries NNS , , and CC problems NNS which WDT had VHD originated VVN in IN China NP . SENT A DT problem NN in IN the DT third JJ section NN of IN Liber NP abaci NNS led VVD to TO the DT introduction NN of IN the DT Fibonacci NP numbers NNS and CC the DT Fibonacci NP sequence NN for IN which WDT Fibonacci NP is VBZ best RBS remembered VVN today NN . SENT A DT certain JJ man NN put VVD a DT pair NN of IN rabbits NNS in IN a DT place NN surrounded VVN on IN all DT sides NNS by IN a DT wall NN . SENT How WRB many JJ pairs NNS of IN rabbits NNS can MD be VB produced VVN from IN that DT pair NN in IN a DT year NN if IN it PP is VBZ supposed VVN that IN every DT month NN each DT pair NN begets VVZ a DT new JJ pair NN which WDT from IN the DT second JJ month NN on IN becomes VVZ productive JJ . SENT The DT resulting VVG sequence NN is VBZ 1 CD , , 1 CD , , 2 CD , , 3 CD , , 5 CD , , 8 CD , , 13 CD , , 21 CD , , 34 CD , , 55 CD , , . SENT . SENT . SENT Fibonacci NP omitted VVD the DT first JJ term NN in IN Liber NP abaci NNS . SENT This DT sequence NN , , in IN which WDT each DT number NN is VBZ the DT sum NN of IN the DT two CD preceding JJ numbers NNS , , has VHZ proved VVN extremely RB fruitful JJ and CC appears VVZ in IN many JJ different JJ areas NNS of IN mathematics NN and CC science NN . SENT The DT Fibonacci NP Quarterly JJ is VBZ a DT modern JJ journal NN devoted VVN to TO studying VVG mathematics NNS related VVN to TO this DT sequence NN . SENT Many JJ other JJ problems NNS are VBP given VVN in IN this DT third JJ section NN , , including VVG these DT types NNS , , and CC many JJ many JJ more JJR . SENT A DT spider NN climbs VVZ so RB many JJ feet NNS up IN a DT wall NN each DT day NN and CC slips VVZ back RB a DT fixed JJ number NN each DT night NN , , how WRB many JJ days NNS does VVZ it PP take VV him PP to TO climb VV the DT wall NN . SENT A DT hound NN whose WP$ speed NN increases NNS arithmetically RB chases VVZ a DT hare NN whose WP$ speed NN also RB increases VVZ arithmetically RB , , how WRB far RB do VVP they PP travel VVP before IN the DT hound NN catches VVZ the DT hare NN . SENT Calculate VV the DT amount NN of IN money NN two CD people NNS have VHP after IN a DT certain JJ amount NN changes NNS hands NNS and CC the DT proportional JJ increase NN and CC decrease NN are VBP given VVN . SENT There EX are VBP also RB problems NNS involving VVG perfect JJ numbers NNS , , problems NNS involving VVG the DT Chinese JJ remainder NN theorem NN and CC problems NNS involving VVG summing VVG arithmetic NN and CC geometric JJ series NN . SENT Fibonacci NP treats VVZ numbers NNS such JJ as IN 10 CD in IN the DT fourth JJ section NN , , both CC with IN rational JJ approximations NNS and CC with IN geometric JJ constructions NNS . SENT A DT second JJ edition NN of IN Liber NP abaci NNS was VBD produced VVN by IN Fibonacci NP in IN 1228 CD with IN a DT preface NN , , typical JJ of IN so RB many JJ second JJ editions NNS of IN books NNS , , stating VVG that IN . SENT . SENT . SENT . SENT new JJ material NN has VHZ been VBN added VVN to TO the DT book NN from IN which WDT superfluous JJ had VHD been VBN removed VVN . SENT . SENT . SENT Another DT of IN Fibonacci's NP books NNS is VBZ Practica NP geometriae NNS written VVN in IN 1220 CD which WDT is VBZ dedicated VVN to TO Dominicus NP Hispanus NN whom WP we PP mentioned VVD above RB . SENT It PP contains VVZ a DT large JJ collection NN of IN geometry NN problems NNS arranged VVN into IN eight CD chapters NNS with IN theorems NNS based VVN on IN Euclid's NP Elements NNS and CC Euclid's NNS On IN Divisions NNS . SENT In IN addition NN to TO geometrical JJ theorems NNS with IN precise JJ proofs NNS , , the DT book NN includes VVZ practical JJ information NN for IN surveyors NNS , , including VVG a DT chapter NN on IN how WRB to TO calculate VV the DT height NN of IN tall JJ objects NNS using VVG similar JJ triangles NNS . SENT The DT final JJ chapter NN presents VVZ what WP Fibonacci NP called VVD geometrical JJ subtleties NNS 1 CD . SENT Among IN those DT included VVN is VBZ the DT calculation NN of IN the DT sides NNS of IN the DT pentagon NN and CC the DT decagon NN from IN the DT diameter NN of IN circumscribed VVN and CC inscribed VVN circles NNS . SENT the DT inverse JJ calculation NN is VBZ also RB given VVN , , as RB well RB as RB that IN of IN the DT sides NNS from IN the DT surfaces VVZ . SENT . SENT . SENT . SENT to TO complete VV the DT section NN on IN equilateral JJ triangles NNS , , a DT rectangle NN and CC a DT square NN are VBP inscribed VVN in IN such PDT a DT triangle NN and CC their PP$ sides NNS are VBP algebraically RB calculated VVN . SENT . SENT . SENT In IN Flos NP Fibonacci NP gives VVZ an DT accurate JJ approximation NN to TO a DT root NN of IN 10 CD x SYM 2 CD x NN 2 CD x SYM 3 CD 20 CD , , one CD of IN the DT problems NNS that IN he PP was VBD challenged VVN to TO solve VV by IN Johannes NP of IN Palermo NP . SENT This DT problem NN was VBD not RB made VVN up RP by IN Johannes NP of IN Palermo NP , , rather RB he PP took VVD it PP from IN Omar NP Khayyam's NP algebra NN book NN where WRB it PP is VBZ solved VVN by IN means NNS of IN the DT intersection NN of IN a DT circle NN and CC a DT hyperbola NN . SENT Fibonacci NP proves VVZ that IN the DT root NN of IN the DT equation NN is VBZ neither RB an DT integer NN nor CC a DT fraction NN , , nor CC the DT square JJ root NN of IN a DT fraction NN . SENT He PP then RB continues VVZ . SENT And CC because IN it PP was VBD not RB possible JJ to TO solve VV this DT equation NN in IN any DT other JJ of IN the DT above JJ ways NNS , , I PP worked VVD to TO reduce VV the DT solution NN to TO an DT approximation NN . SENT Without IN explaining VVG his PP$ methods NNS , , Fibonacci NP then RB gives VVZ the DT approximate JJ solution NN in IN sexagesimal JJ notation NN as IN 1 CD . SENT 22 CD . SENT 7 CD . SENT 42 CD . SENT 33 CD . SENT 4 LS . SENT 40 CD this NN is VBZ written VVN to TO base NN 60 CD , , so RB it PP is VBZ 1 CD 22 CD 60 JJ 7 CD 602 CD 42 CD 603 CD . SENT . SENT . SENT . SENT This DT converts VVZ to TO the DT decimal JJ 1 CD . SENT 3688081075 CD which WDT is VBZ correct JJ to TO nine CD decimal NN places NNS , , a DT remarkable JJ achievement NN . SENT Liber NN quadratorum NN , , written VVN in IN 1225 CD , , is VBZ Fibonacci's NN most RBS impressive JJ piece NN of IN work NN , , although IN not RB the DT work NN for IN which WDT he PP is VBZ most RBS famous JJ . SENT The DT book's NNS name NN means VVZ the DT book NN of IN squares NNS and CC it PP is VBZ a DT number NN theory NN book NN which WDT , , among IN other JJ things NNS , , examines VVZ methods NNS to TO find VV Pythogorean JJ triples NNS . SENT Fibonacci NP first JJ notes NNS that IN square JJ numbers NNS can MD be VB constructed VVN as IN sums NNS of IN odd JJ numbers NNS , , essentially RB describing VVG an DT inductive JJ construction NN using VVG the DT formula NN n NN 2 CD 2 CD n NN 1 CD n NN 1 CD 2 CD . SENT Fibonacci NP writes VVZ . SENT I PP thought VVD about IN the DT origin NN of IN all DT square JJ numbers NNS and CC discovered VVD that IN they PP arose VVD from IN the DT regular JJ ascent NN of IN odd JJ numbers NNS . SENT For IN unity NN is VBZ a DT square JJ and CC from IN it PP is VBZ produced VVN the DT first JJ square NN , , namely RB 1 CD . SENT adding VVG 3 CD to TO this DT makes VVZ the DT second JJ square NN , , namely RB 4 CD , , whose WP$ root NN is VBZ 2 CD . SENT if IN to TO this DT sum NN is VBZ added VVN a DT third JJ odd JJ number NN , , namely RB 5 CD , , the DT third JJ square NN will MD be VB produced VVN , , namely RB 9 CD , , whose WP$ root NN is VBZ 3 CD . SENT and CC so RB the DT sequence NN and CC series NN of IN square JJ numbers NNS always RB rise VVP through IN the DT regular JJ addition NN of IN odd JJ numbers NNS . SENT To TO construct VV the DT Pythogorean JJ triples NNS , , Fibonacci NP proceeds NNS as RB follows VVZ . SENT Thus RB when WRB I PP wish VVP to TO find VV two CD square JJ numbers NNS whose WP$ addition NN produces VVZ a DT square JJ number NN , , I PP take VVP any DT odd JJ square JJ number NN as IN one CD of IN the DT two CD square JJ numbers NNS and CC I PP find VVP the DT other JJ square JJ number NN by IN the DT addition NN of IN all PDT the DT odd JJ numbers NNS from IN unity NN up RB to TO but CC excluding VVG the DT odd JJ square JJ number NN . SENT For IN example NN , , I PP take VVP 9 CD as IN one CD of IN the DT two CD squares NNS mentioned VVN . SENT the DT remaining JJ square NN will MD be VB obtained VVN by IN the DT addition NN of IN all PDT the DT odd JJ numbers NNS below IN 9 CD , , namely RB 1 CD , , 3 CD , , 5 CD , , 7 CD , , whose WP$ sum NN is VBZ 16 CD , , a DT square JJ number NN , , which WDT when RB added VVD to TO 9 CD gives VVZ 25 CD , , a DT square JJ number NN . SENT Fibonacci NP also RB proves VVZ many JJ interesting JJ number NN theory NN results NNS such JJ as RB . SENT there EX is VBZ no DT x NN , , y NN such JJ that IN x NN 2 CD y NN 2 CD and CC x LS 2 CD y NN 2 CD are VBP both DT squares NNS . SENT and CC x LS 4 CD y NN 4 LS cannot NN be VB a DT square NN . SENT He PP defined VVD the DT concept NN of IN a DT congruum NN , , a DT number NN of IN the DT form NN ab NP a DT b NN a DT b NN , , if IN a DT b NN is VBZ even RB , , and CC 4 CD times NNS this DT if IN a DT b NN is VBZ odd JJ . SENT Fibonacci NP proved VVD that IN a DT congruum NN must MD be VB divisible JJ by IN 24 CD and CC he PP also RB showed VVD that IN for IN x NN , , c LS such PDT that DT x NN 2 CD c SYM and CC x NN 2 CD c SYM are NN both CC squares NNS , , then RB c NN is VBZ a DT congruum NN . SENT He PP also RB proved VVD that IN a DT square JJ cannot NN be VB a DT congruum NN . SENT As IN stated VVN in IN 2 CD . SENT . SENT . SENT . SENT the DT Liber NP quadratorum NN alone RB ranks VVZ Fibonacci NP as IN the DT major JJ contributor NN to TO number NN theory NN between IN Diophantus NP and CC the DT 17 CD th NN century NN French JJ mathematician NN Pierre NP de NP Fermat NP . SENT Fibonacci's NP influence NN was VBD more RBR limited VVN than IN one CD might MD have VH hoped VVN and CC apart RB from IN his PP$ role NN in IN spreading VVG the DT use NN of IN the DT Hindu NP Arabic NP numerals NNS and CC his PP$ rabbit NN problem NN , , Fibonacci's NP contribution NN to TO mathematics NNS has VHZ been VBN largely RB overlooked VVN . SENT As IN explained VVN in IN 1 CD . SENT Direct JJ influence NN was VBD exerted VVN only RB by IN those DT portions NNS of IN the DT Liber NP abaci NNS and CC of IN the DT Practica NP that WDT served VVD to TO introduce VV Indian JJ Arabic NP numerals NNS and CC methods NNS and CC contributed VVD to TO the DT mastering VVG of IN the DT problems NNS of IN daily JJ life NN . SENT Here RB Fibonacci NP became VVD the DT teacher NN of IN the DT masters NNS of IN computation NN and CC of IN the DT surveyors NNS , , as IN one PP learns VVZ from IN the DT Summa NP of IN Luca NP Pacioli NP . SENT . SENT . SENT Fibonacci NP was VBD also RB the DT teacher NN of IN the DT Cossists NNS , , who WP took VVD their PP$ name NN from IN the DT word NN causa NP which WDT was VBD first RB used VVN in IN the DT West NP by IN Fibonacci NP in IN place NN of IN res NN or CC radix NN . SENT His PP$ alphabetic JJ designation NN for IN the DT general JJ number NN or CC coefficient NN was VBD first RB improved VVN by IN Vi NP te NN . SENT . SENT . SENT Fibonacci's NNS work VVP in IN number NN theory NN was VBD almost RB wholly RB ignored VVN and CC virtually RB unknown JJ during IN the DT Middle NP ages NNS . SENT Three CD hundred CD years NNS later RBR we PP find VVP the DT same JJ results NNS appearing VVG in IN the DT work NN of IN Maurolico NP . SENT The DT portrait NN above RB is VBZ from IN a DT modern JJ engraving NN and CC is VBZ believed VVN to TO not RB be VB based VVN on IN authentic JJ sources NNS . SENT Article NN by IN . SENT J NP J NP O'Connor NP and CC E NP F NP RobertsonClick NP on IN this DT link NN to TO see VV a DT list NN of IN the DT Glossary NN entries NNS for IN this DT page NN List NP of IN References NNS 21 CD books NNS articles NNS A DT Quotation NN A DT Poster NP of IN Fibonacci NP Mathematicians NNS born VVN in IN the DT same JJ country NN Cross NP references NNS to TO History NN Topics NNS Mathematical JJ games NNS and CC recreations NNS A DT chronology NN of IN pi NN An DT overview NN of IN the DT history NN of IN mathematics NN The DT trigonometric JJ functions NNS Prime NP numbers NNS A DT history NN of IN Zero NP Arabic NP numerals NNS The DT Golden JJ ratio NN Other JJ references NNS in IN MacTutor NP Fibonacci NP numbers NNS and CC the DT Euclidean JJ algorithm NN Continued JJ fractions NNS and CC Fibonacci NP numbers NNS Chronology NN . SENT 1100 CD to TO 1300 CD Other JJ Web NP sitesR NN Knott NP Fibonacci NP numbers NNS and CC other JJ links NNS R NP Knott NP A NP biography NN Pass NP Magazine NP Karen NP H NP Parshall NP Clark NP Kimberling NP Including VVG an DT article NN by IN A DT F NP Horadam NP Previous JJ Chronologically RB Next JJ Biographies NNS Index NN Previous JJ Alphabetically RB Next JJ Main JJ index NN History NN Topics NNS Societies NNS , , honours NNS , , etc FW . SENT Famous JJ curves NNS Time NP lines NNS Birthplace NN maps NNS Chronology NN Search NP Form NP Glossary NN index NN Quotations NNS index NN Poster NP index NN Mathematicians NNS of IN the DT day NN Anniversaries NNS for IN the DT year NN JOC NP EFR NP October NP 1998 CD Copyright NN information NN School NP of IN Mathematics NNS and CC Statistics NPS University NP of IN St NP Andrews NPS , , Scotland NP The NP URL NP of IN this DT page NN is VBZ . SENT http NN . SENT www JJ history NN . SENT mcs NNS . SENT st NP andrews NPS . SENT ac NNS . SENT uk NP Mathematicians NNS Fibonacci NP . SENT html NN