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The "Greatest European Mathematician of the Middle Ages"

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Who was Fibonacci? The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France. They are still called "bougies" in French, but the town is a ruin today says D E Smith (see below). So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others. D E Smith points out that another famous Italian - St Francis of Assisi (a nearby Italian town) - was also alive at the same time as Fibonacci: St Francis was born about 1182 (after Fibonacci's around 1175) and died in 1226 (before Fibonacci's death commonly assumed to be around 1250). By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci). His names Fibonacci Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci. There are a couple of explanations for the meaning of Fibonacci: 1. Fibonacci is a shortening of the Latin "filius Bonacci", used in the title of his book Libar Abaci (of which mmore later), which means "the son of Bonaccio". His father's name was Guglielmo Bonaccio. Fi'-Bonacci is like the English names of Robin-son and John-son. But (in Italian) Bonacci is also the plural of Bonaccio; therefore, two early writers on Fibonacci (Boncompagni and Milanesi) regard Bonacci as his family name (as in "the Smiths" for the family of John Smith). Fibonacci himself wrote both "Bonacci" and "Bonaccii" as well as "Bonacij"; the uncertainty in the spelling is partly to be ascribed to this mixture of spoken Italian and written Latin, common at that time. However he did not use the word "Fibonacci". This seems to have been a nickname probably originating in the works of Guillaume Libri in 1838, accordigng to L E Sigler's in his Introduction to Leonardo Pisano's Book of Squares (see Fibonacci's Mathematical Books below). 2. Others think Bonacci may be a kind of nick-name meaning "lucky son" (literally, "son of good fortune"). Statue of Fibonacci Other names Other names He is perhaps more correctly called Leonardo of Pisa or, using a latinisation of his Hnea mise p, eLrehoanpsa rmdor Pe icosarnreoct. Olycca calsileodn Laelloy nhaer dalos oo wf Proistea Loer,o unsianrdgo a B laigtinoilsalo tsiionnc oef, in hTisu scanamney,, bLiegoonlloa rmdoea Pniss an tora. veOccaller.si onally he also wrote Leonardo Bigollo siWnece sh, ianl lT justsc acany,ll h bimig oFlliob omneaaccins a as tdraove mlolestr. modern authors, but if you are looking him Wupe ishn oalldl ejurst b ocaoks,ll h ibme Fpirbeopnaarccied taos s deoe manoyst o mf tohdee arnb oaveuth voarrs,ia btiount sif oyof uh isa rnea me. lo[Wokiithn gth hainmks u pto i nP oroldf.e Cr lbaouodksio ,G bieo mprienpi oafr eRdo tmo ese foer ahneylp o of nth teh ea bLoavetin vaanrdia Ittioanliasn o nf ames hinis tnhaism see.ct ion.] [With thanks to Prof. Claudio Giomini of Rome for help on the Latin and Italian n ames in this section.] Fibonacci's Mathematical Contributions Fibonacci's Mathematical Contributions Introducing the Decimal Number system into Europe Introducing the Decimal Number system into Europe He was one of the first people to introduce the Hindu-Arabic number system into Europe - the positional system we use today - based on ten digits with its decimal point Haen dw aa ssym oneb oolf ftohre z feirrsto: people to introduce the Hindu-Arabic number system into E1u 2ro 3p e4 -5 th6e 7 p 8o 9si t0io nal system we use today - based on ten digits with its decimal pHoiisn tb aonodk ao nsym howb otol f odro ze arrioth:m etic in the decimal system, called Liber abbaci (meaning 1B 2o o3k 4o f5 t6h e7 A8b 9a cu0 s or Book of Calculating) completed in 1202 persuaded many HEius rboopoeka no nm haothwe mtoa dtioci arnitsh mofe htics idna tyh eto d uesecim thaisl syst"newem" syst, calelemd. Liber abbaci (Tmheea bnoinogk Bdoeoscrk oibf ethse ( iAn bLaacutins) tohre B rouoleks o wf eC aallcl unloawtin lge)a rcon matp eleletemde innt a1r2y0 sch2 ool for paedrdsuinagd neudm mbaenrsy, Esuurbotrpaectanin gm, amthueltmipalyiticinga nasn do fd hiviisd dinagy, ttoo guesteh ethr isw i"tnhe mwa" nsysty preomb.le ms to Tilhluest braootek tdhescr meibtheosd (s:in Latin) the rules we all now learn at elementary school for a d d 1in g7 n4u +m b e 1r s7, su4 -b t r a ct1 i7n g4, xm u l t1ip 7lyi 4n g÷ a2n8d dividing, together with many p r o b l e2m 8s t o i l l u st2 r8a t e t h e m2 e8t h o d s: is 1- -7-- -4 + - - 1-- -7 4 -- - - - - -1- 7 4 x 1 7 4 ÷ 28 2 20 82 1 24 86 3 42 8 0 + 6 isre mainder 6 - -------- - - - - - - - - - - - - - - - -1- 3 9 2 2 0 2 1 4 6 3 -4- -8-- -0- + 6 remainder 6 - - - - - - - - - - 14 38 97 22 ------- L e t ' s f i r s t o f a ll l o o k a t 4th 8e 7R o2m an number system still in use in Europe at that time ( 1 2 0 0 ) a n d s e e h o w a w --kw---a--r d it was for arithmetic. L et's first of all look at the Roman number system still in use in Europe at that tRimoem (a1n20 N0u) manedr aselse how awkward it was for arithmetic. The Numerals are letters Roman Numerals The Numerals are letters The method in use in Europe until then used the Roman numerals: I = 1, T hVe = m 5e,t h od in use in Europe until then used the Roman numerals: XI = = 1 1, 0 , V = 5, X = 10, L L = = 5 500, , CC == 110000,, DD == 550000 aanndd MM == 11000000 YYoouu cacann ststilil l seseee tthheemm uusesedd oonn ffoouunnddaattioionn ststoonneess ooff ooldld bbuuilidldininggss aanndd oonn ssoommee clcloocks.cks. TThhee AAddddiittiivvee rruullee TThhee sisimmpplelesstt systsysteemm wwoouuldld bbee mmeerreelyly ttoo uusese tthhee leletttteerrss ffoorr tthhee vavalulueess aass inin tthhee ttaabblele aabbooveve,, aanndd aadddd tthhee vavalulueess ffoorr eeaacchh leletttteerr uusesedd.. FFoorr ininststaanncece,, 1133 cocouuldld bbee wwrritittteenn aass XXIIIIII oorr ppeerrhhaappss IIIIIIXX oorr eevevenn IIIIXXII.. TThhisis ooccuccurrss in inth teh eR oRmomana nla nlagnugaugaeg eo fo Lf aLtaint inw hwehrer e2 32 3is isps sopkeoken na sa tsr etrse es te vit gviingtini wti hwichhich tr anslates tarasn tslhraetes a ansd tthwrenet ya.n Yd otwu emnatyy. rYeomue mabye rr ethmee nmubrseer rtyh erh nymursee Sryin rgh yma Seo Snign go fa SSoixnpge onfc Se iwxpheichnc bee wghinichs begins SSiningg aa sosonngg ooff sisixxppeenncece AA ppoockeckett ffuull l ooff rryeye FFoouurr aanndd ttwweennttyy bblalackbckbirirddss BBaakekedd inin aa ppieie...... AAbbooveve 110000,, tthhee LLaattinin wwoorrddss uussee tthhee ssaammee oorrddeerr aass wwee ddoo inin EEnngglilshish,, soso tthhaatt wwhheerreeaass 3355 isis qquuininqquuee eett ttrrigigininttaa ((55 aanndd 3300)),, 223355 isis dduucecenntti i ttrrigigininttaa qquuininqquuee ((ttwwoo hhuunnddrreedd tthhirirttyy ffiveive)).. IInn tthhisis sisimmpplele systsysteemm,, uusisinngg aaddddititioionn oonnly,ly, 9999 wwoouuldld bbee 9900++99 oorr,, uusisinngg oonnlyly tthhee nnuummbbeerrss aabbooveve,, 5500++1100++1100++1100 ++ 55++11++11++11++11 wwhhichich ttrraannslslaatteess ttoo LLXXXXXXXXVVIIIIIIII aanndd bbyy tthhee sasammee mmeetthhoodd 11999988 wwoouuldld bbee wwrritittteenn bbyy tthhee RRoommaannss aass MMDDCCCCCCCCLLXXXXXXXXVVIIIIII.. BBuutt sosommee nnuummbbeerrss aarree lolonngg aanndd itit isis tthhisis isis wwhheerree,, ifif wwee aaggrreeee ttoo lelett tthhee oorrddeerr ooff leletttteerrss mmaatttteerr wwee cacann aalsolso uusese susubbttrraactctioionn.. ThTeh es usbutbrtarcatcivtiev eru rluel e TThhee RRoommaann lalanngguuaaggee ((LLaattinin)) aalsolso uusesess aa susubbttrraactctioionn pprrinincicipplele soso tthhaatt wwhheerreeaass 2200 is isvi gviignitni t1i 91 9is is"1 " 1fr ofrmom 2 02"0 o" ro ur nudnedviegviignitni.t iW. We eh ahvaeve it int inE nEgnligshlish w hwehne nw ew esa say tyh teh etim e tiism "e1 0is t"o1 07" t ow h7i"ch w hisic nho its tnhoet sathme esa ams e" 7a s1 0"7". 1T0h"e. Tfirhste mfiresta mnse 1a0n sm 1in0u mteins ubtefso re ( or bsuefbotrrea ct( oerd sfurobmtra) ct7 e0d'cl forock,m) w7h 0e'clreoack,s th weh seerceoansd t hmee seancos 1nd0 meinauntes s1 a0d mdeindu teos ( or aadftdeerd) 7to o ('cloro ackft.e Tr)h 7is o is'cl aolck.so rTehfliesct ise da lsoin Rreofmleacnte ndu inm Reroamls.a nT hnius maebrbarels.vi Tathioisn makes athbeb roervidaetri oonf lmetatekerss i mthpeo ortradnetr. oSfo le ift tae rsms imalpleorr tvaanlut.e S cao imf ae smbefaollreer tvahel unee xtca lmareg er one, bite wfoarse sutheb tnraectxte ladr agnedr oifn iet ,ca it mwea sa fsuterb,t rita wctaesd aadndde idf .i t came after, it was added. FFoorr eexaxammpplele,, XXII mmeeaannss 1100++11==1111 ((sisinnccee tthhee ssmmaallelerr oonnee cocommeess aafftteerr tthhee lalarrggeerr ten) tbeunt) IbXu mt IeXa mnse a1n les ss1 ltehssan t h1a0n o 1r 09 .o r 9. BBuutt 88 isis ststilil l wwrritittteenn aass VVIIIIII ((nnoott IIIIXX)).
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    Infinite Secrets AIRING SEPTEMBER 30, 2003 Learning More Dzielska, Maria. Famous Mathematicians Hypatia of Alexandria. Cambridge, MA: Harvard University The history of mathematics spans thousands of years and touches all parts of the Press, 1996. world. Likewise, the notable mathematicians of the past and present are equally Provides a biography of Hypatia based diverse.The following are brief biographies of three mathematicians who stand out on several sources,including the letters for their contributions to the fields of geometry and calculus. of Hypatia’s student Synesius. Hypatia of Alexandria Bhaskara wrote numerous papers and Biographies of Women Mathematicians books on such topics as plane and spherical (c. A.D. 370–415 ) www.agnesscott.edu/lriddle/women/ Born in Alexandria, trigonometry, algebra, and the mathematics women.htm of planetary motion. His most famous work, Contains biographical essays and Egypt, around A.D. 370, Siddhanta Siromani, was written in A.D. comments on woman mathematicians, Hypatia was the first 1150. It is divided into four parts: “Lilavati” including Hypatia. Also includes documented female (arithmetic), “Bijaganita” (algebra), resources for further study. mathematician. She was ✷ ✷ ✷ the daughter of Theon, “Goladhyaya” (celestial globe), and a mathematician who “Grahaganita” (mathematics of the planets). Patwardhan, K. S., S. A. Naimpally, taught at the school at the Alexandrine Like Archimedes, Bhaskara discovered and S. L. Singh. Library. She studied astronomy, astrology, several principles of what is now calculus Lilavati of Bhaskaracharya. centuries before it was invented. Also like Delhi, India:Motilal Banarsidass, 2001. and mathematics under the guidance of her Archimedes, Bhaskara was fascinated by the Explains the definitions, formulae, father.She became head of the Platonist concepts of infinity and square roots.
  • Fibonacci Is Not a Pizza Topping Bevel Cut April, 2020 Andrew Davis Last Month I Saw an Amazing Advertisement Appearing in Our Woodworking Universe

    Fibonacci Is Not a Pizza Topping Bevel Cut April, 2020 Andrew Davis Last Month I Saw an Amazing Advertisement Appearing in Our Woodworking Universe

    Fibonacci is Not a Pizza Topping Bevel Cut April, 2020 Andrew Davis Last month I saw an amazing advertisement appearing in our woodworking universe. You might say that about all of the Woodpeckers advertisements – promoting good looking, even sexy tools and accessories for the woodworker who has money to burn or who does some odd task many times per day. I don’t fall into either category, though I often click on the ads to see the details and watch a video or two. These days I seem to have time to burn, if not money. Anyway, as someone who took too many math courses in my formative years, this ad absolutely caught my attention. I was left guessing two things: what is a Fibonacci and why would anyone need such a tool? Mr. Fibonacci and his Numbers Mathematician Leonardo Fibonacci was born in Pisa – now Italy – in 1170 and is credited with the first CNC machine and plunge router. Fibonacci popularized the Hindu–Arabic numeral system in the Western World (thereby replacing Roman numerals) primarily through his publication in 1202 called the Book of Calculation. Think how hard it would be to do any woodworking today if dimensions were called out as XVI by XXIV (16 x 24). But for this bevel cut article, the point is that he introduced Europe to the sequence of Fibonacci numbers. Fibonacci numbers are a sequence in which each number is the sum of the two preceding numbers. Here are the first Fibonacci numbers. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418.