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The "Greatest European Mathematician of the Middle Ages"

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The 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.. 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