21. Who Was Fibonacci? His names, mathematical contributions, Introducing the decimal number system into Europe, fibonacci Series. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html

A brief biographical sketch of Fibonacci, his life, times and mathematical achievements. Contents of this Page Who was Fibonacci? His names Fibonacci's Mathematical Contributions Introducing the Decimal Number system into Europe ... References to Fibonacci's Life and Times 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).

22. Matematicos   leonardo Pisano fibonacci Nació 1170 probablemente en Pisa (Ahora Italia)  Falleció 1250 probablemente en Pisa (Ahora Italia) leonardo Pisano es más conocido por su apodo fibonacci. http://www.mat.usach.cl/histmat/html/fibo.html

"Mis Prácticas de geometría" Referencias:

23. Biography Of Leonardo Fibonacci A short biography of the mathematician fibonacci as part of a longer Text called The Art of Algebra . http://www.lib.virginia.edu/science/parshall/fibonacc.html

Biography of Leonardo Fibonacci Leonardo Fibonacci ( PORTRAIT - 42K ) was born in Pisa, Italy around 1170, the son of Guilielmo Bonacci, a secretary of the Republic of Pisa and responsible, beginning around 1192, for directing the Pisan trading colony in Bugia, Algeria. Some time after 1192, Bonacci brought his son with him to Bugia. The father intended for Leonardo to become a merchant and so arranged for his instruction in calculational techniques, especially those involving the Hindu-Arabic numerals which had not yet been introduced into Europe. Eventually, Bonacci enlisted his son's help in carrying out business for the Pisan republic and sent him on trips to Egypt, Syria, Greece, Sicily, and Provence. Leonardo took the opportunity offered by his travel abroad to study and learn the mathematical techniques employed in these various regions. Around 1200, Fibonacci returned to Pisa where, for at least the next twenty-five years, he worked on his own mathematical compositions. The five works from this period which have come down to us are: the Liber abbaci (1202, 1228); the

24. Fibonacci leonardo Pisano fibonacci. Born 1170 in (probably) Pisa (now in Italy) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html

Leonardo Pisano Fibonacci Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. As stated in [1]:- Did his countrymen wish to express by this epithet their disdain for a man who concerned himself with questions of no practical value, or does the word in the Tuscan dialect mean a much-travelled man, which he was? Fibonacci was born in Italy but was educated in North Africa where his father, Guilielmo, held a diplomatic post. His father's job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Bejaia is a Mediterranean port in northeastern Algeria. The town lies at the mouth of the Wadi Soummam near Mount Gouraya and Cape Carbon. Fibonacci was taught mathematics in Bugia and travelled widely with his father, recognising and the enormous advantages of the mathematical systems used in the countries they visited. Fibonacci writes in his famous book Liber abaci When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms.

25. References For Fibonacci Articles A Agostini, leonardo fibonacci (Italian), Archimede 5 (1953), 205206. JWeszely, fibonacci, leonardo Pisano (c. 1170-c. 1240) (Romanian), Gaz. Mat. http://www-gap.dcs.st-and.ac.uk/~history/References/Fibonacci.html

References for Fibonacci Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: J Gies and F Gies, Leonard of Pisa and the New Mathematics of the Middle Ages (Mannheim, 1993) Articles: A Agostini, Leonardo Fibonacci (Italian), Archimede A Agostini, L'uso delle lettere nel "Liber abaci" di Leonardo Fibonacci, Boll. Un. Mat. Ital. I G Basmakova, The 'Liber quadratorum' of Leonardo of Pisa (Russian), in History and methodology of the natural sciences XX (Moscow, 1978), 27-37. P K Chong, The life and work of Leonardo of Pisa, Menemui Mat. M Dunton and R E Grimm, Fibonacci on Egyptian fractions, Fibonacci Quart R Franci and L Toti Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus P Freguglia, The determination of in Fibonacci's 'Practica geometriae' in a fifteenth-century manuscript (Italian), in Contributions to the history of mathematics (Modena, 1992), 75-84. S Glushkov, On approximation methods of Leonardo Fibonacci, Historia Math.

26. Sand Spring Advisors LLC Analysis of global financial trends and advice on alternative investment management. Analytical work includes a strong emphasis on the techniques of R.N. Elliott and leonardo fibonacci. http://www.sandspring.com

27. Fibonacci Numbers, The Golden Section And The Golden String fibonacci numbers and the golden section in nature, art, geometry, architecture, music, geometry Category Science Math Specific Numbers fibonacci Numbers...... It was known to artists such as leonardo da Vinci and musicians and of page to thoseabove, being concerned with speculations about where fibonacci numbers and http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Fibonacci Numbers and the Golden Section This is the Home page for Ron Knott's Surrey University web site on the Fibonacci numbers, the Golden section and the Golden string. The Fibonacci numbers are add the last two to get the next The golden section numbers are The golden string is a sequence of 0s and 1s which is closely related to the Fibonacci numbers and the golden section. There is a large amount of information at this site (more than 200 pages if it was printed), so if all you want is a quick introduction then the first link takes you to an introductory page on the Fibonacci numbers and where they appear in Nature. The rest of this page is a brief introduction to all the web pages at this site on Fibonacci Numbers the Golden Section and the Golden String together with their many applications What's New? 10 February 2003 Fibonacci Numbers and Golden sections in Nature Fibonacci Numbers and Nature Fibonacci and the original problem about rabbits where the series first appears, the family trees of cows and bees, the golden ratio and the Fibonacci series, the Fibonacci Spiral and sea shell shapes, branching plants, flower petal and seeds, leaves and petal arrangements, on pineapples and in apples, pine cones and leaf arrangements. All involve the Fibonacci numbers - and here's how and why.

28. Fibonacci Mathematics By Dr. Peter Reimers Life and work of leonardo of Pisa, by Dr. Peter Reimers. http://vp-reimers.bei.t-online.de/

Fibonacci Mathematics By Dr. Peter Reimers Contents

29. Fibonacci, Leonardo Da Pisa (ca. 1170-ca. 1240) -- From Eric Weisstein's World O Branch of Science " Mathematicians Nationality " Italian Biography Contributors " Barile fibonacci, leonardo da Pisa (ca. 1170ca. 1240) This entry contributed by Margherita Barile Italian mathematician who was the first great Western http://www.treasure-troves.com/bios/Fibonacci.html

Branch of Science Mathematicians Nationality Italian ... Barile Fibonacci, Leonardo da Pisa (ca. 1170-ca. 1240) This entry contributed by Margherita Barile Italian mathematician who was the first great Western mathematician after the decline of Greek science. The son of a merchant, Fibonacci drew the motivation to mathematical inquiry from his commercial trips to the the Orient. It was somewhere between Barbary (Maghreb) and Constantinople (now Istanbul) that he got acquainted with the Hindu-Arabic number system and discovered its enormous practical advantages compared to the Roman numerals which were still current in Western Europe. Performing even the simplest arithmetical operations with a non-positional notation was a difficult endeavor: for this task the merchants were forced to resort to the abacus, a device where the numbers were represented by moving balls. Fibonacci exposed the new alternate computing methodbased on written algorithms rather than on counting objectsin his Liber Abaci , first issued in 1202. The book began with a presentation of what he called the ten "Indian figures" (0, 1, 2, ..., 9). It was intended as an algebra manual for commercial use, and explained the arithmetical rules using numerical examples derived, for example, from measure and currency conversion, which were translated into proportions and solved by multiplication (rule of three). The so-called Fibonacci sequence arose in this book from a concrete question concerning the growth of a rabbit population.

30. Portrait Of Leonardo Fibonacci Portrait of leonardo fibonacci. Return to Bigraphy of leonardo fibonacci. http://www.lib.virginia.edu/science/parshall/fibonacciport.html

Portrait of Leonardo Fibonacci Return to Bigraphy of Leonardo Fibonacci.

31. Fibonacci, Leonardo Da Pisa (ca. 1170-ca. 1240) -- From Eric Weisstein's World O fibonacci, leonardo da Pisa (ca. 1170ca. 1240), Siegler, L. E. (ed.) leonardoPisano fibonacci. The Book of Squares. Orlando, FL Academic Press, 1987. http://scienceworld.wolfram.com/biography/Fibonacci.html

Branch of Science Mathematicians Nationality Italian ... Barile Fibonacci, Leonardo da Pisa (ca. 1170-ca. 1240) This entry contributed by Margherita Barile Italian mathematician who was the first great Western mathematician after the decline of Greek science. The son of a merchant, Fibonacci drew the motivation to mathematical inquiry from his commercial trips to the the Orient. It was somewhere between Barbary (Maghreb) and Constantinople (now Istanbul) that he got acquainted with the Hindu-Arabic number system and discovered its enormous practical advantages compared to the Roman numerals which were still current in Western Europe. Performing even the simplest arithmetical operations with a non-positional notation was a difficult endeavor: for this task the merchants were forced to resort to the abacus, a device where the numbers were represented by moving balls. Fibonacci exposed the new alternate computing methodbased on written algorithms rather than on counting objectsin his Liber Abaci , first issued in 1202. The book began with a presentation of what he called the ten "Indian figures" (0, 1, 2, ..., 9). It was intended as an algebra manual for commercial use, and explained the arithmetical rules using numerical examples derived, for example, from measure and currency conversion, which were translated into proportions and solved by multiplication (rule of three). The so-called Fibonacci sequence arose in this book from a concrete question concerning the growth of a rabbit population.

32. Fibonacci, Leonardo fibonacci, leonardo . http://episte.math.ntu.edu.tw/people/p_fibonacci/

Fibonacci, Leonardo ¶Oªi¨º«´ ·j´M Fibonacci¡]1175?¡ã1250?¡^¬O¤¤¥@¬ö³Ì³Ç¥Xªº¼Æ¾Ç®a¡C ®Ú¾ÚD·N¡A¥H F n ªí¥Ü­Ó¤ë¥H«á¨ß¤lªºÁ`¹ï¼Æ¡A «h F ¡A F ¡A F ¡A F ¡A F ¡A F ¡A F ¡A F ¡A¡K¡A ³o­Ó¼Æ¦C´N¥s§@Fibonacci¼Æ¦C¡]©ÎºÙ¶O¤ó¼Æ¦C¡^¡A¤Þ°_¤F«á¥@·½·½¤£Â_ªº¿³½ì¡CFibonacci¼Æ¦C¦³¤U¦Cªí¹F¦¡¡G ¹ï¥~·j´MöÁä¦r¡G ¡D Fibonacci ¡D ¶O¤ó¼Æ¦C ¡]¼¶½Z¡GªLÁo·½¢A²M¤j¼Æ¾Ç¨t¡^ MacTutor ¡]­Y¦³«ü¥¿¡Bº°Ý¡K¡K¡A¥i¥H¦b¦¹ ¯d¨¥ ¼g«H µ¹§Ú­Ì¡C¡^ ¦Uºô­¶¤å³¹¤º®e¤§µÛ§@Åv¬°­ìµÛ§@¤H©Ò¦³ ½s¿è¡G¬x·ë

33. Fibonacci, Leonardo. The Columbia Encyclopedia, Sixth Edition. 2001 2001. fibonacci, leonardo. (l när´d f b nät´ch ) (KEY) , b. c.1170,d. after 1240, Italian mathematician, known also as leonardo da Pisa. http://www.bartleby.com/65/fi/Fibonacc.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Fibonacci, Leonardo

34. Leonardo Fibonacci Translate this page leonardo fibonacci. un hombre de la Corte sueva que supo, con su sabidurìa,afascinar a Federico II. por Alberto Gentile. leonardo http://www.stupormundi.it/spagnolo/Fibonacci.htm

Leonardo Fibonacci un hombre de la Corte sueva que supo, con su sabidurìa, afascinar a Federico II por Alberto Gentile Leonardo Fibonacci (Pisa 1170-1240) era hijo del empleado de la aduana de Bogia, en Argelia, donde los Pisanos entretenìan florecientes tràficos comerciales. Por mèrito de su padre aprendiò desde muy joven E l àbaco a la manera de los Hindis : las cifrar àrabas con el cero, aùn desconocidas en Italia. El mismo Leonardo dice de haber perfeccionado estos conocimientos en sus viajes en Egipto, Siria, Sicilia y sur de la Francia, donde tuvo que ir por razones de comercio A trenta y dos años publicò la primera ediciòn del "Liber Abaci" : una obra que revolucionaba los sistemas de numeraciòn, y al mismo tiempo un manual de càlculo para el uso de los mercaderes, mejorado en el 1228 para ser dedicado a Miguel Scoto. Es del 1220 el "De practica geometriae" , en el cual aplicò el nuevo sistema aritmètico para la soluciòn de problemas geomètricos: un tratado de Geometria y Trigonometria, con el cual tuvo inicio el estudio de las relaciones entre las extensiones figuradas. En el 1225 realizò el "Liber quadratorum" que constituye un brillante trabajo sobre las ecuaciones indeterminadas de 2° grado: un trabajo en el cual es visible la influencia de la tradiciòn cultural àraba.

35. Leonardo Fibonacci Da Pisa Translate this page leonardo fibonacci. un uomo della Corte sveva che seppe, con il suo sapere,affascinare Federico II. di Alberto Gentile. leonardo fibonacci http://www.stupormundi.it/Fibonacci.htm

Leonardo Fibonacci un uomo della Corte sveva che seppe, con il suo sapere, affascinare Federico II di Alberto Gentile Leonardo Fibonacci (Pisa 1170-1240) era figlio dell’addetto alla dogana di Bogia, in Algeria, ove i Pisani intrattenevano fiorenti traffici commerciali. Per merito del padre, apprese giovanissimo l'abaco alla maniera degli Hindi : le cifre arabe con lo zero, ancora sconosciute in Italia. Lo stesso Leonardo ci dice di aver perfezionato questa conoscenza nei suoi viaggi in Egitto, Siria, Sicilia e Provenza dove dovette recarsi per cagion di commercio "Liber Abaci" : un saggio che rivoluzionava i sistemi di numerazione, ed allo stesso tempo un manuale di calcolo ad uso dei mercanti, rivisto nel 1228 per essere dedicato a Michele Scoto. "De practica geometriae" "Liber quadratorum" "Liber quadratorum" ) un protettore capace di comprendere le sue ricerche scientifiche e di apprezzarne il valore. Flos e nel Liber quadratorum. Note bibliografiche essenziali Antonino De Stefano, La cultura alla Corte di Federico II Imperatore , Edizioni all'insegna del Veltro, Parma 1990.

36. Fibonacci, Leonardo encyclopediaEncyclopedia fibonacci, leonardo, lAOnär'dO fEbOnät'chEPronunciation Key. fibonacci, leonardo , b. c. 1170, d. after http://www.infoplease.com/ce6/people/A0818607.html

The # 1 wireless color security cam! Ultimate home movie ! Genuine Indian and Asian astrology reports and consultations by reputed Vedic Astrologers. Step-by-step guide to finding money for a growing business All Infoplease All Almanacs General Entertainment Sports Biographies Dictionary Encyclopedia Infoplease Home Almanacs Atlas Dictionary ... Fact Monster Kids' reference Info:Daily Fun facts Homework Center Newsletter You've got info! Help Site Map Visit related sites from: Family Education Network Encyclopedia Fibonacci, Leonardo [l A O O f E b O E Pronunciation Key Fibonacci, Leonardo , b. c. 1170 , d. after 1240 , Italian mathematician, known also as Leonardo da Pisa. In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In Practica geometriae Fibiger, Johannes Fichte, Johann Gottlieb Search Infoplease Info search tips Search Biographies Bio search tips About Us Contact Us Link to Infoplease ... Privacy

37. Fibonacci, Leonardo, Also Known As Leonardo Of Pisa fibonacci, leonardo, also known as leonardo of Pisa ((c. 1170c.1250). Italian mathematician. He published Liber abaci/The Book http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/F/Fibonacci/1.ht

Fibonacci, Leonardo, also known as Leonardo of Pisa ((c. 1170-c. 1250) Italian mathematician. He published Liber abaci/The Book of the Calculator in Pisa 1202, which was instrumental in the introduction of Arabic notation into Europe. From 1960, interest increased in Fibonacci numbers, in their simplest form a sequence in which each number is the sum of its two predecessors (1, 1, 2, 3, 5, 8, 13, ...). They have unusual characteristics with possible applications in botany, psychology, and astronomy (for example, a more exact correspondence than is given by Bode's law to the distances between the planets and the Sun). In 1220, Fibonacci published Practica geometriae, in which he used algebraic methods to solve many arithmetical and geometrical problems. Fibonacci was born in Pisa but learned mathematics in Algeria. He travelled extensively in the Mediterranean region. Returning to Pisa in about 1200, he began his mathematical writings. In 1225 he won a mathematical tournament in the presence of Holy Roman Emperor Frederick II at the court of Pisa. A marble tablet dated 1240 appears to refer to Fibonacci as being awarded an annual pension for his accountancy services to the state. Liber abaci was a thorough treatise on algebraic methods and problems in which he strongly advocated the introduction of the Indo-Arabic numeral system, comprising the figures 1 to 9, and the innovation of the 'zephirum' - the figure (zero). Dealing with operations in whole numbers systematically, he also proposed the idea of a bar (solidus) for fractions.

38. Fibonacci, Leonardo fibonacci, leonardo b. c.1170, d. after 1240, Italian mathematician,known also as leonardo da Pisa. In Liber fibonacci, leonardo. b. c http://www.slider.com/enc/19000/Fibonacci_Leonardo.htm

SubmitWolf - Award winning Internet Software Home Encyclopeadia F Fed - Fer ... Rope Ladders Trellian WebPage Slider Search: The Web Encyclopaedia Shopping Index Help Encyclopaedia Fibonacci, Leonardo b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In Practica geometriae Add URL Advertise Contact Us Rope Ladder

39. Leonardo Da Pisa Slider Search The Web, Index. Help. Encyclopaedia. leonardo da Pisa. seefibonacci, leonardo. fibonacci, leonardo Rope Ladder. http://www.slider.com/enc/31000/Leonardo_da_Pisa.htm

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40. FIBONACCI, Leonardo [Leonardo Of Pisa], Scritti Di Leonardo Pisano Matematico De fibonacci, leonardo leonardo of Pisa Scritti di leonardo Pisano matematicodel secolo decimoterzo pubblicati da Baldassarre Boncompagni http://www.polybiblio.com/watbooks/2559.html

[bound with:] BONCOMPAGNI, Baldassarre. Della vita e delle opere di Leonardo Pisano matematico del secolo decimoterzo. Notizie raccolte da Baldassarre Boncompagni. Rome: Tipografia delle Belle Arti, 1852. W. P. Watson Antiquarian Books FIBONACCI, Leonardo [Leonardo of Pisa] Scritti di Leonardo Pisano matematico del secolo decimoterzo pubblicati da Baldassarre Boncompagni... [bound with:] BONCOMPAGNI, Baldassarre. Della vita e delle opere di Leonardo Pisano matematico del secolo decimoterzo. Notizie raccolte da Baldassarre Boncompagni. Rome: Tipografia delle Belle Arti, 1852. Rome, Tipografia delle Scienze Matematiche e Fisiche, 1857-62 3 vols in two, 4to (328 x 248 mm), pp [iv] 459 [1]; [iv] 283 [1]; 128; with numerous diagrams in text; some occasional spotting, but a very nice, uncut and unopened copy in contemporary half vellum. £3500 First edition of the only complete edition of the writings of Fibonacci, 'the first great mathematician of the Christian West' (DSB), accompanied by Boncompagni's bio-bibliography, the first extensive biography of Fibonacci. The revival of mathematical learning in the West is almost entirely due to the influence of Fibonacci's works. His contributions are so fundamental, important, and extensive, that it would be impossible to do them justice in a short note. The reader is referred to the detailed account in DSB, IV, pp 604-613. Boncompagni's Vita was prefatory to his edition of Fibonacci. It gives a detailed account of the various manuscripts Boncompagni consulted.

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