81. Fibonacci Translate this page leonardo von Pisa, genannt fibonacci. leonardo von Pisa wurde zwischen1170 und 1180 geboren. Bekannt wurde er unter dem Namen fibonacci http://www.mathe.tu-freiberg.de/~hebisch/cafe/fibonacci.html

Leonardo von Pisa, genannt Fibonacci Liber Abaci In der modernen Mathematik ist sein Name mit der folgenden rekursiv definierten Zahlenfolge verbunden. Mit den Startwerten a und a wird die Folge der Fibonacci-Zahlen a n+2 = a n+1 + a n Liber Abaci auf: Jedes Kaninchenpaar bringt von da an jeden Monat ein neues Paar zur Welt. Alle Kaninchen leben ewig. Wenn a n die Anzahl der Kaninchenpaare bezeichnet, die im n Diese Fibonacci-Zahlen stehen in einem engen Zusammenhang mit dem Goldenen Schnitt Lucas -Folgen, die in den verschiedensten Gebieten der Mathematik eine Rolle spielen. Es gibt sogar eine mathematische Fachzeitschrift Fibonacci Quarterly

82. Biografie - Leonardo Fibonacci Translate this page leonardo fibonacci Pisa 1170ca. - Pisa 1240ca. Ancora fanciullo seguìil padre Guglielmo dei Bonacci, facoltoso mercante pisano http://galileo.imss.firenze.it/milleanni/cronologia/biografie/fiboncc.html

Leonardo Fibonacci Pisa 1170ca. - Pisa 1240ca. publicus scriba pro pisanis mercatoribus Liber abaci e la Practica geometriae (con l'applicazione dell'algebra alla soluzione di problemi geometrici); il Liber quadratorum ; l 'Epistola ad magistrum Theodorum e il Flos super solutionibus quorundam questionum ad numerosum vel ad geometriam vel ad utrumque pertinentium dedicata a Raniero Capacci, cardinal diacono. Indietro Indice Biografie Inizio

83. Biographie : Leonardo Fibonacci (1170 [Pise] - 1245 [Pise]) Translate this page leonardo fibonacci (1170 Pise - 1245 Pise). Leonard de Pise, plusconnu sous le nom de fibonacci, est le premier grand mathématicien http://www.bibmath.net/bios/index.php3?action=affiche&quoi=fibonacci

84. Gacetilla Matematica Fibonacci Translate this page leonardo de Pisa. fibonacci. http://www.arrakis.es/~mcj/fibonacc.htm

85. Leonardo Fibonacci. Matematica E Società Nel Mediterraneo Del Secolo XIII Translate this page leonardo fibonacci. ore 16.30 Intervallo Agostino Paravicini Bagliani (Universitàdi Losanna) leonardo fibonacci e la Corte papale del XIII secolo. http://www.sismelfirenze.it/attivita/ita/fibonacci.htm

Comune di Pisa Università di Firenze Università di Pisa Il Giardino di Archimede – Un museo per la matematica Provincia di Pisa Micrologus – Natura, scienze e società medievali Regione Toscana Società Internazionale per lo Studio del Medioevo Latino Con il contributo della Camera di Commercio di Pisa Sotto l’Alto Patronato del Presidente della Repubblica e con il patrocinio dell’Unesco Leonardo Fibonacci. Matematica e società nel Mediterraneo del secolo XIII Convegno internazionale di studi: Pisa-Firenze, 20–23 novembre 2002 Programma Mercoledì 20 Novembre – Pisa Aula Magna Storica dell’Università – Palazzo “La Sapienza” via Curtatone e Montanara, 15 ore 10.00: Inaugurazione e saluti delle Autorità Franco Cardini (Università di Firenze) La Politica nel Mediterraneo ai tempi di Fibonacci. ore 12.00: Inaugurazione della mostra documentaria: Un Ponte sul Mediterraneo. Leonardo Pisano, la scienza araba e la rinascita della matematica in Occidente. (Chiesa di San Paolo all’orto) ore 15.00 Djamil Aïssani, (Università di Bejaïa) Mathématiques, Commerce et Société à Béjaïa (Bugia) au moment du séjour de Léonardo Fibonacci.

86. Jiskha Homework Help - Social Studies: People: Leonardo Fibonacci Jiskha Homework Help, Friday, May 21, 2004 Homework Help Forum HomeworkHelp Experts. leonardo fibonacci by Chloe Sizzler. leonardo http://www.jiskha.com/social_studies/people/l_fibonacci.html

Monday, May 31, 2004 Homework Help Forum Homework Help Experts Leonardo Fibonacci by Chloe Sizzler Leonardo Fibonacci 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 calculation related 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 Practica geometriae (1220/1221); an undated letter to Theodorus, the imperial philosopher to the court of the Hohenstaufen emperor Frederick II; Flos (1225), a collection of solutions to problems posed in the presence of Frederick II; and the Liber quadratorum (1225), a number-theoretic book concerned with the simultaneous solution of equations quadratic in two or more variables. So great was Leonardo's reputation as a mathematician as a result of these works that Frederick summoned him for an audience when he was in Pisa around 1225.

87. Fibonacci It is called the fibonacci series after leonardo of Pisa or (Filius Bonacci), aliasleonardo fibonacci, born in 1175, whose great book The Liber Abaci (1202 http://www.goldenmeangauge.co.uk/fibonacci.htm

THE FIBONACCI SERIES No consideration of the Golden Proportion can be complete without mention of the Fibonacci Series which is the complementary view of the Golden Proportion. These numbers are also abundant in the beauty of nature and teeth. Definition In this series of numbers each term is the sum of the previous two terms as follows: etc. The division of any two adjacent numbers gives the amazing Golden number e.g. 34 / 55 = 0.618 or inversely 55 /34 = 1.618. It is called the Fibonacci series after Leonardo of Pisa or (Filius Bonacci), alias Leonardo Fibonacci, born in 1175, whose great book The Liber Abaci (1202) , on arithmetic, was a standard work for 200 years and is still considered the best book written on arithmetic. It was the principal means of demonstrating and introducing the enormous advantages of the Hindu Arabic system of numeration over the Roman System. Leonardo's reputation amongst scholars was deservedly great. It was so outstanding that King Frederick II, visiting Pisa in 1225, held a public competition in mathematics to test Leonardo's skill and he was the only one able to answer the questions (Huntley 158) One of the most spectacular examples of the Fibonacci Series in nature is in the head of the sunflower.

88. MathSeek.com - Site Profile For Fibonacci - Who Was Fibonacci? fibonacci Who was fibonacci? - leonardo of Pisa (1175?-1250) Site Profile.Title fibonacci - Who was fibonacci? - leonardo of Pisa (1175?-1250). http://www.mathseek.com/profiles/4396.php

@import url(http://www.animationseek.com/style.css); Search Directory Forum Fibonacci - Who was Fibonacci? - Leonardo of Pisa (1175?-1250) Site Profile Title: Fibonacci - Who was Fibonacci? - Leonardo of Pisa (1175?-1250) Description: His names, mathematical contributions, Introducing the decimal number system into Europe, Fibonacci Series. Url: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html Category: Science/Math/History/People Add / Update Url Become an Editor Link to Us ... MathSeek.com - Math Search Engine - Seeking Sites about Math,Applications,Education,Recreations,Statistics,Algebra,Analysis,Chaos,Fractals,Combinatorics,Differential,Equations,Geometry,Logic,Foundations,Number,Theory,Numerical,Analysis,Operations,Research,Precalculus. PhysicsSeek.com SocialScienceSeek.com TechnologySeek.net BaseballSeek.com ... MartialArtsSeek.com

89. PORCELAINia/Series/Leonardo Da Vinci/820 This piece is named for leonardo Pisano fibonacci (1175 1250), the great Italianmathematician best remembered for the fibonacci sequence, the mathematical http://www.porcelainia.com/820.html

PORCELAINia HOME PROCESS SERIES STYLE ... Site Map "Fibonacci" LEONARDO Da VINCI SERIES Height 5.2 in Mass 1047 g Fired High Glaze None Started Finished Style Geometrica Series Leonardo da Vinci This piece is named for Leonardo Pisano Fibonacci (1175 - 1250), the great Italian mathematician best remembered for the Fibonacci sequence, the mathematical sequence of the Golden Mean. Fibonacci (Leonard of Pisa) played an important role in reviving ancient mathematics and made significant contributions of his own. Fibonacci's other book of major importance, "Practica Geometriae" in 1220 contains a large collection of geometry and trigonometry.

90. 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.

91. I NUMERI DI FIBONACCI fibonacci, vinse la gara. Figlio d un http://www.criad.unibo.it/~galarico/calcolo/fibonacci.htm

I NUMERI DI FIBONACCI Nel 1223 a Pisa, l'imperatore Federico II di Svevia, fu ben felice di assistere a un singolare torneo tra abachisti e algoritmisti, armati soltanto di carta, penna e pallottoliere. In quella gara infatti si dimostrò che col metodo posizionale indiano appreso dagli arabi si poteva calcolare più velocemente di qualsiasi abaco. Il test era il seguente: "Quante coppie di conigli si ottengono in un anno -salvo i casi di morte- supponendo che ogni coppia dia alla luce un'altra coppia ogni mese e che le coppie più giovani siano in grado di riprodursi già al secondo mese di vita?". Un pisano, Leonardo, detto Bigollo, conosciuto anche col nome paterno di "fillio Bonacci" o Fibonacci, vinse la gara. Figlio d'un borghese uso a trafficare nel Mediterraneo, Leonardo visse fin da piccolo nei paesi arabi e apprese i principi dell'algebra, il calcolo, dai maestri di Algeri, cui era stato affidato dal padre, esperto computista. Più tardi, sempre esercitando la mercatura, Leonardo viaggiò in Siria, Egitto, Grecia, conoscendo i massimi matematici musulmani. Da queste esperienze nacque il Liber Abaci , un colossale trattato che dischiuse all'Occidente i misteri delle nove "figure" indiane e del segno sconosciuto ai greci e ai latini, "quod arabice zephirum appellantur", che indica un numero vuoto come un soffio di vento: zefito appunto, zefr, o zero.

92. Porträt: Fibonacci Leben bekannt. Die Schaffung http://www.zahlenjagd.at/fibonacc.html

Porträt: Leonardo von Pisa (Fibonacci) Leonardo wurde 1170 in Pisa geboren. Wenig ist über Leonardo's Leben bekannt. Die Schaffung eines auf dem Positionssystem beruhenden dezimalen Stellenwertsystems ist eine der bedeutendsten kulturellen Leistungen der indischen Völker. Das indische System ist in Bagdad im 8.Jahrhundert bekannt. Die Araber greifen dieses indische System auf und dadurch, daß der größte Teil Spaniens von den Arabern beherrscht wird, gelangen die indischen Ideen auch nach Europa und wurden auch den lateinischen Gelehrten bekannt. Den entscheidenden Durchbruch der 'indischen Rechenweise' geschieht durch das Buch 'Liber abbaci' (1202) von Leonardo von Pisa. Als Sohn eines italienischen Diplomaten in Nordafrika lernte er die arabische Wissenschaft bald kennen und er verwendet konsequent die indisch-arabischen Ziffern und zeigt damit auch die Vorteile des dekadischen Stellenwertsystems auf. In immer schnellerem Tempo beginnen jetzt die indischen Rechenverfahren in das Rechnungswesen der Kaufleute und damit der Schulstuben einzudringen. Die 'Practica geometriae' (1220) verbreitete die arabischen Ziffern und die indischen Rechenverfahren in Europa. Die Annäherung an pi wurden mit 864/275 (=3.14182) und mit 1440/458.33 (=3.14182) angegeben. Die in diesen Büchern behandelten zahlentheoretischen Probleme und die angegebenen Lösungsverfahren gingen erstmals über die Kenntnisse der arabischen (und auch des griechischen) Kulturkreises hinaus. Auch dürfte Leonardo von Pisa, wenn auch sehr vorsichtig, negative Zahlen - als Schulden veranschaulicht haben.

93. ThinkQuest : Library : The Fibonnaci Series The fibonacci Series is a sequence of numbers first created by Leonardofibonacci in 1202. A deceptively simple series, its ramifications http://library.thinkquest.org/27890/mainIndex.html

Index Math Algebra The Fibonnaci Series "The Fibonacci Series: The Series, The Applications, The Web Page" is an educational webpage dedicated to the exploration of and sharing of knowledge about the Fibonacci Series, a sequence of numbers constructed first by Leonardo Fibonacci in 1202. Topics covered include formulae for finding terms of the series, Golden mathematics, practical applications of the series, the appearance of the series in nature and art, and biographies of Fibonacci and his contemporaries. There is also a forum provided for the discussion of the series and sharing of knowledge thereof. The site uses a lesson-by-lesson format as well as interactive Flash animations to teach about this fascinating series and to foster in its readers a sense of wonder about mathematics. Visit Site 1999 ThinkQuest Internet Challenge Languages English Students Jeffrey Norman High School North, Norman, OK, United States Matthew Norman High School North, Norman, OK, United States Kris Logan High School, N Logan, UT, United States Coaches Steven University of Oklahoma, Norman, OK, United States

94. Fibonacci Sequence (PRIME) The fibonacci Sequence. edieval mathematician and businessman fibonacci (LeonardoPisano) posed the following problem in his treatise Liber Abaci (pub. 1202) http://www.mathacademy.com/pr/prime/articles/fibonac/

BROWSE ALPHABETICALLY LEVEL: Elementary Advanced Both INCLUDE TOPICS: Basic Math Algebra Analysis Biography Calculus Comp Sci Discrete Economics Foundations Geometry Graph Thry History Number Thry Physics Statistics Topology Trigonometry The Fibonacci Sequence edieval mathematician and businessman Fibonacci ( Leonardo Pisano ) posed the following problem in his treatise Liber Abaci (pub. 1202): How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on? It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers: This is an example of a recursive sequence , obeying the simple rule that to calculate the next term one simply sums the preceding two: F(1) = 1 F(2) = 1 F( n ) = F( n n Thus 1 and 1 are 2, 1 and 2 are 3, 2 and 3 are 5, and so on.

95. Fibonacci fibonacci Numbers. and how they are related to flowers, pine cones,.pineapples, palm fibonacci Links and Downloads. Downloads. You can http://www.branta.connectfree.co.uk/fibonacci.htm

Fibonacci Numbers and how they are related to flowers, pine cones, pineapples, palm trees, suspension bridges, spider webs, dripping taps, CDs, your savings account, and quite a few other things 26th October 2000 Back to Home Page Back to Flowers Back to Nature's Maths Two curved lines have been drawn on the first photograph of a thistle head - one spiralling out clockwise, and one spiralling out anti-clockwise. There are thirteen of the first kind, and twenty-one of the second. In the second photograph the situation is reversed. The third photograph shows a teazle flower head, which is longer than the almost spherical thistles. Flatter versions of the patterns are seen in many plants like sunflowers and daisies. More cylindrical versions are seen in the arrangement of leaves on plant stems, and in the scars on some tree trunks. These are not random numbers - they are members of the following sequence - 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 etc This sequence is known as the Fibonacci series, and is well known in mathematics. Each number is the sum of the previous two. The ratio of successive pairs tends to the so-called golden section (GS) - 1.618033989 . . . . . whose reciprocal is 0.618033989 . . . . . so that we have

96. Biographies More picture taken from Eric s Treasure Troves, fibonacci, Leonardode Pisa (ca. 1170 ca. 1240). Appeared in Lecture 7. The http://www-2.cs.cmu.edu/~15251/Biographies/index.htm.save

leib Biographies Short biographies of famous mathematicians and computer scientists mentioned in class, along with links to more information about them. picture taken from Eric's Treasure Troves Euclid (ca. 325 - ca. 270 BC) Appeared in: Lecture 7 Euclid's greatest accomplishment was the Elements , his 13-chapter book outlining everything he knew about geometry. He based all of his geometrical theorems on just five postulates, making the work very rigorous and complete, but for two millenia mathematicians wondered if the fifth postulate (the so-called "Parallel Postulate") could in fact be derived from the other four. This was finally answered (in the negative) by Lobachevsky, Bolyai, and Gauss, leading to the branch of mathematics we now call Non-Euclidean Geometry More... Al-Karaji, Abu Bekr ibn Muhammad ibn al-Husayn (953 - ca. 1029) Appeared in: Lecture 9 Al-Karaji's work centered around algebra and polynomials, giving rules for arithmetic operations to manipulate polynomials. Woepcke describes his work as introducing the "theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle. Additionally, Al-Karaji used induction to prove his results. More...

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