61. Leonardo Of Pisa (Fibonacci) - Mathematics And The Liberal Arts leonardo fibonacci. fibonacci Quarterly 1 (1963), 1519. A brief survey of thework of fibonacci, leonardo of Pisa. Reprinted in Swetz, Frank J., http://math.truman.edu/~thammond/history/Fibonacci.html

Leonardo of Pisa (Fibonacci) - Mathematics and the Liberal Arts To expand search, see Medieval Europe . Laterally related topics: Gerbert, Pope Sylvester II The Liberal Arts Alexander de Villa Dei Sacrobosco (John of Holywood) ... England in the Middle Ages , and France in the Middle Ages The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Biggs, N. L. The roots of combinatorics.

62. Leonardo Pisano --  Encyclopædia Britannica English leonardo of Pisa , original name leonardo fibonacci medieval Italian leonardo Pisano fibonacci Biography of this medieval Italian mathematician. http://www.britannica.com/eb/article-9047817

Home Browse Newsletters Store ... Subscribe Already a member? Log in Content Related to this Topic This Article's Table of Contents Introduction Life Contributions to number theory Additional Reading Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Leonardo Pisano  Encyclopædia Britannica Article Page 1 of 4 born c. 1170, , Pisa? died after 1240 English Leonardo of Pisa , original name Leonardo Fibonacci medieval Italian mathematician who wrote Liber abaci Leonardo Pisano... (75 of 1029 words) var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: "Leonardo Pisano."

63. AllRefer.com - Leonardo Fibonacci (Mathematics, Biography) - Encyclopedia AllRefer.com reference and encyclopedia resource provides complete informationon leonardo fibonacci, Mathematics, Biographies. http://reference.allrefer.com/encyclopedia/F/Fibonacc.html

AllRefer Channels :: Health Yellow Pages Reference Weather September 01, 2005 Medicine People Places History ... Maps Web AllRefer.com You are here : AllRefer.com Reference Encyclopedia Mathematics, Biographies ... Leonardo Fibonacci By Alphabet : Encyclopedia A-Z F Leonardo Fibonacci, Mathematics, Biographies Related Category: Mathematics, Biographies Leonardo Fibonacci [l A O O f E b O E Pronunciation Key , 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 Topics that might be of interest to you: mathematics Related Categories: People Science and Technology Science and Technology Mathematics ... Biographies More articles from AllRefer Reference on Leonardo Fibonacci SITE MAPS Encyclopedia US Gazetteer: US States A-C US States D-H US States I-L US States M ... Countries A-Z Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities. About Us Contact Us Privacy Links Directory ... Link to AllRefer.com

64. Fibonacci Translate this page leonardo Pisano es más conocido por su apodo fibonacci. Jugó un rol muy importanteal revivir las matemáticas antiguas y realizó importantes contribuciones http://www.sectormatematica.cl/biografias/fibonacci.htm

Fibonacci, Leonardo Leonardo Pisano es más conocido por su apodo Fibonacci. Jugó un rol muy importante al revivir las matemáticas antiguas y realizó importantes contribuciones propias. Liber abaci, publicado en el 1202 después de retornar a Italia, esta basado en trozos de aritmética y álgebra que Fibonacci había acumulado durante sus viajes. Liber abacci introduce el sistema decimal Hindú-Arábico y usa los números arábicos dentro de Europa. Un problema en Liber abaci permite la introducción de los números de Fibonacci y la serie de Fibonacci por las cuales Fibonacci es recordado hoy en día. El Diario Trimestral de Fibonacci es un moderno periódico dedicado al estudio de las matemáticas que llevan estas series. Otros libros de Fibonacci de mayor importancia es Prácticas de Geometría en el año 1220 que contiene una extensa colección de geometría y trigonometría. También en Liber quadratorum del año 1225 aproximó las raíces cúbicas obteniendo una respuesta que en la notación decimal es correcta en 9 dígitos. "Mis Prácticas de geometría" del año 1220 entrega una compilación de la geometría al mismo tiempo que introduce algo de trigonometría.

65. PANI'S WEB PAGE leonardo fibonacci (11751250) fibonacci s Life The fibonacci Sequence fibonacci s Rabbits The fibonacci Spiral. Other web sites on fibonacci http://www.bath.ac.uk/~ma2pi/MATH0126.html

Leonardo Fibonacci (1175-1250) Fibonacci's Life The Fibonacci Sequence Fibonacci's Rabbits The Fibonacci Spiral Other web sites on fibonacci Fibonacci and Lucas Factorisations Fibonacci facts Fibonacci, Leonardo - MSN Encarta Links My homepage Bath homepage

66. Who Was Leonardo Fibonacci? leonardo fibonacci (11701250) was born in Pisa, the son of Guilelmo and a memberof the Bonacci family. He was educated in North Africa, where he grew up http://www.bath.ac.uk/~ma1jmp/link1.html

Leonardo Fibonacci Leonardo Fibonacci (1170-1250) was born in Pisa, the son of Guilelmo and a member of the Bonacci family. He was educated in North Africa, where he grew up because of his father being a representative for the merchants of Pisa in the important of port of Bugia. This port, now known as Bejaia is in Algeria on the Mediterranean coast. He followed his father in his travels and appreciated the importance of various peoples mathematical skills. He finished his travels around 1200 and returned to Pisa. On his return he began to write mathematical texts which helped revive some ancient mathematics and he also made some significant discoveries of his own. In a time when Europe was more interested in war than scholarship his works were amazingly popular and recognised in Italy. This was mainly due to the fact that unlike many mathematical works of the time his work had many practical applications. The Holy Roman Emperor of the time was Frederik II. He became aware of the brilliance of Fibonacci and invited him to his court in Pisa so they could meet. Here another member of Frederik's court, Johannes of Palermo, presented a number of problems to the great mathematician. Fibbonacci solved three of these problems and sent the solution back to Frederik in his book 'Flos' (1225). One of these solutions involved solving the equation: x x x Firstly he proved that the solution was neither integer, a fraction or a root of a fraction so he then approximated the solution in sexagecimal notation as 1.22.7.42.33.4.40 this translates to 1.3688081075 which is correct to an impressive nine decimal places.

67. Biographies fibonacci, leonardo de Pisa (ca. 1170 ca. 1240). Appeared in Lecture 7.The fibonacci numbers are taught to schoolchildren around the world as a fun and 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...

68. FIBONACCI, Leonardo (1170 - 1230) leonardo fibonacci nin en büyük hizmeti, Hârizmî nin matematigi ile, çok kullanisliolan Hint ve Arap karisimi sayilarini batiya tanitmakla çok büyük bir http://www.matematikci.com/unluler/Leonardo_FIBONACCI.htm

Leonardo FIBONACCI Pisa'lý Fibonacci Rönenans'tan önce, Asya ülkelerinin matematiðini Avrupa'ya en etkili olarak taþýyan ve götüren biri olarak bilinir. Doðumundan 1230 yýlýna kadar yaþam öyküsü hakkkýnda hemen hemen hiç bir þey bilinmiyor. Yalnýz, o zamanýn Ýtalya'sýnda en büyük ticaret merkezlerinden biri olan Pisa'da doðduðu bilinmektedir. Öðretmenlerin ona verdiði matematik dersleri daha çok yaþam koþullarý ile ilgiliydi. O, bunlarý öðrendikten, matematiði iyice kavradýktan sonra çevresine öðretti. Sonra, sayýlar kuramý ve geometri üzerine iki kitap yazmýþtýr. O, artýk öðretmenlerinin kuru matematiðinden daha da ileri giderek yeni rakamlarla düþünebiliyor ve onlarý birer oyuncak gibi kullanýyordu. Ünlü Fibonacci dizisi bu buluþlarýn en ünlüleridir. Baþlangýçta birer rakam oyunu gibi görünen bu dizisi, daha sonra Mendel yasalarýyla uygulama alaný bulmuþtur. Doðadaki çiçeklerin yapraklarý üzerinde bile araþtýrma yapýyor, onlarýn düzenini ve doðadaki olaylarý sayýlarla ifade edilebileceðini keþfetmeye çalýþyordu . Bunlara daha sonra, "altýn oranlar" dendiðini biliyoruz. Bulduðu bu dizinin, neye yaradýðýný göstermek için birçok matematik ve geometri problemi düzenlenmiþtir.

69. Elsevier.com - Leonardo Pisano (Fibonacci) leonardo PISANO (fibonacci). leonardo Pisano (fibonacci) The Book of Squares Toorder this title, and for more information, go to External link http://www.elsevier.com/wps/product/cws_home/700311

Home Site map Regional Sites Advanced Product Search ... Leonardo Pisano (Fibonacci) Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book related information Submit your book proposal Other books in same subject area About Elsevier Select your view LEONARDO PISANO (FIBONACCI) The Book of Squares To order this title, and for more information, go to http://books.elsevier.com/bookscat/links/details.asp?isbn=0126431302 Edited By L. Sigler , Bucknell University Description The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers with special properties such as prime numbers, squares, and odd numbers. The faithful translation into modern English and the commentary by the translator make this book accessible to professional mathematicians and amateurs who have always been intrigued by the lure of our number system. Audience Mathematicians, historians of science, and interested laypeople.

70. Fibonacci 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 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.

71. Leonardo Pisano (Fibonacci) leonardo Pisano is better known by his nickname fibonacci. He was born in Italybut was educated in North Africa where his father held a diplomatic post. http://www.stetson.edu/~efriedma/periodictable/html/F.html

Leonardo Pisano (Fibonacci) Leonardo Pisano is better known by his nickname Fibonacci. He was born in Italy but was educated in North Africa where his father held a diplomatic post. Fibonacci was taught mathematics in Bugia and travelled widely with his father, recognising the enormous advantages of the mathematical systems used in the countries they visited. Fibonacci ended his travels around the year 1200 and at that time he returned to Pisa. There he wrote a number of important texts which played an important role in reviving ancient mathematical skills and he made significant contributions of his own. Of his books we still have copies of Liber abbaci Practica geometriae Flos (1225), and Liber quadratorum Even at a time when Europe was little interested in scholarship, there was widespread interest in Fibonacci's work. Fibonacci was a contemporary of Jordanus, but he was a far more sophisticated mathematician and his achievements were clearly recognised, although it was the practical applications rather than the abstract theorems that made him famous to his contemporaries. Liber abbaci was based on the arithmetic and algebra that Fibonacci had accumulated during his travels. The book, which went on to be widely copied and imitated, introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. Indeed, although mainly a book about the use of Arab numerals, which became known as algorism, simultaneous linear equations are also studied in this work. The second section of

72. Fibonacci, Leonardo The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. 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

73. Maggie's Teachers' Lounge leonardo fibonacci was born in Italy around 1175. At that time, most people inEurope used Roman Here is a famous observation leonardo fibonacci made. http://www.missmaggie.org/mission4_parts/eng/teaching/thanksfibonacci.html

Thank You Leonardo Fibonacci! ...For making math easier! When Leonardo returned to Pisa he wrote a book called Liber Abbaci . This means, Book of Calculating . The book showed how easy it is to do calculations using Hindu-Arabic numerals. European mathematicians were eventually persuaded to use these numerals. More Fibonacci Fun Here is a famous observation Leonardo Fibonacci made. He saw a pattern in a number sequence that starts with and 1. Look at his famous sequence and see if you spot the pattern. What is the pattern? If you studied the sequence, you know the pattern is made when you add the first two numbers to get the next number. Keep doing that and you will have the Fibonacci Sequence! You can see how this works. See if you can find the first 11 numbers in the Fibonacci Sequence. Complete this table: Look at the petals of flowers such as lilies, buttercups, marigolds, and daises. How many petals are there? Why do you think it is special to find a four-leaf clover? Look at your hands. How many fingers are on each hand?

74. World Mysteries - Science Mysteries, Fibonacci Numbers And Nature Introduction to fibonacci numbers and the golden section in nature. His fullname was leonardo of Pisa, or leonardo Pisano in Italian since he was born http://www.world-mysteries.com/sci_17.htm

Mystic Places Strange Artifacts ... Home You are here: world-mysteries.com science mysteries fibonacci numbers in nature Science Mysteries The Big Bang Nuclear Energy Asteroid Belt Pole Shifting ... Fibonacci in Nature Fibonacci Numbers in Nature Science Mysteries History Fibonacci and Nature Golden Ratio Books ... Links The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind. Stan Grist http://www.stangrist.com/fibonacci.htm

75. LEONARDO DE PISA "FIBONACCI" Translate this page leonardo de Pisa, mejor conocido por su apodo fibonacci (que significa hijo deBonacci) nació en la ciudad italiana de Pisa y vivió de 1170 a 1250. http://redescolar.ilce.edu.mx/redescolar/act_permanentes/mate/mate4k.htm

EONARDO DE PISA "FIBONACCI" L eonardo de Pisa, mejor conocido por su apodo Fibonacci (que significa hijo de Bonacci) nació en la ciudad italiana de Pisa y vivió de 1170 a 1250. S e hacía llamar a sí mismo "Bigollo" que quiere decir "bueno para nada". E ra hijo de Guilielmo Bonacci quien trabajaba como representante de la casa comercial italiana más importante de la época, en el norte de África. E s en medio de esta actividad comercial que Leonardo de Pisa comienza a formarse como mercader y matemático en la ciudad de Bugia, hoy Bejaia un puerto al noreste de Argelia. Se conoce muy poco sobre su vida; sin embargo, en el prefacio de uno de sus libros más importantes, el Liber Abaci, Leonardo comenta que fue su padre quien le enseñó Aritmética y lo animó a estudiar matemáticas. En Bugia Leonardo recibió este tipo de enseñanza de maestros árabes, lo cual era, sin duda, lo mejor que podía sucederle a un joven medieval italiano que quisiera saber matemáticas. S e convirtió en un especialista en Aritmética y en los distintos sistemas de numeración que se usaban entonces. Muy pronto se convenció de que el sistema hindo-arábigo era superior a cualquiera de los que se usaban en los distintos países que había visitado. Decidió llevar este sistema a Italia y a toda Europa de ser posible, en donde aún se usaban los numerales romanos y el ábaco. El estudio de las matemáticas y de formas más prácticas de aplicarlas como un instrumento indispensable para el desarrollo del comercio le ocuparon prácticamente toda la vida.

76. FIBONACCI, Leonardo Da Pisa (1170?1240 Után) Itáliai fibonacci, leonardo da Pisa (1170?1240 után) itáliai matematikus. BONACCIO pisai kereskedõ fia, innen a fibonacci név. Egy északafrikai városban http://www.tiszaparti-szolnok.sulinet.hu/Sulinetverseny/12b2001/Uses/Safar/Fibon

Fibonacci, Leonardo da Pisa

77. Fibonacci Series leonardo fibonacci discovered the series which converges on phi. leonardo fibonacciIn the 12th century, leonardo fibonacci discovered a simple numerical http://goldennumber.net/fibonser.htm

GoldenNumber.net Home Contact Meet the Phi Guy "Phriends" in Phi ... News Phi The Golden Number Fibonacci Series SITE SECTIONS: Home Overview Design/Composition Life ... Other Resources IN THIS SECTION: Fibonacci Series Golden Section The Symbol for Phi History Phi to 20,000 places ... Phi Phonetics Jump to any topic Home Phi Overview Acoustics Architecture Art Bible Bucky Balls Color Compositions Cosmology Credit Cards Divine Proportion Energy Fibonacci Series Fibo's 24 Pattern Five (5) and Phi Geometry Golden Section/ History Life Human Hand Human Face Human Body Human Beauty Development Human Heartbeat Human Health Body Temperatures Animals 1 Animals 2 Plants DNA Mathematics Marketing/Design Means Music Orthogons Pascal's Triangle Penrose Tiling Phi Phonetics Phi's Phormula Phi Symbol Phi to 20000 places Poetry Population Growth Powers of Phi Pronouncing Phi Quasi-crystals Quantum Time Quincy Park Solar System Spirals Stock Markets Theology Universe Affliates Do It Yourself!!! Feedback Golden Mean Gauges Use of Images Links to other sites Meet the Phi Guy News 'Phriends' in Phi Phi Logo Merchandise School Projects Search the Site Translate this site WTC Proposal Phi and the Fibonacci Series Leonardo Fibonacci discovered the series which converges on phi In the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi.

78. Fibonacci Flim-Flam. leonardo of Pisa (11701250), nickname fibonacci, was born in Pisa, Italy.He made many contributions to mathematics, but is best known by laypersons for http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

f Fibonacci Flim-Flam j by Donald E. Simanek The Fibonacci Series Fibonacci Leonardo of Pisa (1170-1250), nickname Fibonacci, was born in Pisa, Italy. He made many contributions to mathematics, but is best known by laypersons for the sequence of numbers that carries his name: This sequence is constructed by choosing the first two numbers (the "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. This simple rule generates a sequence of numbers having many surprising properties, of which we list but a few: Take any three adjacent numbers in the sequence, square the middle number, multiply the first and third numbers. The difference between these two results is always 1. Take any four adjacent numbers in the sequence. Multiply the outside ones. Multiply the inside ones. The first product will be either one more or one less than the second. The sum of any ten adjacent numbers equals 11 times the seventh one of the ten. Mesoamericans thought the numbers 7 and 11 were special. This is but one example of many sequences with simple recursion relations.

79. Leonardo Fibonacci Translate this page leonardo fibonacci, llamado leonardo Pisano (1175 - 1240) fibonacci,El matemático italiano leonardo de Pisa se le conocía más por fibonacci (o hijo de http://es.geocities.com/fisicas/cientificos/matematicos/fibonacci.htm

80. Jiskha Homework Help - Social Studies: People: Leonardo Fibonacci Homework Help Social Studies People leonardo fibonacci. by Chloe Sizzler.leonardo fibonacci was born in Pisa, Italy around 1170, the son of Guilielmo http://www.jiskha.com/social_studies/people/l_fibonacci.html

Thursday, September 1, 2005 Hip Hop Vinyl Homework Help Forum Homework Help Experts Subjects Art Business Computers English ... Social Studies Features Advice from Anika Contribute Experts Forum ... WebRing Which school subject is hardest? Math Science English Social Studies view results Homework Help: Social Studies: People: 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.

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