41. Fibonacci, Leonardo Da Pisa (ca. 1170-ca. 1240) -- From Eric Weisstein's World O leonardo Pisano fibonacci. The Book of Squares. Orlando, FL Academic Press, 1987.© Eric W. Weisstein. header. mathematica calculationcenter. 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.

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

43. Fibonacci, Leonardo fibonacci, leonardo. Italian mathematician. He published Liber abaci/The Book ofthe Calculator in Pisa in 1202, which was instrumental in the introduction http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0001287.html

// Show bread crumbs navigation path. breadcrumbs('four'); //> From: www.tiscali.co.uk/reference/ ENCYCLOPAEDIA Hutchinson's Encyclopaedia Men's Health ... Wildlife Frames not supported Frames not supported Encyclopaedia Search Click a letter for the index A B C D ... Z Or search the encyclopaedia: Fibonacci, Leonardo Italian mathematician. He published Liber abaci/The Book of the Calculator in Pisa in 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 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. Related Links mathematics geometry Pascal, Blaise Samoa Flag Red and white are traditional colours, dating back to the flag of 19th-century Samoan king, Malietoa Laupepa. The Southern Cross constellation links Samoa to other countries in the southern hemisphere. Effective date 4 July 1997.

44. Leonardo Fibonacci Analysis Work of leonardo fibonacci which introduced the numbers used in theWest today fibonacci, leonardo (The Columbia Encyclopedia, Sixth Edition) http://www.infoplease.com/ce6/people/A0818607.html

in All Infoplease Almanacs Biographies Dictionary Encyclopedia Daily Almanac for Sep 1, 2005 Skip Navigation Home Almanacs ... Word of the Day Editor's Favorites Back to School Hurricanes Daylight Saving Time Energy Consumption ... Mississippi Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map College Center Scholarship Search College Resources Career Center Job Search Post Your Resume Continuing Ed. more . . . Search: Infoplease Info search tips Search: Biographies Bio search tips google_ad_client = 'pub-1894504138907931'; google_ad_width = 120; google_ad_height = 240; google_ad_format = '120x240_as'; google_ad_type = 'text'; google_ad_channel =''; google_color_border = ['336699','B4D0DC','DFF2FD','B0E0E6']; google_color_bg = ['FFFFFF','ECF8FF','DFF2FD','FFFFFF']; google_color_link = ['0000FF','0000CC','0000CC','000000']; google_color_url = ['008000','008000','008000','336699']; google_color_text = ['000000','6F6F6F','000000','333333']; Encyclopedia Fibonacci, Leonardo Pronunciation Key Fibonacci, Leonardo , b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In

45. Leonardo Da Pisa leonardo fibonacci fibonacci, leonardo , bc1170, d. after 1240, AnalysisWork of leonardo fibonacci which introduced the numbers used in the West http://www.infoplease.com/ce6/people/A0915573.html

var zflag_nid="162"; var zflag_cid="57/1"; var zflag_sid="53"; var zflag_width="728"; var zflag_height="90"; var zflag_sz="14"; in All Infoplease Almanacs Biographies Dictionary Encyclopedia Daily Almanac for Sep 1, 2005 Skip Navigation Home Almanacs ... Word of the Day Editor's Favorites Back to School Hurricanes Daylight Saving Time Energy Consumption ... Mississippi Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map College Center Scholarship Search College Resources Career Center Job Search Post Your Resume Continuing Ed. more . . . Search: Infoplease Info search tips Search: Biographies Bio search tips google_ad_client = 'pub-1894504138907931'; google_ad_width = 120; google_ad_height = 240; google_ad_format = '120x240_as'; google_ad_type = 'text'; google_ad_channel =''; google_color_border = ['336699','B4D0DC','DFF2FD','B0E0E6']; google_color_bg = ['FFFFFF','ECF8FF','DFF2FD','FFFFFF']; google_color_link = ['0000FF','0000CC','0000CC','000000']; google_color_url = ['008000','008000','008000','336699']; google_color_text = ['000000','6F6F6F','000000','333333']; Encyclopedia Leonardo da Pisa: Leonardo da Pisa: see Fibonacci, Leonardo

46. Leonardo Fibonacci fibonacci, leonardo, laonär do febonät che Pronunciation Key. fibonacci,leonardo , bc1170, d. after 1240, Italian mathematician, known also as leonardo http://www.factmonster.com/ce6/people/A0818607.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites 2006 TFK Almanac Quiz: Charlie and the Chocolate Factory SpongeBob Lemony Snicket ... Fantasy Books Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Encyclopedia Fibonacci, Leonardo 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 The Columbia Electronic Encyclopedia, Page Tools: Cite Print More on Leonardo Fibonacci from Fact Monster: numeral - numeral, symbol denoting anumber. The symbol is a member of a family of marks, such as letters, ... mathematics: Development of Mathematics - Development of Mathematics The earliest records of mathematics show it arising in response to ... See more Encyclopedia articles on: Mathematics: Biographies AD AD AD ADS Business Cards Link to Fact Monster Add Fact Monster search ... Privacy Brought to you by: Information Please

47. Pisa leonardo da Pisa leonardo da Pisa see fibonacci, leonardo. leonardo fibonacci -fibonacci, leonardo , bc1170, d. after 1240, Italian mathematician, http://www.factmonster.com/ce6/world/A0839175.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites 2006 TFK Almanac Quiz: Charlie and the Chocolate Factory SpongeBob Lemony Snicket ... Fantasy Books Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Site Map Sponsored Links TripAdvisor Pisa (Tuscany) Encyclopedia Pisa Pronunciation Key Pisa , city (1991 pop. 98,928), capital of Pisa prov., Tuscany, N central Italy, on the Arno River. It is now c.6 mi (9.7 km) from the Tyrrhenian Sea, which once reached the city. Pisa is a commercial and industrial center; manufactures include auto and truck parts, glass, pharmaceuticals, and processed food. Probably a Greek colony, later certainly an Etruscan town, it became a Roman colony (180 B.C. ) and prospered. During the 9th to 11th cent. A.D. it developed into a powerful maritime republic, fighting the Arabs throughout the Mediterranean and rivaling Genoa and Venice. Pisa's political and commercial power increased upon acquisition of possessions and trading privileges in the eastern Mediterranean during the Crusades. While competing with Genoa for the possession of Corsica and Sardinia, Pisa was crushed by the Genoese in the naval battle of Meloria (1284). As a Ghibelline center in the 13th and 14th cent., the city was also chronically at war with Florence, to which it fell in 1406. At the same time, a school of sculpture founded by Nicola

48. Fibonacci, Leonardo. The Columbia Encyclopedia, Sixth Edition. 2001-05 fibonacci, leonardo. The Columbia Encyclopedia, Sixth Edition. 200105. http://www.bartleby.com/65/fi/Fibonacc.html

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49. FUSION Anomaly. Fibonacci Liber Abaci by Italian travelermathematician leonardo fibonacci (leonardo leonardo was posthumously given the nickname fibonacci (for filius Bonacci, http://fusionanomaly.net/fibonacci.html

Telex External Link Internal Link Inventory Cache Fibonacci This nOde last updated January 20th, 2004 and is permanently morphing... (9 Ik (Wind) / 10 (Muan ( Owl Fibonacci sequence noun The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers. [After Leonardo Fibonacci (died c. 1250), Italian mathematician.] Fibonacci numbers In mathematics, an infinite series in which each successive integer is the sum of the two that precede it- for example, 1, 1, 2, 3, 5, 8, 13, 21, 34.... Fibonacci numbers are named for the thirteenth-century mathematician Leonardo Fibonacci. In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence. For example, a data set of 34 items would be divided into one group of 21 and another of 13. If the item being sought were in the group of 13, the group of 21 would be discarded, and the group of 13 would be divided into 5 and ; the search would continue until the item was located. The ratio of two successive terms in the Fibonacci sequence converges on the Golden Ratio, a "

50. MSN Encarta - Fibonacci fibonacci, leonardo or leonardo of Pisa (1170?1240?), Italian mathematician fibonacci, leonardo, Microsoft® Encarta® Online Encyclopedia 2005 http://encarta.msn.com/encyclopedia_761579463/Fibonacci.html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Upgrade your Encarta Experience Spend less time searching and more time learning. Learn more Tasks Find in this article Print Preview Related Items Fibonacci series importance to the history of algebra more... Further Reading Search for books and more related to Fibonacci, Leonardo Encarta Search Search Encarta about Fibonacci, Leonardo Advertisement document.write(' Fibonacci, Leonardo Encyclopedia Article Multimedia 1 item Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and who made contributions to the mathematical fields of algebra and number theory . Fibonacci was born in Pisa, Italy, a commercial city, where he learned the basics of business calculation. When Fibonacci was about 20, he went to Algeria, where he began to learn Indian numerals and Arabic calculating methods, knowledge he supplemented during more extensive travels. Fibonacci used this experience to improve on the commercial computing techniques he knew and to extend the work of classical mathematical writers, such as the Greek mathematicians Diophantus and Euclid. Few works by Fibonacci still exist; he wrote on number theory, practical problems of business mathematics and surveying, advanced problems in algebra, and recreational mathematics. His writings on recreational mathematics, which were often posed as story problems, became classic mental challenges as early as the 13th century. Such problems often involved the summation of recurrent series, such as the

51. 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 of the Calculator in Pisa 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.

52. Allmath.com - Math Site For Kids! Home Of Flashcards, Math fibonacci, leonardo. fibonahchee , also known as leonardo Pisano. (c.1170c.1250).Mathematician, born in Pisa, Italy. Arguably the most outstanding http://www.allmath.com/biosearch.php?QMeth=ID&ID=11691

53. Biography Of Leonardo Fibonacci fibonacci was best known as leonardo of Pisa. World Book CD Deluxe; fibonacci,leonardo The fibonacci Numbers The fibonacci Numbers and the Golden http://www.andrews.edu/~calkins/math/biograph/199899/biofibo.htm

Back to the Table of Contents Biographies of Mathematicians - Fibonacci Table of Contents Introduction Biography Accomplishments Effects ... Bibliography Introduction Fibonacci was known for many things. He was best known for the Fibonacci Numbers, which is a number sequence that he had discovered while solving a problem about rabbits. There is a lot more that we will talk about him and his discoveries which are now coming up. Biography From 529 until 1500 A.D. there were no big improvements in european mathematics. Except for Fibonacci, who was a great 13th century mathematician. He was born in Pisa, Italy, and was the son of a pisan merchant. Fibonacci was best known as Leonardo of Pisa. His father was also a customs officer for the North African city of Bugia. Since Fibonacci was the son of a merchant, he was able go travel freely all over the Byzantine Empire. Merchants at the time were immuned, so they were allowed to move about freely. This allowed him to visit many of the area's centers of trade. While he was there, he was able to learn both the mathematics of the scholars and the calculating schemes in popular use, at the time. Accomplishments He published a book called Liber Abaci In 1202 he published the first of his four books

54. Leonardo Fibonacci http://serge.mehl.free.fr/chrono/Fibonacci.html

FIBONACCI Leonardo, italien, 1175 De son vrai nom Léonard de Pise, dit Fibonacci (signifiant "fils de Bonaccio"). Commerçant et grand voyageur. Dans son Liber Abac i ( Livre de calcul Al Khwarizmi Fibonacci fait grand usage des nombres "arabes" ( fausse position Practica geometriae (1220), où il applique des méthodes algébriques à des problèmes géométriques et un traité sur le calcul des racines carrées et cubiques ( Liber Quadratorum Le Liber Abaci u o = u et pour tout n : u n+2 = u n + u n+1 nombre d'or F limite du quotient u n+1 u n La section dorée ( divine proportion ) et le nombre d'or : divine proportion (appellation due à Pacioli On parle aussi de rectangle d'or . Si, dans le rectangle jaune, vous "ôtez" le carré de côté AK, vous obtiendrez encore un rectangle d'or. La divine proportion ou section dorée (étude ci-après 1/s = s + 1, soit : s + s - 1 = Son inverse, soit s + 1 est le nombre d'or , noté généralement F , de valeur : F vérifie alors l'équation F F - 1 = 0, soit

55. Do You Believe In Fibonacci Numbers ? Andrew s fibonacci Dreams. Srpski leonardo iz Pize Compress some Unsolved fibonacci fibonacci Numbers. The fibonacci Association Official website http://alas.matf.bg.ac.yu/~mm97106/math/fibo/fibo.htm

Do you believe in Fibonacci Numbers ? Andrew's Fibonacci Dreams Srpski : Leonardo iz Pize Compress some Unsolved Fibonacci St Andrew's Leonardo Fibonacci Find Fibonacci numbers divisible by p^2 Fibonacci numbers mod p Divisors of Fibonacci numbers ... Fibonacci Powers Bibliography : St Andrews Leonardo Pisano Clark Kimberling Fibonacci Ron Knott Who was Fibonacci ? University of Virginia Fibonacci Fibonacci Leonardo Fibonacci University of Michigan Fibonacci Italian-American Website Fibonacci Back to Andrew Home Page Andrew Math Page Fibonacci Numbers The Fibonacci Association Official website Ron Knott The Fibonacci Numbers Holy Cros Fibonacci Numbers Evansville Fibonacci Number-Theorists Team 27890 The Fibonacci Series Team 27890 The Fibonacci Series Forum Marc Renault Fibonacci modulo m The Fibonacci Quarterly 9th International Conference The Access Indiana Guide to Fibonacci Willem's Fibonacci site R.Jovanovic Fibonaci i Paskalov trougao Search Fibonacci Numbers Yahoo Fibonacci Numbers Google Fibonacci Numbers Dmoz.org

56. References fibonacci,leonardo. Reference. Context. Shadow, Structure of brain and plants.Natsums, Structure of plants. Thinkmat, Structure of plants http://members.fortunecity.com/templarser/f1-4.html

web hosting domain names photo sharing Reference Guide Fibonacci,Leonardo Reference Context Shadow Structure of brain and plants Natsums Structure of plants Thinkmat Structure of plants Friction Rabbit breeding/Fractals Chaos Aesthetics/Golden Mean MAIN INDEX REFERENCE GUIDE TRANSCRIPTS GLOSSARY ... Maths File Info: Created Updated Page Address: http://members.fortunecity.com/templarser/f1-4.html web hosting domain names web design ... advertising online

57. FIBONACCI fibonacci, also known as leonardo of Pisa, was born in Pisa, 2 fibonacci,Scritti di leonardo Pisano (ed. Baldassarre Boncompagni, 18571862). http://faculty.evansville.edu/ck6/bstud/fibo.html

Fibonacci (c.1175 - c.1240) mathematician Fibonacci was probably the greatest genius of number theory during the 2000 years between Diophantus and Fermat. The sequence defined by F(1) = 1, F(2) = 1, and F(n) = F(n-1) + F(n-2) for n = 3, 4, 5, ... is named the Fibonacci sequence. Fibonacci, also known as Leonardo of Pisa, was born in Pisa, home of the famous leaning tower (inclined at an angle of 16.5 degrees to the vertical). Little is known of his life, and no portrait exists. However, a statue of Fibonacci was erected by the citizens of Pisa. In 1978, Frank Johnson took a picture, seen here, of the head of the Fibonacci statue, some fifteen feet above ground. Since then, the statue has been moved to its present (and original) location at Camposanto Monumentale (at Piazza dei Miracoli, where the Leaning Tower stands.) For more about this statue, visit Fibonacci's statue in Pisa One of the best modern sources of information about Fibonacci is the following article: A. F. Horadam , "Eight hundred years young," The Australian Mathematics Teacher With the kind permission of Professor Horadam and the editor of The Australian Mathematics Teacher

58. Leonardo Fibonacci Translate this page leonardo fibonacci. Los enlaces en color anaranjado lo llevan a las páginas leonardo fibonacci fue un matemático italiano que vivió entre 1170 y 1240. http://www.windows.ucar.edu/tour/link=/people/middle_ages/fibonacci.sp.html

Leonardo Fibonacci Los enlaces en color anaranjado lo llevan a las páginas en Inglés, que aún no han sido traducidas al Español. Leonardo Fibonacci fue un matemático italiano que vivió entre 1170 y 1240. realizó muchos viajes de negocios con su padre y esto lo expuso a gran cantidad de diferentes técnicas matemáticas usadas alrededor del mundo. Fibonacci recopiló todas estas ideas en varios libros, de manera que cualquier persona pudiera conocerlas sin necesidad de tener que viajar como él lo había hecho. Sus escritos introdujeron los numerales árabicos a la matemática europea. Fibonacci realizó contribuciones matemáticas propias, en teoría de números y en secuencias recursivas. Es famoso por la secuencia Fibonacci, donde todo número es la suma de los dos anteriores. Última modificación el 25 de febrero de 1997 por el equipo de Windows La fuente de este material es Windows to the Universe (Ventanas al Universo) , en http://www.windows.ucar.edu/ de University Corporation for Atmospheric Research (UCAR). ©1995-1999, 2000 Los Regentes de la Universidad de Michigan; ©2000-02 University Corporation for Atmospheric Research. Todos los Derechos son Reservados. Políticas del Portal y Renuncia a Reclamos

59. Leonardo Fibonacci: A Who2 Profile Also known as leonardo of Pisa, fibonacci introduced to Europe and popularizedthe HinduArabic number system (also called the decimal system). http://www.who2.com/leonardofibonacci.html

LEONARDO FIBONACCI Mathematician Also known as Leonardo of Pisa, Fibonacci introduced to Europe and popularized the Hindu-Arabic number system (also called the decimal system). He contributed greatly to number theory, and during his life published many important texts, including Liber abbaci Practica geometriae (1220) and Liber quadratorum (1225). He is also known for the Fibonacci Series, a numerical series found frequently in the natural world. In the sequence, each number is equal to the sum of the preceding two (1, 1, 2, 3, 5, 8, 13, 21 ...). For other explanations of terms and phrases from famous names, see our loop of Who's What? The Fibonacci Series Slick and supercool examples and explanations Fibonacci Good text introduction to Fibonacci and his work Who Was Fibonacci? A brief bio that leads to a great all-around site on numbers Fibonacci An analysis that discusses the series' relationship to the Golden Ratio Birth: c. Birthplace: Pisa Italy Death: c. Best Known As: The guy who brought the Hindu-Arabic number system to Europe Shop for Posters at AllPosters.com

60. Fibonacci.html leonardo da Pisa fibonacci, Mathematician. by Linnea. leonardo fibonacci, alsoknown as leonardo Pisano, or leonardo of Pisa, was the greatest Italian http://www.northstar.k12.ak.us/schools/ryn/connections/1000-1200/Fibonacci.html

Leonardo da Pisa Fibonacci, Mathematician by Linnea Leonardo Fibonacci, also known as Leonardo Pisano, or Leonardo of Pisa, was the greatest Italian mathematician of medieval Christian Europe. He was born in 1170 a.d in Pisa, Italy. As a child he traveled on business trips to the Middle East with his father, Bonaccio, who was involved with the merchantile business. They visited Eygpt, Sicily, Seria, Greece and many more. As a result of his travels, Leonardo was raised in Bougie, Asia. Where his father served as the secretary to the Republic of Bougie. While he was there he would often join in discussions about math, from mathematicians: he learned from the book Fakhione, on the works of al- Khowarizmi on algerbra, by al-Karhki. From them and others young Leonardo learned new and different concepts of math. When he returned to Pisa he put all the ideas into a book called Liber Abbci (book of the abucus) which was published in 1202. The Emperor, Fredrick II, noticed Fibonacci's genius and invited him to the court, to a math tourniment. Each contestent was asked 3 different questions about algerbra. After that Fibonacci visited the court feriquently. Fibonacci helped introduce Hindu-Araibec numbers to Western Europe, which at the time was using the Roman numbers. In 1220, Fibonacci's second book Mis Practia Geometriae (practice of geometry) was published. It introduced trigonomtry as well as geometry. Fibonacci was best known for his discovery of the Fibonacci number series, where each number is a sum of the two proceding it. (ex. 1+1+2+3+5+8+13...) Also, Fibonacci discovered the golden ratio, rectangle, and the golden proportion; 1.618. Leonardo Fibonacci died in 1240.

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