Leonardo Fibonacci
Leonardo Fibonacci
The Italian mathematician and merchant Leonardo Fibonacci (ca. 1180ca. 1250), also known as Leonardo of Pisa, was the most original and capable mathematician of the medieval Christian world.
Leonardo Fibonacci was born in Pisa and was brought up in Bougie, Algeria, where his father was a warehouse official. Fibonacci traveled extensively for business and pleasure throughout Europe and in Egypt, Syria, and Greece. During his travels he observed and analyzed the arithmetical systems employed in commerce and learned the HinduArabic numerals. He helped to introduce them into European mathematics.
In the Liber abaci (1202; revised version 1228), a thorough treatise on algebraic methods and problems, Fibonacci strongly advocates the use of the new Indian numerals, that is, the nine numerals, plus the zephirum, or symbol for zero. This work can be regarded as symptomatic of the mathematical renaissance of the West. In it, Fibonacci deals with the fundamental operations on integers, with fractions, with the extraction of roots, and with mathematical applications to commercial transactions. The Liber abaci also contains the famous "Fibonacci sequence," where each term after the first two is the sum of the two terms immediately preceding it, a sequence that has been found to have many significant and interesting properties. The Liber abaci remained a standard work for about 2 centuries.
In another work, entitled Flos (1225), Fibonacci considers indeterminate problems that are reminiscent of the work of Diophantus and analyzes determinate problems with methods similar to those employed by Euclid, the Chinese, and the Arabs. Another mathematical treatise by Fibonacci, the Liber quadratorum (1225), is an original and brilliant work on indeterminate analysis. Some of the problems dealt with in this book derived from the mathematical contests sponsored by the court of Frederick II, to which Fibonacci had been invited.
Though he was primarily an arithmetician and an algebraist, Fibonacci also wrote a book on geometry entitled Practica geometriae (1220), which seems to be based on Euclid's lost work On the Division of Figures. In his work Fibonacci uses algebraic methods to solve a large number of arithmetical and geometrical problems.
Further Reading
Despite Fibonacci's importance, none of his work has been translated into English. Some appreciation of his significance in Florian Cajori, A History of Mathematical Notations (2 vols., 19281929), and N. N. Vorobev, Fibonacci Numbers, edited by lan N. Sneddon (trans. 1961). See also Cajori's A History of Elementary Mathematics (1896; 2d ed. 1917); David Eugene Smith, History of Mathematics (2 vols., 19231925); W. W. Rouse Ball, A Short Account of the History of Mathematics (1924); George Sarton, Introduction to the History of Science, vol. 2 (1931); and H. A. Freebury, A History of Mathematics (1958). □
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Leonardo Fibonacci." Encyclopedia of World Biography. . Encyclopedia.com. 19 Jul. 2018 <http://www.encyclopedia.com>.
"Leonardo Fibonacci." Encyclopedia of World Biography. . Encyclopedia.com. (July 19, 2018). http://www.encyclopedia.com/history/encyclopediasalmanacstranscriptsandmaps/leonardofibonacci
"Leonardo Fibonacci." Encyclopedia of World Biography. . Retrieved July 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/history/encyclopediasalmanacstranscriptsandmaps/leonardofibonacci
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
Fibonacci, Leonardo
Leonardo Fibonacci (lāōnär´dō fēbōnät´chē), 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 (1220) he organized and extended the material then known in geometry and trigonometry. The sequence of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … , formed by adding consecutive members, is named for him; it occurs in higher mathematics in various connections. Baldassare Boncompagni edited his works (2 vol., 1857–62).
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Fibonacci, Leonardo." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 19 Jul. 2018 <http://www.encyclopedia.com>.
"Fibonacci, Leonardo." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (July 19, 2018). http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/fibonaccileonardo
"Fibonacci, Leonardo." The Columbia Encyclopedia, 6th ed.. . Retrieved July 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/fibonaccileonardo
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
Fibonacci, Leonardo
Fibonacci, Leonardo (c.1170–c.1240) Italian mathematician. He wrote Liber abaci (c.1200), the first Western work to propose the adoption of the Arabic numerical system. He produced the mathematical sequence named after him, in which each term is formed by the addition of the two terms preceding it. The sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21…. and so on. Many natural forms, such as spiral shells and leaf systems, are delimited by the Fibonacci series.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Fibonacci, Leonardo." World Encyclopedia. . Encyclopedia.com. 19 Jul. 2018 <http://www.encyclopedia.com>.
"Fibonacci, Leonardo." World Encyclopedia. . Encyclopedia.com. (July 19, 2018). http://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/fibonaccileonardo
"Fibonacci, Leonardo." World Encyclopedia. . Retrieved July 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/fibonaccileonardo
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.