Fibonacci
Portrait by unknown artist
Born	c. 1170
Died	c. 1250 (aged around 80)
Nationality	Italian
Fields	Mathematician
Known for	Fibonacci number Fibonacci prime Brahmagupta–Fibonacci identity Fibonacci polynomials Fibonacci pseudoprime Fibonacci word Reciprocal Fibonacci constant Introduction of digital notation to Europe Pisano period Practical number

Leonardo Pisano Bigollo (c. 1170 – c. 1250)^[1] also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."^[2]

Fibonacci is best known to the modern world for ^[3] the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.^[4]

Life[link]

Leonardo Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant. Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled with him to help; it was there he learned about the Hindu–Arabic numeral system.^[5]

Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honored Leonardo, referred to as Leonardo Bigollo,^[6] by granting him a salary.

In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.^[7]

[edit] Liber Abaci

In the Liber Abaci (1202), Fibonacci introduces the so-called modus Indorum (method of the Indians), today known as Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought.

Fibonacci sequence[link]

Liber Abaci also posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century,^[8][9][10] but it was Fibonacci's Liber Abaci that introduced it to the West.

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ... ^[11]

The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).

In popular culture[link]

• Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1981 to 1987.
• Stock traders frequently look to the "Fibonacci retracement" when predicting future share prices.
• A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans (1973). He was left out of the 2006 movie version, however.

19th century statue of Fibonacci in Camposanto, Pisa.

Bibliography[link]

Fibonacci wrote the following books:

• Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
• Practica Geometriae (1220), a compendium on geometry and trigonometry.
• Flos (1225), solutions to problems posed by Johannes of Palermo
• Liber quadratorum, ("The Book of Squares") on Diophantine equations, dedicated to Emperor Frederick II. See in particular the Brahmagupta–Fibonacci identity.
• Di minor guisa (on commercial arithmetic; lost)
• Commentary on Book X of Euclid's Elements (lost)

See also[link]

• List of topics named after Fibonacci
• Brahmagupta–Fibonacci identity
• Elliott wave principle
• Engel expansion
• Fibonacci search technique
• Golden ratio
• Hylomorphism (computer science)
• Pisano period
• Practical number
• Primefree sequence
• Verner Emil Hoggatt, Jr.

Notes[link]

References[link]

• Goetzmann, William N. and Rouwenhorst, K.Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets (2005, Oxford University Press Inc, USA), ISBN 0-19-517571-9.
• Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104.
• A. F. Horadam, "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123-134.

External links[link]

• Fibonacci Biography
• Who was Fibonacci? by Ron Knott.
• Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03-28
• Fibonacci at Convergence
• O'Connor, John J.; Robertson, Edmund F., "Leonardo Pisano Fibonacci", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html .

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Keith J. Devlin
Keith Devlin (2011)
Born	East Hull, England
Nationality	English and American
Fields	Mathematics
Institutions	Stanford University, Kings College London, University of Bristol, University of Manchester, University of Aberdeen, University of Oslo, University of Heidelberg, University of Bonn, University of Toronto, University of Lancaster, Colby College, St. Mary's College of California
Alma mater	Kings College London, University of Bristol
Doctoral advisor	Frederick Rowbottom[1]

Keith J. Devlin is a British mathematician and popular science writer. He has lived in the United States since 1987 and has dual American-British citizenship.

Biography[link]

Devlin earned a B.Sc. (Special) in Mathematics at Kings College London and a Ph.D. in Mathematics at the University of Bristol under the supervision of Frederick Rowbottom.^[1] He is co-founder and Executive Director of Stanford University's Human-Sciences and Technologies Advanced Research Institute (H-STAR), a co-founder of Stanford Media X university-industry research partnership program, and a Senior Researcher in the Center for the Study of Language and Information (CSLI). He is a commentator on National Public Radio's Weekend Edition Saturday, where he is known as "The Math Guy."^[2]

As of 2011, he is the author of 31 books and over 80 research articles.^[3] Several of his books are aimed at an audience of the general public, as opposed to much academic work.

His recent research work has focused on the development of new tools and protocols to assist intelligence analysis and the development and use of videogames in mathematics education.

Devlin is also creator of the concept "soft mathematics," introduced in the final chapter of his book Goodbye, Descartes.

Research publications[link]

• Devlin, Keith I.; Jensen, R. Björn (1975), "Marginalia to a theorem of Silver", ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974), Lecture notes in mathematics, 499, Berlin, New York: Springer-Verlag, pp. 115–142, DOI:10.1007/BFb0079419, ISBN 978-3-540-07534-9, MR 0480036, http://books.google.com/books?id=9UHU_bq-wc8C&dq=Marginalia+to+a+theorem+of+Silver  [First proof of Jensen's covering theorem; Keith J. Devlin is credited as Keith I. Devlin in the paper.]

List of books[link]

This list is incomplete; you can help by expanding it.

• Mathematics Education for a New Era: Video Games as a Medium for Learning. A K Peters. 2011. ISBN 978-1-56881-431-5. 
• The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. Basic Books. 2008. ISBN 978-0-465-00910-7. 
• The Numbers Behind NUMB3RS: Solving Crime with Mathematics. Plume. 2007. ISBN 0-452-28857-6.  with coauthor Gary Lorden
• The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). Thunder's Mouth Press. 2006. ISBN 1-56025-839-X. 
• The Millennium Problems: the Seven Greatest Unsolved Mathematical Puzzles of Our Time. Basic Books. 2002. ISBN 0-465-01730-4. 
• The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Basic Books. 2000. ISBN 0-465-01619-7. 
• Mathematics: The New Golden Age. Columbia University Press. 1999. ISBN 0-231-11639-X. 
• The Language of Mathematics: Making the Invisible Visible. Holt Paperbacks. 1998. ISBN 0-8050-7254-3. 
• Mathematics: The Science of Patterns. Holt Paperbacks. 1996. ISBN 0-8050-7344-2. 
• The Joy of Sets: Fundamentals of Contemporary Set Theory. Springer. 1993. ISBN 0-387-94094-4. 
• Logic and Information. Cambridge University Press. 1991. ISBN 0-521-49971-2. 
• Constructibility. Springer. 1984. ISBN 3-540-13258-9. 
• The Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Publishing Co. 2011. ISBN 978-0-8027-7812-3. 

Awards[link]

• Joint Policy Board for Mathematics Communications Award^[4]
• In 2007 he received Wonderfest's Carl Sagan Prize for Science Popularization.^[5]
• 2004 International Pythagoras Prize in Mathematics, in the category Best Expository Text in the Mathematical Sciences for the Italian translation of The Millennium Problems^[6]

References[link]

1. ^ ^{a b} Devlin, K. (1973). "Some weak versions of large cardinal axioms". Annals of Mathematical Logic 5 (4): 291–325. DOI:10.1016/0003-4843(73)90010-7.  edit
2. ^ Archive of The Math Guy series from NPR's Weekend Edition accessed 2007-11-09
3. ^ http://www.stanford.edu/~kdevlin/
4. ^ Keith Devlin at Stanford University
5. ^ "Sagan Prize Recipients". wonderfest.org. 2011 [last update]. http://wonderfest.org/sagan-prize/sagan-prize-recipients/. Retrieved 10 September 2011. 
6. ^ Stanford Report—2 November 2005

External links[link]

• Official website including his curriculum vitae
• Devlin's Angle — column at the Mathematical Association of America
• Radio interview on Philosophy Talk
• The Unfinished Game, Google Authors talk, 9 October 2008.
• Keith Devlin at the Mathematics Genealogy Project