Leonardo of Pisa
Leonardo of Pisa, "Fibonacci"
Born	c. 1170 Pisa, Italy
Died	c. 1250 Pisa, Italy
Residence	Italy
Nationality	Italian
Fields	Mathematician
Known for	Fibonacci number Fibonacci prime Brahmagupta-Fibonacci identity Fibonacci polynomials Fibonacci pseudoprime Fibonacci word Reciprocal Fibonacci constant Fibonacci family Introducing decimals to Europe Pisano period Practical number
Religious stance	Catholic

Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages".^[1] A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is... This is a list of characters in the Fox television drama, Prison Break. ... December 29: Assassination of Thomas Becket, Archbishop of Canterbury, in Canterbury cathedral City of Dublin captured by the Normans According to folklore, the Welsh prince Madoc sailed to North America and founded a colony. ... For other uses, see Pisa (disambiguation). ... // April 30 - King Louis IX of France released by his Egyptian captors after paying a ransom of one million dinars and turning over the city of Damietta. ... For other uses, see Pisa (disambiguation). ... Image File history File links Flag_of_Italy. ... Image File history File links Flag_of_Italy. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is... A Fibonacci prime is a Fibonacci number that is prime. ... In algebra, Brahmaguptas identity, also sometimes called Fibonaccis identity, says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares (and in two different ways). ... In mathematics, Fibonacci polynomials are a generalization of Fibonacci numbers. ... In number theory, a pseudoprime is a number that passes some test that all primes pass, but is actually composite. ... The Fibonacci word is a specific infinite sequence of binary digits (or symbols from any two-letter alphabet). ... The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. ... I like cream cheese, it tastes good on toast. ... The nth Pisano period, written π(n), is the period with which the sequence of Fibonacci numbers, modulo n, repeats. ... A practical number or panarithmic number is a positive integer n such that all preceding positive integers are a sum of distinct divisors of n. ... December 29: Assassination of Thomas Becket, Archbishop of Canterbury, in Canterbury cathedral City of Dublin captured by the Normans According to folklore, the Welsh prince Madoc sailed to North America and founded a colony. ... // April 30 - King Louis IX of France released by his Egyptian captors after paying a ransom of one million dinars and turning over the city of Damietta. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...

Fibonacci is best known to the modern world for:^[2]

• The spreading of the Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.
• A modern number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.^[3]

I like cream cheese, it tastes good on toast. ... For other uses, see Europe (disambiguation). ... Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ... For other senses of this word, see sequence (disambiguation). ... A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is...

Biography

Leonardo was born in Pisa, Italy. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).^[4] Pisas coat of arms. ... Japanese name Kanji: Hiragana: Korean name Hangul: Hanja: Vietnamese name Quốc ngữ: Hán tá»±: A posthumous name (諡號) is an honorary name given to royalty, nobles, and sometimes others, in some cultures after the persons death. ...

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 there to help him. This is where he learned about the Hindu-Arabic numeral system. Bugia is either: A western (e. ... The Almohad Dynasty (From Arabic الموحدون al-Muwahhidun, i. ...  Northern Africa (UN subregion)  geographic, including above North Africa or Northern Africa is the northernmost region of the African continent, separated by the Sahara from Sub-Saharan Africa. ... Bejaïa is a port in Béjaïa province, Algeria. ... I like cream cheese, it tastes good on toast. ...

Statue of Fibonacci. Camposanto, Pisa.

Recognizing that arithmetic with Hindu 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 introduced Hindu-Arabic numerals to Europe. Image File history File links Metadata Size of this preview: 398 × 599 pixelsFull resolution (2000 × 3008 pixel, file size: 3. ... Image File history File links Metadata Size of this preview: 398 × 599 pixelsFull resolution (2000 × 3008 pixel, file size: 3. ... This article is about the Hindu concept of numeration. ... Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. ... Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ...

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, referred to as Leonardo Bigollo,^[5] by granting him a salary. Frederick II (December 26, 1194 – December 13, 1250), of the Hohenstaufen dynasty, was a pretender to the title of King of the Romans from 1212 and unopposed holder of that monarchy from 1215. ...

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.^[6] Panoramic view The Piazza del Duomo (Cathedral Square) is a wide, walled area at the heart of the city of Pisa, Tuscany, Italy, recognized as one of the main centers for medieval art in the world. ...

Liber Abaci

Main article: Liber Abaci

In the Liber Abaci (1202), Fibonacci introduces the so-called modus Indorum (method of the Indians), today known as Hindu-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. Nevertheless, the use of decimal numerals did not become widespread until much later.^{[citation needed]} Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ... Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ... The place value system is a method of writing numbers with a base 10 numerical system. ... This article is about different methods of expressing numbers with symbols. ... A multiplication algorithm is an algorithm (or method) to multiply two numbers. ... An Egyptian fraction is a sum of distinct unit fractions, i. ... Bookkeeping (also book-keeping or book keeping) is the recording of all financial transactions undertaken by an individual or organization. ...

Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical 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, but it was Fibonacci's Liber Abaci that introduced it to the West. A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is...

Fibonacci sequence

Chimney of Turku Energia, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian artist Mario Merz for an environmental art project (1994)

Main article: Fibonacci number

In the Fibonacci sequence of numbers, each number after the first two is the sum of the previous two numbers. Thus the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc. Image File history File links Fibonacci. ... Image File history File links Fibonacci. ... A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is...

The higher up in the sequence, the closer two consecutive numbers of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1). Not to be confused with Golden mean (philosophy), the felicitous middle between two extremes, Golden numbers, an indicator of years in astronomy and calendar studies, or the Golden Rule. ...

In popular culture

• Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1982-1987.
• A "word jazz" piece called "Fibonacci Numbers" was recorded by vocal artist Ken Nordine in 2001, referring in it to Fibonacci's life and work.
• Fibonacci and the Fibonnaci numbers are mentioned as a code to unlock a vessel in Dan Brown's best selling novel, The DaVinci Code, and its movie adaptation.
• The Fibonacci Sequence is one of the key concepts used in the cult film, Pi: Faith in Chaos.
• The Fibonnaci Sequence is heavily used in the song "Lateralus" by Tool
• 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.
• The Fibonnaci Sequence, as the God's Equation, is seen in the episode of the same name in Taken.
• The Fibonacci Sequence (Fibonacci Retracement, Fibonacci Fan, Fibonacci Time Zone, and Fibonacci Arc) were often used by global traders (Forex, Stock, Commodities) as the most powerful indicator for predicting movement of the market prices.
• FIB and PHI: The golden Proportion in Musical Form by Charles Madden Connects the Fibonacci series with Music Theory.
• The musician Dr. Steel has recorded a song titled "Fibonacci Sequence".
• Electronic musician BT has a song titled "Fibonacci Sequence" on disc 2 of the album "R&R."

Flag Seal Nickname: City of Angels Location Location within Los Angeles County in the state of California Coordinates , Government State County California Los Angeles County Mayor Antonio Villaraigosa (D) Geographical characteristics Area     City 1,290. ... Art rock is a term used to describe a subgenre of rock music with experimental or avant-garde influences that emphasizes novel sonic texture. ... The Fibonaccis were an art rock group from Los Angeles. ... Ken Nordine (born April 13, 1920) is an American voiceover and recording artist best known for his series of Word Jazz albums. ... Dan Brown (born June 22, 1964) is an American author of thriller fiction, best known for the 2003 bestselling novel, The Da Vinci Code. ... The Da Vinci Code book cover The Da Vinci Code is a novel written by American author Dan Brown and published in 2003 by Random House (ISBN 0385504209). ... This article is about the film. ... Ï€ (also known as Pi or Pi - Faith in Chaos) is a 1998 American psychological thriller directed by Darren Aronofsky. ... This article or section does not adequately cite its references or sources. ... Tool is an American rock band that was formed in 1990 in Los Angeles, California. ... Crusade in Jeans (1973) is a childrens novel written by Thea Beckman. ... Crusade in Jeans is a 2006 film adaptation of the book Crusade in Jeans. ... For other uses, see Taken (disambiguation). ... Sir Charles Madden when he was Vice Admiral. ...

Books written by Fibonacci

• 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, devoted to Emperor Frederick II. See in particular Fibonacci's identity.
• Di minor guisa (on commercial arithmetic; lost)
• Commentary on Book X of Euclid's Elements (lost)

Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ... For other uses, see Geometry (disambiguation). ... Wikibooks has a book on the topic of Trigonometry The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. ... Location of the city of Palermo (red dot) within Italy. ... The Book of Squares (Liber Quadratorum in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225. ... In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ... Frederick II (December 26, 1194 – December 13, 1250), of the Hohenstaufen dynasty, was a pretender to the title of King of the Romans from 1212 and unopposed holder of that monarchy from 1215. ... In algebra, Fibonaccis identity states that and thus shows that the set of all sums of two squares is closed under multiplication. ... For other uses, see Euclid (disambiguation). ...

References

1. ^ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
2. ^ Leonardo Pisano - page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Accessed 18 September 2006.
3. ^ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]
4. ^ See the incipit of the Liber Abaci: "Incipit liber Abaci Compositus a leonardo filio Bonacij Pisano" (copied from the "Prologus" of the Liber Ab(b)aci at Latin Wikisource - emphasis added), in English: "Here starts the book of Calculation Written by leonardo son of Bonaccio, from Pisa"
5. ^ See the incipit of Flos: "Incipit flos Leonardi bigolli pisani..." (quoted in the MS Word document Sources in Recreational Mathematics: An Annotated Bibliography by David Singmaster, 18 March 2004 - emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."
   The basic meanings of "bigollo" appear to be "good-for-nothing" and "traveller" (so it could be translated by "vagrant", "vagabond" or "tramp"). A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of "Eight hundred years young"), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.
6. ^ Fibonacci's Statue in Pisa

Howard Whitley Eves (10 January 1911 New Jersey - 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics. ... The Encyclopædia Britannica is a general English-language encyclopaedia published by Encyclopædia Britannica, Inc. ... The incipit of a text, such as a poem, song, or book, is its first few words or opening line. ... Microsoft Word is a word processor program from Microsoft. ...

Bibliography

• 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 0195175719.
• 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.

See also

• Brahmagupta-Fibonacci identity
• Fibonacci heap
• Pisano period
• Lagged Fibonacci generator
• Fibonacci coding
• Fibonacci prime
• Reciprocal Fibonacci constant
• Fibonacci search technique
• Fibonacci family
• Golden ratio
• Retracement
• Lucas number
• Negafibonacci
• Elliott wave principle
• Acharya Hemachandra
• Zeckendorf's theorem
• Viswanath's constant
• Casey Mongoven
• Hylomorphism (computer science)
• Verner Emil Hoggatt, Jr.
• Practical number
• Virahanka
• Carmichael's theorem
• Primefree sequence
• Engel expansion
• Egyptian fraction
• NegaFibonacci coding

In algebra, Brahmaguptas identity, also sometimes called Fibonaccis identity, says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares (and in two different ways). ... In computer science, a Fibonacci heap is a data structure similar to a binomial heap but with a better amortized running time. ... The nth Pisano period, written π(n), is the period with which the sequence of Fibonacci numbers, modulo n, repeats. ... A Lagged Fibonacci generator (LFG) is an example of a pseudorandom number generator. ... The Fibonacci code is a universal code which encodes positive integers into binary code words. ... A Fibonacci prime is a Fibonacci number that is prime. ... The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. ... The Fibonacci search technique is a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers. ... Not to be confused with Golden mean (philosophy), the felicitous middle between two extremes, Golden numbers, an indicator of years in astronomy and calendar studies, or the Golden Rule. ... Retracement may mean: A share trading term expressed as a percentage of price movement from the most recent high in relation to the previous low. ... The Lucas numbers are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. ... In mathematics, negaFibonacci numbers are the negatively indexed elements of the Fibonacci sequence. ... It has been suggested that some of the information in this articles Criticism or Controversy section(s) be merged into other sections to achieve a more neutral presentation. ... Hemachandra SurÄ« (Sanskrit: ) (1089–1172) was an Indian Jain scholar, poet, and polymath who wrote on grammar, philosophy, prosody, and contemporary history. ... Zeckendorfs theorem, named after Belgian mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers. ... Viswanaths constant is a mathematical constant, occurring in number theory - more specifically in the study of randomized Fibonacci sequences. ... This article, image, template or category should belong in one or more categories. ... In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism (which first builds a set of results; also known as unfolding) and a catamorphism (which then folds these results into a final return value). ... A practical number or panarithmic number is a positive integer n such that all preceding positive integers are a sum of distinct divisors of n. ... Virahanka (विरहाङ्क) was an Indian prosodicist who is also known for his work on mathematics. ... Carmichaels theorem, named after American mathematician R.D. Carmichael, states that for n greater than 12, the nth Fibonacci number F(n) has at least one prime factor that is not a factor of any earlier Fibonacci number. ... In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. ... // Definition The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers such that: Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. ... An Egyptian fraction is the sum of distinct unit fractions, such as . ...

External links

• www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html
• Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003),Yale School of Management International Center for Finance Working Paper No. 03-28 [1]
• Charles Burnett, Leonard of Pisa (Fibonacci) and Arabic Arithmetic - the Medieval background to Fibonacci's work
• Fibonacci at Convergence
• wallstreetcosmos.com, Fibonacci numbers and stock market analysis, (2008).
• O'Connor, John J and Robertson, Edmund F. "Leonardo Pisano Fibonacci – 1170 - 1250" in The MacTutor History of Mathematics archive. University of St Andrews website, Scotland, 1998.
• Liber Abaci and its Egyptian fraction methods