Gourt > Science > Math > Recreations > Specific Numbers > Fibonacci Numbers
In mathematics, the Fibonacci numbers, named after Leonardo of Pisa, known as Fibonacci, form a sequence defined recursively by:
Origins
The "Fibonacci" numbers first appear, under the name maatraameru (mountain of cadence), in the work of the Sanskrit grammarian Pingala (Chhandah-shāstra, the Art of Prosody, 450 or 200 BC). The Indian mathematician Virahanka gave explicit rules for the Fibonacci sequence in the 8th century. The Indian Jain philosopher Hemachandra (c.1150) (and also Gopala) revisited the problem in some detail. Sanskrit vowel sounds can be long (L) or short (S), and Hemachandra wished to compute how many cadences of a given overall length can be composed of these. If the long syllable is twice as long as the short, the solutions are: More on [ Fibonacci number ]
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10th International Conference on Fibonacci Numbers and their Applications - Northern Arizona University, Flagstaff, Arizona, USA; 24--28 June 2002.
Amof:Info on Fibonacci Sequences - Information on Fibonacci Sequences.
Animation of Binet's formula for Reals - Interesting Applets showing Binet's formula for Fibonacci numbers extended for Reals.
Extensions of the golden section and Fibonacci series - Describes an extended Fibonacci series in which each number is the sum of the preceding three or more numbers. A corresponding extended golden section is also described.
Meta Description: [ 先行する３個以上の数の和の列からなる拡張フィボナッチ数列と、これに対応する３分割以上の黄金分割。アインシュタインの特許へのリンク ]
Fibonacci and Lucas Factorizations - Tables of known factorizations of the first 10,000 Fibonacci and Lucas numbers.
Fibonacci and Lucas Numbers - Electrical equivalence of discrete lumped cascaded T sections with the infinitesimal transmission line of distributed elements and with the Fibonacci and Lucas Numbers of 2n.
Meta Description: [ This paper will discuss the electrical equivalence of discrete lumped cascaded T sections with the infinitesimal transmission line of distributed elements and with the Fibonacci and Lucas Numbers of 2n. ]
Fibonacci Facts - Facts about the Fibonacci Sequence.
Fibonacci Number-Theorists - Biographies, photographs.
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Fibonacci Numbers - A directory of material related to the Fibonacci numbers.
Fibonacci Numbers - Describes the series and lists a some iterations.
Fibonacci Numbers - Describes the mathematic theory behind the numbers.
Fibonacci Numbers and the Golden Section - Fibonacci numbers and the golden section in nature, art, geometry, architecture, music, geometry and even for calculating pi! Puzzles and investigations.
Meta Description: [ Fibonacci numbers and the golden section
in nature, art, geometry, architecture, music and even for
calculating pi! Puzzles and investigations. ]
Fibonacci Numbers Formulae - Presented by Rajesh Ram.
Fibonacci Numbers Spelled Out - Derivations usually omitted by gurus and left for the reader to agonize over.
Fibonacci Numbers, Phi and the Golden Ratio - Mathematical calculations; explanations of Phi, the Golden Ratio and Golden Rectangles; examples from art, architecture, music and nature.
Fibonacci Numbers, the Golden Section and the Golden String - A site about fibonacci numbers in nature, art, geometry, architecture and music.
Meta Description: [ Fibonacci numbers and the golden section
in nature, art, geometry, architecture, music and even for
calculating pi! Puzzles and investigations. ]
Fibonacci Quarterly - The official publication of the Fibonacci Association tries to serve as a focal point for interest in Fibonacci numbers and related questions, especially with respect to new results, research proposals, challenging problems, and innovative proofs of old ideas.
Fibonacci resources - Includes details of systematic matrix derivation of identities for Fibonacci and related sequences.
Meta Description: [ Fibonacci resources -
identities for Fibonacci numbers and generalised sequences ]
Fibonacci Sequence - Overview article in the Platonic Realms website.
Meta Description: [ The Fibonacci Sequence, an exposition from the Platonic Realms Interactive Math Encyclopedia. ]
Mongoven, Casey - Official site of California-born artist who specializes in Fibonacci and golden proportion compositions. Includes music, art, writings on Fibonacci Numbers, favorite sequences, pictures, contact information, and links. In English and German.
Meta Description: [ Personal Homepage of Composer Casey Mongoven ]
Textism - Flash animation describing the series and the Golden Section
The Fibonacci Association - Focuses on Fibonacci numbers and related mathematics, emphasizing new results, research proposals, challenging problems, and new proofs of old ideas.
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The Golden Section - A description of the Golden Section and its importance in architecture. Includes instruction on how to construct a Golden Section starting with a square.
Meta Description: [ A description of the Golden Section and its importance in architecture. Includes how to construct a Golden Section starting with a square. ]
The Life and Numbers of Fibonacci - An article in PASS mathematics magazine.
Meta Description: [ Fibonacci, famous for the Fibonacci sequence, also introduced
the decimal system into Europe.
]
Willem's Fibonacci site - Provides information about fibonacci numbers, description, formulas and relation to other mathematical issues.
Meta Description: [ This site contains information about fibonacci numbers. ]
| Each number above is the sum of the two numbers before it. Though most of us are unfamiliar with it, this numerical ... | |
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