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• Fibonacci's sequence

語源

Named after the Italian mathematician later known as Fibonacci (c.1175 – c.1250), who introduced the sequence to a European readership in his 1202 book Liber Abaci.

名詞

Fibonacci sequence (plural Fibonacci sequences)

1. (mathematics) The sequence of integers, each of which is the sum of the preceding two, the first and second numbers both being 1.
   • 1999, Walter Steurer, Torsten Heibach, “3. Crystallography of Quasicrystals”, in Zbigniew M. Stadnik, editor, Physical Properties of Quasicrystals, Springer, page 60:

     If the Fibonacci sequence is chosen for the quasiperiodic direction of a 1D QC, it may simply be called a Fibonacci phase.

   • 2000, Martin Nowak, Robert M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, page 6:

     The number of adult rabbit pairs being present in consecutive months is then given by the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, ... (every term is the sum of its two predecessors). This work can be seen as the very beginning of mathematical biology, though one has to admit that the Fibonacci sequence exerts a greater fascination for number theorists than for reproductive biologists.

   • 2009, Roger V. Jean, Phyllotaxis: A Systemic Study in Plant Morphogenesis, Cambridge University Press, page 1:

     In a well-known chapter on phyllotaxis, Coxeter (1969) calls the appearance of the Fibonacci sequence in botany a "fascinatingly prevalent tendency," called by Cook (1914) the "Law of Wiesner." The prevalence of the Fibonacci sequence in phyllotactic patterns is often referred to as “the mystery of phyllotaxis,” and “the bugbear of botanists.”

   • 2019 June 24, Juan Triana, “Negafibonacci Numbers via Matrices”, in Bulletin of TICMI‎, volume 23, number 1, →ISSN, archived from the original on 2019-07-13, Introduction, page 1:

     The Fibonacci sequence {f_n} is defined by the following recurrence relation […]

2. (mathematics) Any sequence of numbers such that each is the sum of the preceding two.
   • 1977, Scientific American, volume 236, page 137:

     Indeed, these pairs belong to a Fibonacci sequence of what are called Lucas numbers that begins 2, 1, 3, 4, 7, 11,...

   • 2007, Anthony Nicolaides, Make The Grade At GCSE Mathematics, Higher Tier, P.A.S.S. Publications, 3rd Edition, page 169,

     19. The first two terms of a Fibonacci sequence are a and b. Write out a few terms.

使用する際の注意点

In modern usage, the sequence is often defined by specifying 0 as the zeroth number and 1 as the first. The notation ${\displaystyle F(n)}$ is often used for the nth number in the sequence.

関連する語

• Fibonacci number
• Fibonacci spiral

参考

• Lucas sequence
• Tribonacci

Further reading

• Golden ratio on Wikipedia.Wikipedia
• Generalizations of Fibonacci numbers on Wikipedia.Wikipedia
• Lucas number on Wikipedia.Wikipedia
• Padovan sequence on Wikipedia.Wikipedia
• Fibonacci polynomials on Wikipedia.Wikipedia
• Fibonacci retracement on Wikipedia.Wikipedia