Fibonacci sequence

plural Fibonacci sequences · alternative Fibonacci's sequence

1. mathematicsThe sequence of integers, each of which is the sum of the preceding two, the first and second numbers both being 1.

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

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

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   If the Fibonacci sequence is chosen for the quasiperiodic direction of a 1D QC,^([quasicrystal]) it may simply be called a Fibonacci phase.

   1999, Walter Steurer, Torsten Heibach, “3. Crystallography of Quasicrystals”, in Zbigniew M. Stadnik, editor, Physical Properties of Quasicrystals, Springer, page 60

   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.

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

   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.”

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

   "Fibonacci was the most famous mathematician of his time," Noah explained. "He created the Fibonacci Sequence, where every number is the sum of the two numbers before it—one, two, three, five, eight, and so on. [...]"

   2026, Gordon Korman, Hypergifted, page 139

2. mathematicsAny sequence of numbers such that each is the sum of the preceding two.

   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.

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

   1977, Scientific American, volume 236, page 137