Numeri Fibonacciani

Quadrata quorum laterum longitudines numeros Fibonaccianos sequuntur.

Numeri Fibonacciani^[1] sunt series numerorum. Primus et secundus numerus sunt 0 et 1. Tota series est 0, 1, 1, 2, 3, 5, 8, 13, … Regula est: proximus numerus est summa duorum priorum, vel

a_{n}=a_{n-2}+a_{n-1}

Leonardus Pisanus seriem anno 1202 descripsit.

Anno 1843 Iacobus Philippus Maria Binet^(d)(en) formulam generalem invenit quae omnes numeros Fibonaccianos gignit:^[2]^[3]^[4]^[5]

a_{n}={\frac {\left({\frac {1+{\sqrt {5}}}{2}}\right)^{n}-\left({\frac {1-{\sqrt {5}}}{2}}\right)^{n}}{\sqrt {5}}}

Tres quantitates constantes in formula Binettiana sunt: ${\frac {1+{\sqrt {5}}}{2}}\approx 1.618033989$ , ${\frac {1-{\sqrt {5}}}{2}}\approx -0.618033989$ , et ${\sqrt {5}}\approx 2.236067977$ .

Nota

↑ Giovanni Damiani: Perché Fibonacci? (Italiane)
↑ Weisstein, Ericus Wolfgangus. Binet's Formula. Wolfram MathWorld.
↑ Livio, Marius (2002). The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. Novi Eboraci: Broadway Books. p. 106.
↑ Séroul, Raymond (2000). Programming for Mathematicians. Berolini: Springer-Verlag. p. 21.
↑ Belcastro, Sarah Maria (2018). Discrete Mathematics with Ducks (2a. ed.). Londinii: CRC Press. p. 260. ISBN 978-1-351-68369-2.

Nexus interni

Nexus externus

La successione di Fibonacci (Latine, Italiane)

[1] Giovanni Damiani: Perché Fibonacci? (Italiane)

[2] Weisstein, Ericus Wolfgangus. Binet's Formula. Wolfram MathWorld.

[3] Livio, Marius (2002). The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. Novi Eboraci: Broadway Books. p. 106.

[4] Séroul, Raymond (2000). Programming for Mathematicians. Berolini: Springer-Verlag. p. 21.

[5] Belcastro, Sarah Maria (2018). Discrete Mathematics with Ducks (2a. ed.). Londinii: CRC Press. p. 260. ISBN 978-1-351-68369-2.

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