Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence. Each number is the sum of the two preceding ones, starting from 0 and 1. Leonardo of Pisa introduced the sequence to Western European mathematics. Outside India, it is used to calculate the growth of rabbit populations.
About Fibonacci number in brief
In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence. Each number is the sum of the two preceding ones, starting from 0 and 1. In his 1202 book Liber Abaci, Leonardo of Pisa introduced the sequence to Western European mathematics. The sequence had been described earlier in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. Outside India, it is used to calculate the growth of rabbit populations, where a newly born pair of rabbits mates at the age of one month and at the end of their second month they always produce another pair. The number of mature pairs alive plus the number of rabbits to mature pairs is equal to the number in the nth month. The name was taken from the Fib onacci puzzle: how many pairs will there be in one year, and how many will be alive in the next? It is also used in computer algorithms such as the fibonacci search technique and the FibOnacci heap data structure. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangements of a pine cone’s bracts.
They are also closely related to Lucas numbers Ln, in that they form a complementary pair of Lucas sequences: Un(1,−1)=Fn and Vn(1,.+1)=Ln (Fn + Vn + Ln) (Fm + Fm + Ll) (or Fm+Ll) + Fn+Fn+Ln, or Fm-Ll+Fm+Fl, and Fm/Ln/Ll/Fn/Fm/Fl/Nl/FN/Nn/Nm/Ng/Nh/Np/Nr/Nt/Nc/Nv/Nb/Nd/Ns/Nu/Nf/Nk/Nj/Nz/Nq/Nx/Ny/Nw/N+Ng, or FN/Ngn/Nch/Npn/Nci/Nsq/Nsh/Nqq, or Fn/Ngl/Nsp/Nsn/Nhy/Nth/Nsi, or Fn, Fn, Fn, Fn+Nn+Nc, Fn-Nn, FN-Nm+Nh, Fn+.Fn-Nt, FN+Nl, Fn=Fn−1, Fn +Nn−2, Nn-1, FN-2, FN=F n+1, Nn+2, Np, Nk, Nm, Nl, Nh, Ng, Nv, Nj, Nt, Nz, Nr, Nx, Nd, Nu, Nc, Nw, Nf, Ns, Nb, Nq, Ny, Nsh, Ngn, Nsp, Nth, Nsq, Nch, Npn, Nsn, Nsi, Fm, F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12, F13, F14, F15, F16, F17, F18, F19, F20, F21, F22, F23, F24, F25, F26, F27, F28, F29, F30, F31, F32, F33, F34, F35, F36, F38, F39, F40, F41, F43, F44, F45, F46, F47, F48, F49, F50, F51, F52, F53, F54, F55, F56, F57, F58, F59, F60, F61, F62, F63, F64, F65, F66, F67, F68, F69, F70, F72, F73, F74, F75, F77, F78, F79, F80, F81, F82, F83, F84, F85, F86, F87, F88, F89, F90, F91, F92, F93, F94, F95, F96, F98, F97, F99, F102, F103, F100, F104, F0, F105, F110, F106, F107, F108, F109, F111,
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This page is based on the article Fibonacci number published in Wikipedia (as of Dec. 09, 2020) and was automatically summarized using artificial intelligence.
