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Fibonacci group information


In mathematics, for a natural number , the nth Fibonacci group, denoted or sometimes , is defined by n generators and n relations:

  • .

These groups were introduced by John Conway in 1965.

The group is of finite order for and infinite order for and . The infinitude of was proved by computer in 1990.

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Fibonacci group

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mathematics, for a natural number n ≥ 2 {\displaystyle n\geq 2} , the nth Fibonacci group, denoted F ( 2 , n ) {\displaystyle F(2,n)} or sometimes F ( n ) {\displaystyle...

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Fibonacci sequence

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mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are...

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Fibonacci numbers in popular culture

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The Fibonacci numbers are a sequence of integers, starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13, ..., each new number being the sum of the previous...

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Generalizations of Fibonacci numbers

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In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = { 0 n = 0 1 n = 1 F n − 1 + F n − 2 n > 1 {\displaystyle...

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Golden ratio

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calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry...

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The Fibonaccis

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The Fibonaccis were an American art rock band formed in 1981 in Los Angeles.[citation needed] The band consisted of songwriters John Dentino (keyboards)...

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Pisano period

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the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of...

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Topological quantum computer

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examples in topological quantum computing is with a system of Fibonacci anyons. A Fibonacci anyon has been described as "an emergent particle with the property...

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Greedy algorithm for Egyptian fractions

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algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian...

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5

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and the third Mersenne prime exponent, as well as the fourth or fifth Fibonacci number; 5 is the first congruent number, as well as the length of the...

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Modular group

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the Fibonacci numbers and solutions to Pell's equation. In both cases, the numbers can be arranged to form a semigroup subset of the modular group. The...

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8

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or 12. 8 is the sixth Fibonacci number and the first even, non-prime Fibonacci number. It is also the only positive Fibonacci number aside from 1 that...

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Planning poker

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in the deck have numbers on them. A typical deck has cards showing the Fibonacci sequence including a zero: 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89; other...

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Domino tiling

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{\displaystyle 2\times n} rectangle with n dominoes: the sequence reduces to the Fibonacci sequence. Another special case happens for squares with m = n = 0, 2,...

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0

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transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common names for the number 0...

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APL syntax and symbols

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a Fibonacci number sequence, where each subsequent number in the sequence is the sum of the prior two: ⎕CR 'Fibonacci' ⍝ Display function Fibonacci...

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Mandelbrot set

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conform to the Fibonacci number sequence, the sequence that is made by adding the previous two terms – 1, 2, 3, 5, 8, 13, 21... The Fibonacci sequence manifests...

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Lateralus

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Meshuggah, and King Crimson. The title track, "Lateralus", incorporates the Fibonacci sequence. The theme of the song describes the desire of humans to explore...

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3

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Fermat primes, which include 5, 17, 257, and 65537. It is the second Fibonacci prime (and the second Lucas prime), the second Sophie Germain prime, the...

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