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Algebraic structure
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
Fibonacci_group
Numbers obtained by adding the two previous ones
the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence
Fibonacci_sequence
American art rock band
The Fibonaccis were an American art rock band formed in 1981 in Los Angeles.[citation needed] The band consisted of songwriters John Dentino (keyboards)
The_Fibonaccis
Particle
condensed matter physics, a Fibonacci anyon is a type of anyon which lives in two-dimensional topologically ordered systems. The Fibonacci anyon τ {\displaystyle
Fibonacci_anyons
Numerous conjectures by mathematician Irving Kaplansky
counterexample in a crystallographic group, namely the fundamental group of the Hantzsche–Wendt manifold; see also Fibonacci group. A later preprint by Gardam
Kaplansky's_conjectures
The Fibonacci numbers are a sequence of integers, typically starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13, ..., each new number being the sum of
Fibonacci numbers in popular culture
Fibonacci_numbers_in_popular_culture
British string quartet
The Fibonacci Quartet is a European string quartet based in the United Kingdom. Formed in 2019 at the Guildhall School of Music and Drama in London the
Fibonacci_Quartet
Number, approximately 1.618
calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry
Golden_ratio
Period of the Fibonacci sequence modulo an integer
the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of
Pisano_period
British chamber ensemble
The Fibonacci Sequence is a British chamber ensemble cofounded by horn player Stephen Stirling in 1984. Purposefully flexible, the ensemble is capable
Fibonacci_Sequence_(ensemble)
Mathematical sequences
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
Generalizations of Fibonacci numbers
Generalizations_of_Fibonacci_numbers
Rational numbers with root 5 added
{\bigr )}} . Calculations in the golden field can be used to study the Fibonacci numbers and other topics related to the golden ratio, notably the geometry
Golden_field
Orientation-preserving mapping class group of the torus
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
Modular_group
Number
transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common names for the number 0
0
Natural number
their limbs. 5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length of the
5
Type of quantum computer
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
Topological_quantum_computer
Mathematics conference
International Conference on Fibonacci Numbers and their Applications (ICFNTA) is a five-day biennial conference of the Fibonacci Association. Typically, 50
International Conference on Fibonacci Numbers and their Applications
International_Conference_on_Fibonacci_Numbers_and_their_Applications
Particular mathematical group
with the golden ratio as its base, the same rate as the growth of the Fibonacci numbers. In some cases the growth rate is studied with respect to two
Lamplighter_group
Geometric construct
{\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,
Domino_tiling
Natural number
yx, where in its case x and y both equal 2. 8 is a Fibonacci number and the only nontrivial Fibonacci number that is a perfect cube. Sphenic numbers always
8
Natural number
following 22 and 16. It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number. 34
34_(number)
Method for finding sums of unit fractions
algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian
Greedy algorithm for Egyptian fractions
Greedy_algorithm_for_Egyptian_fractions
American mathematician
photographer and mathematician and was known mostly as a founder of the Fibonacci Association and as an educator. Brother Alfred Brousseau was born in North
Alfred_Brousseau
the other most significant example of a differential poset is the Young–Fibonacci lattice. A poset P is said to be a differential poset, and in particular
Differential_poset
Technique for estimating
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
Planning_poker
Natural number
prime. It is also the first of five known Fermat primes. It is the second Fibonacci prime (and the second Lucas prime), the second Sophie Germain prime, and
3
Ethnic group native to Italy
the Middle Ages, Leonardo Fibonacci introduced the Hindu–Arabic numeral system to the Western world and invented the Fibonacci sequence. Gerolamo Cardano
Italians
Natural number
both the square of twelve (a dozen dozens, or one gross) and the twelfth Fibonacci number, and the only nontrivial number in the sequence that is square
144_(number)
Kleinian Groups and Hyperbolic Geometry" (PDF). American Mathematical Society. 6 (3): 357–381. Mednykh, Alexander; Vesnin, Andrei (1995). "On the Fibonacci Groups
Hyperbolic_Dehn_surgery
Most common system for writing numbers
spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century Liber Abaci; until the evolution of the printing press in
Hindu–Arabic_numeral_system
1987 studio album by The Fibonaccis
Discotheques is the sole LP release of Los Angeles art rock band The Fibonaccis, released in 1987 on Blue Yonder Sounds. The album's title is an obvious
Civilization and Its Discotheques
Civilization_and_Its_Discotheques
Fractal named after mathematician Benoit Mandelbrot
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
Mandelbrot_set
Finite or infinite ordered list of elements
the nth element of the sequence; for example, the nth element of the Fibonacci sequence F {\displaystyle F} is generally denoted as F n {\displaystyle
Sequence
Open source game engine
the Fibonacci sequence is: func _ready() -> void: var nterms: int = 5 print("Fibonacci sequence:") for i: int in range(nterms): print(fibonacci(i)) func
Godot_(game_engine)
Topics referred to by the same term
hypothesis of Donald Dines Wall in number theory on the non-existence of Fibonacci-Wieferich primes This disambiguation page lists articles associated with
Wall's_conjecture
A006327 (Fibonacci(n) - 3. Number of total preorders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. "Sloane's A000045 : Fibonacci numbers"
1000_(number)
Natural number
representations of the Monster group. 194!! - 1 is prime. 194 (disambiguation) Sloane, N. J. A. (ed.), "Sequence A111032 (Non-Fibonacci Markoff numbers)", The
194_(number)
"Thrice reveal how challenging their songwriting and transforming the Fibonacci sequence into a guitar riff shaped bold new album, Horizons/East". Guitar
List_of_post-hardcore_bands
2001 studio album by Tool
Meshuggah, and King Crimson. The title track, "Lateralus", incorporates the Fibonacci sequence. The theme of the song describes the desire of humans to explore
Lateralus
Online database of integer sequences
For example, consider: the prime numbers, the palindromic primes, the Fibonacci sequence, the lazy caterer's sequence, and the coefficients in the series
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Athletic competition
and Lucy Campbell for the women's. The top 25% of the individual and age group competitors proceeded to the Quarterfinals. This was an increase from the
2026_CrossFit_Games
Mural painting by Leonardo da Vinci
interpreted using the Fibonacci series: one table, one central figure, two side walls, three windows and figures grouped in threes, five groups of figures, eight
The_Last_Supper_(Leonardo)
Algebraic theory
of Fibonacci anyons, this normalization is given below. Unitary modular tensor category (and Modular tensor category) Fibonacci anyons (and Fibonacci category)
Algebraic theory of topological quantum information
Algebraic_theory_of_topological_quantum_information
Species of flowering plant in the family of Asteraceae
number of left spirals and the number of right spirals are successive Fibonacci numbers. Typically, there are 39 spirals in one direction and 55 in the
Common_sunflower
English computer scientist (1912–1954)
around the apical meristem during plant growth and development, forming Fibonacci series. One of the early applications of Turing's paper was the work by
Alan_Turing
Vegetable, member of the cabbage family
sufficiently small. The number of spirals on the head of Romanesco broccoli is a Fibonacci number. The causes of its differences in appearance from the normal cauliflower
Romanesco_broccoli
-= 1 until i = 2 Upon termination, x1 is the (n−1)-th Fibonacci number and x2 is the nth Fibonacci number. i is an iterator variable that goes from n to
Janus (time-reversible computing programming language)
Janus_(time-reversible_computing_programming_language)
2017 film by Paul Schrader
the leader of the Abundant Life youth group Ramon Nuñez as Jason, a happy member of the Abundant Life youth group Delano Montgomery as Jake, a conservative
First_Reformed
2003 novel by Dan Brown
Saunière left during the final minutes of his life. The message includes a Fibonacci sequence out of order and an anagram: "O, draconian devil! Oh, lame saint
The_Da_Vinci_Code
American rock band
line in the lyrics to "Lateralus" correspond to an arrangement of the Fibonacci numbers. Problems playing this file? See media help. According to Guitar
Tool_(band)
Casino game of chance
this strategy. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence. Regardless of the specific progression
Roulette
2013 two-part film by Lars von Trier
penetrated her three times vaginally and five anally, resembling the Fibonacci sequence. Years later, Joe and her friend B engage in a contest to see
Nymphomaniac_(film)
Routine that generates a sequence of values
yield $current; } } foreach (fibonacci() as $number) { echo $number, "\n"; } Fibonacci sequence with limit: function fibonacci(int $limit): Generator { yield
Generator (computer programming)
Generator_(computer_programming)
aspect ratio is 1:1 – square-shaped Flag of Togo – the aspect ratio is of Fibonacci's golden ratio that is approximately 1:1.618 ≈ 13:21 Flag of Vatican City
List of national flags by design
List_of_national_flags_by_design
that Made the World Modern. Basic Books. p. 35. a. Donald E. Simanek. "Fibonacci Flim-Flam". Archived from the original on February 1, 2010. Retrieved
List of common misconceptions about science, technology, and mathematics
List_of_common_misconceptions_about_science,_technology,_and_mathematics
primes? Are there infinitely many Euclid primes? Are there infinitely many Fibonacci primes? Are there infinitely many Kummer primes? Are there infinitely
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Species of flowering plant
Britton (7 May 2005). "Fibonacci Numbers in Nature". Archived from the original on 5 September 2016. "Achillea ptarmica (The Pearl Group) - Plant Finder".
Achillea_ptarmica
Species of flowering plant in the family Bromeliaceae
helices, often with 8 in one direction and 13 in the other, each being a Fibonacci number. The pineapple carries out CAM photosynthesis, fixing carbon dioxide
Pineapple
Set of rules defining correctly structured programs
a Fibonacci number sequence, where each subsequent number in the sequence is the sum of the prior two: ⎕CR 'Fibonacci' ⍝ Display function Fibonacci
APL_syntax_and_symbols
Integer side lengths of a right triangle
{\displaystyle (5^{12}+12^{5})/13=18799189} . Starting with 5, every second Fibonacci number is the length of the hypotenuse of a right triangle with integer
Pythagorean_triple
American actor (born 1959)
Professor Rothschild, a well-educated serial killer obsessed with the Fibonacci sequence who sends the team into a race against time to save his last
Jason_Alexander
Painting by Leonardo da Vinci
pages 93–102) The Fibonacci Sequence - The Mona Lisa on thefibonaccisequence.weebly.com Fiona Grießhammer, Rebekka Maas: Fibonacci-Zahlen und der Goldene
Mona_Lisa
escapees, he separates from the group and reunites with his family in New York. No longer interested in finding out Fibonacci's location, he plans to flee
List of Prison Break characters
List_of_Prison_Break_characters
German-American piano company
recordings. In 2015, Steinway made its 600,000th piano. The piano features the Fibonacci spiral and Macassar ebony veneer. It took 6,000 hours of work over 4 years
Steinway_&_Sons
Canadian musician
and solo works with ensembles. In 1998 Julie-Anne founded the Trio Fibonacci. The group plays music for piano trio of all eras, being particularly recognised
Julie-Anne_Derome
Visible regularity of form found in the natural world
tree-branches. In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book Liber Abaci. Fibonacci presented a thought experiment
Patterns_in_nature
Used to count, measure, and label
resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted
Number
distribution under Summit Entertainment only; produced by AGC Studios, Fibonacci Films, Freecss Films, Ingenious Media, Thunder Road Films and Nota Bene
List of Lionsgate films (2020–2029)
List_of_Lionsgate_films_(2020–2029)
2006 mystery thriller film by Ron Howard
secret message, readable only by UV light. It contains an out-of-order Fibonacci sequence. Police cryptographer Sophie Neveu, Saunière's granddaughter
The_Da_Vinci_Code_(film)
Canadian-British writer (born 1971)
Alice Taylor in October 2008; they have a daughter named Poesy Emmeline Fibonacci Nautilus Taylor Doctorow, who was born in 2008. Doctorow became a British
Cory_Doctorow
Number, approximately 3.14
Aryabhata used a value of 3.1416 in his Āryabhaṭīya (499 AD). Around 1220, Fibonacci computed 3.1418 using a polygonal method devised independently of Archimedes
Pi
this symbol with n as subscript; for example, the nth element of the Fibonacci sequence F is generally denoted Fn. For example, (M, A, R, Y) is a sequence
Glossary_of_computer_science
2002 song by Tool
time signatures. Then it turned out that 987 was the 16th number of the Fibonacci sequence. So that was cool." In a 2001 interview, singer Maynard James
Lateralus_(song)
Number divisible only by 1 and itself
considering only the prime divisors up to the square root of the upper limit. Fibonacci took the innovations from Islamic mathematics to Europe. His book Liber
Prime_number
2026). "'Hadestown: The Musical' acquired by Universal Pictures Content Group for UK-Ireland and beyond". Screen Daily. Retrieved 5 August 2026. Keslassy
List_of_Bleecker_Street_films
2021 film by Neil Burger
Archie Madekwe, and Quintessa Swindell in their film debut, and follows a group of teenage astronauts sent on a multi-generational mission in the year 2063
Voyagers_(film)
Lecturer in English at the University of Warwick 29 November 2007 The Fibonacci Sequence Marcus du Sautoy, Professor of Mathematics at the University
List of In Our Time programmes
List_of_In_Our_Time_programmes
Number used for counting
is paired with exactly one apple. As such, the group of apples has the same cardinality as the group of oranges, or put more simply the number of apples
Natural_number
Mongolian telecommunications company
share from the Korean side). In 2011, Unitel renewed its logo. Logo (Fibonacci spiral) represents growth and harmony. Major shareholder of the company
Unitel_(Mongolia)
Holy Roman Emperor from 1220 to 1250
polymath Michael Scotus, astrologer Guido Bonatti, mathematician Leonardo Fibonacci, philosopher Theodore of Antioch, poet Giacomo da Lentini and the jurist
Frederick II, Holy Roman Emperor
Frederick_II,_Holy_Roman_Emperor
American singer (born 1964)
lyrics in "Lateralus" were written to correspond to an arrangement of the Fibonacci numbers,. In "Jambi", the metrical foot iamb is used. Keenan's lyrics
Maynard_James_Keenan
Topics referred to by the same term
grammar, a theory of syntax Lagged Fibonacci generator, an example of a pseudorandom number generator "Looking for group", a phrase often used in MMORPGs
LFG
Iterative algorithm on numbers
(1981). "The determination of all decadic Kaprekar constants" (PDF). Fibonacci Quarterly. 19 (1): 45–52. Hirata, Yumi (2005). "The Kaprekar transformation
Kaprekar's_routine
American TV series
Michael in exchange for the location of the eyewitness to his crimes, Otto Fibonacci. He appears regularly in the first half of the first season and makes
Prison_Break
Bony fish with a natural lure
Davis, 2025 (fanfin frogfishes) Subfamily Antennariinae Jarocki, 1822 (Fibonacci frogfishes) Subfamily Lophichthyinae Boeseman, 1964 (lophichthyin frogfishes)
Anglerfish
1973 children's time travel novel by Thea Beckman
accidentally Dolf is stranded in the 13th century. He saves the life of Leonardo Fibonacci da Pisa, without realizing who he is, and teaches him Arabic numerals
Crusade_in_Jeans
Ancient Indian empire (c. 3rd century CE – 575 CE)
Yativṛṣabha made contributions on units of measurement. Virahanka described Fibonacci numbers. Indian astronomy also saw progress in this era. The names of
Gupta_Empire
Section of text in a book
Below by László Krasznahorkai has chapters numbered according to the Fibonacci sequence. The Curious Incident of the Dog in the Night-Time by Mark Haddon
Chapter_(books)
calculator. Mathematics: F201107 is a 42,029-digit Fibonacci prime; the largest known certain Fibonacci prime as of September 2023[update]. Mathematics:
Orders_of_magnitude_(numbers)
English musician and TikToker (born 1999)
New EP, "Fibonacci Part 1: Oblivion"". EDM. Retrieved 22 April 2025. Lavezzo, Derek (6 April 2025). "Subtronics Releases Scorching EP 'Fibonacci Part 1:
A_Little_Sound
Natural number
GF(2) 120,284 = Keith number 120,960 = highly totient number 121,393 = Fibonacci number 123,717 = smallest digitally balanced number in base 7 123,867
100,000
Legislative capital of South Africa
average of R120 000 for rent". CapeTown ETC. Retrieved 15 May 2025. "Fibonacci development set to attract property investors and to aid CPT rental shortage"
Cape_Town
On distances between points on a circle
1017/S0305004100039013, MR 0202668, S2CID 123400321 Chevallier, Nicolas (2007), "Cyclic groups and the three distance theorem", Canadian Journal of Mathematics, 59 (3):
Three-gap_theorem
Brigade sized commando force of the United Kingdom
the Amphibious Ready Group, the Amphibious Task Group (ATG) is a mobile, balanced amphibious warfare force, based on a Commando Group and its supporting
United_Kingdom_Commando_Force
publication, as the preannouncement of names is condemned by the Working Group for Small Bodies Nomenclature of the International Astronomical Union. 1
List of minor planets: 6001–7000
List_of_minor_planets:_6001–7000
Israeli commodities and futures trader
Development. Robert used Gann and fibonacci methods in his trading and coaching of new traders, encouraging them to use his fibonacci trader three timeframe method
Robert_Krausz
Programming language
any changes on many major platforms. The following code calculates the Fibonacci sequence of a number n inputted. It uses tail recursion and pattern matching
OCaml
Natural number
299,709 = 100,000th prime number 1,336,336 = 11562 = 344 1,346,269 = Fibonacci number, Markov number 1,367,631 = 1113, palindromic cube 1,388,705 = number
1,000,000
Photosynthetic part of a vascular plant
in three gyres. Most divergence angles are related to the sequence of Fibonacci numbers Fn. This sequence begins 1, 1, 2, 3, 5, 8, 13; each term is the
Leaf
Topological quantum field theory
describes the simplest non-abelian anyonic model of a TQC, the Yang–Lee–Fibonacci model. The dynamics of Chern–Simons theory on the 2-dimensional boundary
Chern–Simons_theory
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