# Category: Fibonacci numbers

Fibonacci word
A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers ar
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and
Candido's identity
Candido's identity, named after the Italian mathematician Giacomo Candido, is an identity for real numbers. It states that for two arbitrary real numbers and the following equality holds: The identity
Lucas pseudoprime
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequenc
Fibonacci cube
In the mathematical field of graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in number theory. Mathemat
Pingala
Acharya Pingala (piṅgala; c. 3rd–2nd century BCE) was an ancient Indian poet and mathematician, and the author of the Chandaḥśāstra (also called the Pingala-sutras), the earliest known treatise on San
Golden-section search
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval,
Alphabet (poetry collection)
Alphabet is one of the most well-known poems of Inger Christensen, who was broadly considered to be Denmark's most prominent poet. The poem was originally published in 1981 in Danish as alfabet. An En
Ring lemma
In the geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing.
Fibonacci polynomials
In mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numb
Pisano period
In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better know
Fibonorial
In mathematics, the Fibonorial n!F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e. where Fi is the ith
Young–Fibonacci lattice
In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. An
Negafibonacci coding
In mathematics, negafibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative inte
Generalizations of Fibonacci numbers
In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been s
Fibonacci prime
A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime. The first Fibonacci primes are (sequence in the OEIS): 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 29
Fibbinary number
In mathematics, the fibbinary numbers are the numbers whose binary representation does not contain two consecutive ones. That is, they are sums of distinct and non-consecutive powers of two.
Cassini and Catalan identities
Cassini's identity (sometimes called Simson's identity) and Catalan's identity are mathematical identities for the Fibonacci numbers. Cassini's identity, a special case of Catalan's identity, states t
Fibonacci numbers in popular culture
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 two. The Fibonacci numbers, often presented in
Leonardo Bonacci
No description available.
Missing square puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only tex
Virahanka
Virahanka (Devanagari: विरहाङ्क) was an Indian prosodist who is also known for his work on mathematics. He may have lived in the 6th century, but it is also possible that he worked as late as the 8th
Fibonacci retracement
In finance, Fibonacci retracement is a method of technical analysis for determining support and resistance levels. It is named after the Fibonacci sequence of numbers, whose ratios provide price level
Carmichael's theorem
In number theory, Carmichael's theorem, named after the American mathematician R.D. Carmichael,states that, for any nondegenerate Lucas sequence of the first kind Un(P,Q) with relatively prime paramet
Reciprocal Fibonacci constant
The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. Since
Markov number
A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation studied by Andrey Markoff . The first few Markov numbers are 1, 2, 5, 13
Fibonacci heap
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priori
Keith number
In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number in a given number base with digits such that when a sequence is created such that th
Hosoya's triangle
Hosoya's triangle or the Hosoya triangle (originally Fibonacci triangle; OEIS: ) is a triangular arrangement of numbers (like Pascal's triangle) based on the Fibonacci numbers. Each number is the sum
Lucas number
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci num
Random Fibonacci sequence
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation , where the signs + or − are chosen at random with equal probability
Wythoff array
In mathematics, the Wythoff array is an infinite matrix of integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff. Every positive integer occurs exactl
Fibonomial coefficient
In mathematics, the Fibonomial coefficients or Fibonacci-binomial coefficients are defined as where n and k are non-negative integers, 0 ≤ k ≤ n, Fj is the j-th Fibonacci number and n!F is the nth Fib
Hemachandra
Hemachandra was a 12th century (c. 1088 – c. 1172/1173 CE) Indian Jain saint, scholar, poet, mathematician, philosopher, yogi, grammarian, law theorist, historian, lexicographer, rhetorician, logician
The Fibonacci Association
The Fibonacci Association is a mathematical organization that specializes in the Fibonacci number sequence and a wide variety of related subjects, generalizations, and applications, including recurren
Fibonacci nim
Fibonacci nim is a mathematical subtraction game, a variant of the game of nim. Players alternate removing coins from a pile, on each move taking at most twice as many coins as the previous move, and
Fibonacci
Fibonacci (/ˌfɪbəˈnɑːtʃi/; also US: /ˌfiːb-/, Italian: [fiboˈnattʃi]; c. 1170 – c. 1240–50), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from
Solving the Riddle of Phyllotaxis
Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur in Plants is a book on the mathematics of plant structure, and in particular on phyllotaxis, the arrangement of
Édouard Lucas
François Édouard Anatole Lucas (French pronunciation: ​[fʁɑ̃swa edwaʁ anatɔl lykɑ]; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. T
Fibonacci coding
In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers.
FISH (cipher)
The FISH (FIbonacci SHrinking) stream cipher is a fast software based stream cipher using Lagged Fibonacci generators, plus a concept from the shrinking generator cipher. It was published by Siemens i
Zeckendorf's theorem
In mathematics, Zeckendorf's theorem, named after Belgian amateur mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers. Zeckendorf's theorem
Lagged Fibonacci generator
A Lagged Fibonacci generator (LFG or sometimes LFib) is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear c
Alfred Brousseau
Brother Alfred Brousseau, F.S.C. (February 17, 1907 – May 31, 1988), was an educator, photographer and mathematician and was known mostly as a founder of the Fibonacci Association and as an educator.
Leonardo number
The Leonardo numbers are a sequence of numbers given by the recurrence: Edsger W. Dijkstra used them as an integral part of his smoothsort algorithm, and also analyzed them in some detail. A Leonardo