Fibonacci number
In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence:or (often, in modern usage):By definition, the first two numbers in the Fibonacci sequence...
Fibonacci number - Wikipedia
15 Uncanny Examples of the Golden Ratio in Nature
The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature sugge...
Fibonacci prime
A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime.The first Fibonacci primes are (sequence A005478 in OEIS):
It is not known whether there are infinitely many...
Pisano period
In number theory, the nth Pisano period, written π(n), is the period with which the sequence of Fibonacci numbers, modulo n repeats. For example, the Fibonacci numbers modulo 3 are 0, 1, 1, 2, 0, 2, ...
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, and in conjunction...
Fibonacci numbers in popular culture - Wikipedia
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 stu...
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relat...
Golden ratio - Wikipedia
15 Uncanny Examples of the Golden Ratio in Nature
The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature sugge...
Random Fibonacci sequence
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation fn = fn−1 ± fn−2, where the signs + or − are chosen at random with e...
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...
Leonardo Bonacci
Leonardo Bonacci (c. 1170 – c. 1250)—known as Fibonacci ([fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano Bigollo, Leonardo Fibonacci—was an Italian mathematician, considered to be "the most...
Leonardo Bonacci - Wikipedia
Acharya Hemachandra
Acharya Hemachandra was a Jain scholar, poet, and polymath who wrote on grammar, philosophy, prosody, and contemporary history. Noted as a prodigy by his contemporaries, he gained the title Kalikāl Sa...
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.Computing a ...
List of works designed with the golden ratio
Many works of art are believed to have been designed using the golden ratio, an irrational number that is approximately 1.618; it is often denoted by the Greek letter φ (phi).
It is claimed that S...
List of works designed with the golden ratio - Wikipedia
Lute of Pythagoras
The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams.
The lute may be drawn from a sequence of pentagrams.The centers of the pentagraphs lie on a line and (...
Lute of Pythagoras - Wikipedia
Fibonomial coefficient
In mathematics, the Fibonomial coefficients or Fibonacci-binomial coefficients are defined aswhere n and k are non-negative integers, 0 ≤ k ≤ n, Fj is the j-th Fibonacci number and...
Fibonacci heap
In computer science, a Fibonacci heap is a heap data structure consisting of a collection of trees. It has a better amortized running time than a binomial heap. Fibonacci heaps were developed by Micha...
Fibonacci heap - Wikipedia
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...
Przemysław Prusinkiewicz
Przemysław (Przemek) Prusinkiewicz [ˈpʐɛmɛk pruɕiŋˈkjevit͡ʂ] is a Polish computer scientist who advanced the idea that Fibonacci numbers in nature can be in part understood as the expression of c...
Cassini and Catalan identities
Cassini's identity and Catalan's identity are mathematical identities for the Fibonacci numbers. The former is a special case of the latter, and states that for the nth Fibonacci number,Catalan's iden...
Cassini and Catalan identities - Wikipedia
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...
Jay Hambidge
Jay Hambidge (1867–1924) was a Canadian born American artist. He was a pupil at the Art Students' League in New York and of William Chase, and a thorough student of classical art. He conceived the ide...
Jay Hambidge - Wikipedia
Golden spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every q...
Golden spiral - Wikipedia
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 i Fi...
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. ...