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List Of Things Named After Fibonacci ...
The Fibonacci numbers are the best known concept named after Leonardo of Pisa, known as Fibonacci. Among others are the following. ;Concepts in mathematics and computing ;A professional association and a scholarly journal that it publishes * The Fibonacci Association * ''Fibonacci Quarterly'' ;An asteroid * 6765 Fibonacci ;An art rock band: * The Fibonaccis {{Fibonacci Fibonacci Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci numbers, commonly denoted , 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 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described 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. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 are formed by repeated addition. It is a paradigmatic example of a Sturmian word and specifically, a morphic word. The name "Fibonacci word" has also been used to refer to the members of a formal language ''L'' consisting of strings of zeros and ones with no two repeated ones. Any prefix of the specific Fibonacci word belongs to ''L'', but so do many other strings. ''L'' has a Fibonacci number of members of each possible length. Definition Let S_0 be "0" and S_1 be "01". Now S_n = S_S_ (the concatenation of the previous sequence and the one before that). The infinite Fibonacci word is the limit S_, that is, the (unique) infinite sequence that contains each S_n, for finite n, as a prefix. Enumerating items from the above definition produces: S_0 0 S_1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Art Rock
Art rock is a subgenre of rock music that generally reflects a challenging or avant-garde approach to rock, or which makes use of modernist, experimental, or unconventional elements. Art rock aspires to elevate rock from entertainment to an artistic statement, opting for a more experimental and conceptual outlook on music."Art Rock" Encyclopædia Britannica. Retrieved 15 December 2011. Influences may be drawn from genres such as , avant-garde music, |
Fibonacci Quarterly
The ''Fibonacci Quarterly'' is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year. It is the primary publication of The Fibonacci Association, which has published it since 1963. Its founding editors were Verner Emil Hoggatt Jr. and Alfred Brousseau; by Clark Kimberling the present editor is Professor Curtis Cooper of the Mathematics Department of the . The ''Fibonacci Quarterly'' has an editorial board of nineteen members an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 recurrence relations, combinatorial identities, binomial coefficients, prime numbers, pseudoprimes, continued fractions, the golden ratio, linear algebra, geometry, real analysis, and complex analysis. History The organization was founded in 1963 by Brother Alfred Brousseau, F.S.C. of St. Mary's College (Moraga, California) and Verner E. Hoggatt Jr. of San Jose State College (now San Jose State University). Details regarding the early history of The Fibonacci Association are given Marjorie Bicknell-Johnson's "A Short History of The Fibonacci Quarterly", published in The Fibonacci Quarterly 25:1 (February 1987) 2-5, during the Twenty-Fifth Anniversary year of the journal. Publications Since the year of its founding, the Fibonacci Association has published an international mathematical journa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Any digit sequence of this type can be assigned a ''rank'', the sum of its digits: for instance, the rank of 11212 is 1 + 1 + 2 + 1 + 2 = 7. As was already known in ancient India, the number of sequences with a given rank is a Fibonacci number. The Young–Fibonacci lattice is an infinite modular lattice having these digit sequences as its elements, compatible with this rank structure. The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. The Young–Fibonacci graph and the Young–Fibonacci lattice were both initially studied in two papers by and . They are named after the closely related Young's lattice and after the Fibonacci nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Fibonacci Constant
The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: :\psi = \sum_^ \frac = \frac + \frac + \frac + \frac + \frac + \frac + \frac + \frac + \cdots. The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. Since this is less than 1, the ratio test shows that the sum converges. The value of ψ is known to be approximately :\psi = 3.359885666243177553172011302918927179688905133732\dots . Gosper describes an algorithm for fast numerical approximation of its value. The reciprocal Fibonacci series itself provides O(''k'') digits of accuracy for ''k'' terms of expansion, while Gosper's accelerated series provides O(''k''2) digits. ψ is known to be irrational; this property was conjectured by Paul Erdős, Ronald Graham, and Leonard Carlitz, and proved in 1989 by Richard André-Jeannin. The continued fraction representation of the constant is: : \psi = ;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,2,4,8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pisano Period
In number theory, the ''n''th Pisano period, written as '(''n''), is the period with which the sequence of Fibonacci numbers taken modulo ''n'' repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774. Definition The Fibonacci numbers are the numbers in the integer sequence: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, ... defined by the recurrence relation :F_0 = 0 :F_1 = 1 :F_i = F_ + F_. For any integer ''n'', the sequence of Fibonacci numbers ''Fi'' taken modulo ''n'' is periodic. The Pisano period, denoted '(''n''), is the length of the period of this sequence. For example, the sequence of Fibonacci numbers modulo 3 begins: :0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, ... This sequence has period 8, so '(3) = 8. Properties With the exce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 congruential generator. These are based on a generalisation of the Fibonacci sequence. The Fibonacci sequence may be described by the recurrence relation: :S_n = S_ + S_ Hence, the new term is the sum of the last two terms in the sequence. This can be generalised to the sequence: :S_n \equiv S_ \star S_ \pmod, 0 < j < k In which case, the new term is some combination of any two previous terms. ''m'' is usually a power of 2 (''m'' = 2''M''), often 232 or 264. The operator denotes a general . This may be either addition, subtraction, multiplication, or the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
