Fibonacci sequence

The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, ... , in which each successive number is equal to the sum of the two preceding numbers.

[After Leonardo Fibonacci (died c. 1250), Italian mathematician.]

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Fibonacci sequence

(ˌfɪbəˈnɑːtʃɪ) or

Fibonacci series

(Mathematics) the infinite sequence of numbers, 0, 1, 1, 2, 3, 5, 8, etc, in which each member (Fibonacci number) is the sum of the previous two

[named after Leonardo Fibonacci]

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Fibonacci sequence

The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, ... , in which each successive number is equal to the sum of the two preceding numbers. Many shapes occurring in nature, such as certain spirals, have proportions that can be described in terms of the Fibonacci sequence.

The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

ThesaurusAntonymsRelated WordsSynonymsLegend:

Noun

Fibonacci sequence - a sequence of numbers in which each number equals the sum of the two preceding numbers

sequence - serial arrangement in which things follow in logical order or a recurrent pattern; "the sequence of names was alphabetical"; "he invented a technique to determine the sequence of base pairs in DNA"

Translations

Fibonacciho posloupnost

Mentioned in

References in periodicals archive

While Max is plugging away at identifying the patterns buried within the stock market (or, per his example, 'the wax and wane of caribou populations'), the film itself is densely populated with numerical patterns - the most prominent being the Fibonacci sequence and its associated golden ratio.

Cinema Science: PI AND THE RAPTURE OF COMPLEX MATHEMATICS: While its title already indicates one of its central mathematical topics of concern, Darren Aronofsky's cult paranoid thriller also offers ample prompts for senior secondary students to explore sequences, phenomena such as the golden ratio and Pythagoras' theorem, and more intricate concepts like irrational numbers and recursion, as DAVE CREWE outlines

The curriculum for the 2019-20 school year will focus on a creative exploration of the Fibonacci sequence and spiral as it is seen in nature and math.

Creative partners

Among their topics are hypercubes and the generalized Cohn cycle, the Fibonacci sequence as metric suspension in Luigi Nono's Il Canto Sospeso, one note samba: navigating notes and their meanings within modes and exo-modes, theoretical physics and category theory as tools for analyzing musical performance and composition, and examining fixed and relative similarity metrics through jazz melodies.

Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena

To this is added the mathematical complexity of the Fibonacci sequence where each number is the sum of the previous two digits.

Music enlightens audience with luminous beauty; REVIEW: BBC National Orchestra of Wales at Hoddinott Hall, Cardiff ?????....

And do you remember the Fibonacci sequence from school?

4 REASONS TO EAT; DR MIRIAM STOPPARD; Helping to keep you fit and healthy

We denote the n-th term of the Fibonacci sequence by [F.sub.n] and the Binet form of [F.sub.n] is [[alpha].sup.n] - [[beta].sup.n]/[alpha] - [beta], where [alpha] = 1 + [square root of 5]/2 and [beta] = 1 - [square root of 5]/2.

Analytic continuation of the multiple Fibonacci zeta functions

where [x.sub.0] = a, [x.sub.-1] = b, [x.sub.-2] = c, [y.sub.0] = d, [y.sub.-1] = e, [y.sub.-2] = f and where fn is the Fibonacci Sequence with [f.sub.-2] = 1, [f.sub.-1] = 0.

On the Solutions of a System of Third-Order Rational Difference Equations

For such a case, considering its simple operation, a modified type of Fibonacci sequence is used in our key generation algorithm.

New Key Generation and Encryption Algorithms for Privacy Preservation in Mobile Ad Hoc Networks

Variable Fibonacci sequence. We now introduce a variable block size based on a Fibonacci sequence.

VARYING THE S IN YOUR S-STEP GMRES

where [([f.sub.n]).sub.n[member of]N] is the Fibonacci sequence defined by [f.sub.n+2] = [f.sub.n+1] + [f.sub.n], [f.sub.1] = [f.sub.2] = 1.

Golden warped product Riemannian manifolds

Tying the Fibonacci sequence to patterns in nature, making leaf gradients, snow painting, practicing with a compass, map reading, and other creative ways to work together skillfully demonstrate how a simple picnic can become an anticipated event.

A Year of Picnics; Recipes for Dining Well in the Great Outdoors

A Lucas sequence is a generalisation of the Fibonacci sequence. In this case

Addition chains: a resolve lesson