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Family of graphs based on the Fibonacci sequence
In the mathematical field of graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived
Fibonacci_cube
Numbers obtained by adding the two previous ones
technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also
Fibonacci_sequence
demonstrates knowledge of Fibonacci numbers. In L: Change the World (2008), Near is seen arranging sugar cubes in a Fibonacci sequence. In 21 (2008), the
Fibonacci numbers in popular culture
Fibonacci_numbers_in_popular_culture
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
Brahmagupta–Fibonacci identity Fibonacci coding Fibonacci cube Fibonacci heap Fibonacci polynomials Fibonacci prime Fibonacci pseudoprime Fibonacci quasicrystal
List of things named after Fibonacci
List_of_things_named_after_Fibonacci
Graphs formed by a hypercube's edges and vertices
graph Cube-connected cycles Fibonacci cube Folded cube graph Frankl–Rödl graph Halved cube graph Hypercube internetwork topology Partial cube Watkins
Hypercube_graph
Natural number
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 have exactly
8
Numbers whose binary representation does not contain two consecutive ones
then the subset of vertices indexed by the fibbinary numbers forms a Fibonacci cube as its induced subgraph. Every number has a fibbinary multiple. For
Fibbinary_number
Partially ordered set with alternatingly-related elements
a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube. A partially ordered set is series-parallel if and only if it does not
Fence_(mathematics)
Number raised to the third power
and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted
Cube_(algebra)
Mathematical problem
by different integral squares using the Fibonacci series (see figure) 1. Tiling with squares with Fibonacci-number sides is almost perfect except for
Squaring_the_square
Natural number
is a cube; B consists of 1000 cubes the size of cube A, C consists of 1000 cubes the size of cube B; and D consists of 1000 cubes the size of cube C. Thus
1,000,000,000
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
Natural number
number 1,336,336 = 11562 = 344 1,346,269 = Fibonacci number, Markov number 1,367,631 = 1113, palindromic cube 1,388,705 = number of prime knots with 16
1,000,000
Isometric subgraph of a hypercube
cubes. The trees and hypercube graphs are examples of median graphs. Since the median graphs include the squaregraphs, simplex graphs, and Fibonacci cubes
Partial_cube
Graph representing connectivity between cliques of another graph
graph. The simplex graph of the complement graph of a path graph is a Fibonacci cube. The complete subgraphs of G can be given the structure of a median
Simplex_graph
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
Infinite integer series where the next number is the sum of the two preceding it
closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary
Lucas_number
Number of matchings in a graph
structure of the matchings in these graphs may be visualized using a Fibonacci cube. The largest possible value of the Hosoya index, on a graph with n {\displaystyle
Hosoya_index
theory with more consolidated theories. Integer sequence Fibonacci sequence Golden mean base Fibonacci coding Lucas sequence Padovan sequence Figurate numbers
List of recreational number theory topics
List_of_recreational_number_theory_topics
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)
Positive real number which when multiplied by itself gives 5
{\displaystyle {\sqrt {5}}} then figures in the closed form expression for the Fibonacci numbers: F ( n ) = φ n − φ ¯ n 5 . {\displaystyle F(n)={\frac {\varphi
Square_root_of_5
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
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
Polynomial equation of degree 3
of cubic equations. In his book Flos, Leonardo de Pisa, also known as Fibonacci (1170–1250), was able to closely approximate the positive solution to
Cubic_equation
Natural number
notation). It is a perfect power, harshad number, square number (1,000,0002), cube number (10,0003), tesseractic number (1,0004), and a 6-hypercube number (1006)
1,000,000,000,000
Number used to approximate the square root of 2
calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally
Pell_number
itself. 7, the first and only prime number preceding a cube. 8, the largest cube in the Fibonacci sequence. 9, the first odd number that is composite. 10
List_of_numbers
American mathematician (1923–2002)
10 x 10 Latin cubes" (PDF). Fibonacci Quarterly. 12 (2): 133–40. Arkin, Joseph; Strauss, E. G. (1974). "Latin k-Cubes" (PDF). Fibonacci Quarterly. 12
Joseph_Arkin
Natural number
100,544,625 = 4653, the smallest 9-digit cube 102,030,201 = 101012, palindromic square 102,334,155 = Fibonacci number 102,400,000 = 405 104,060,401 = 102012
100,000,000
Number, product of consecutive integers
the only prime pronic number. It is also the only pronic number in the Fibonacci sequence and the only pronic Lucas number. The arithmetic mean of two
Pronic_number
Numbers whose prime factors all divide the number more than once
prime factorization is larger than 1. It is the product of a square and a cube. A powerful number is a positive integer m such that for every prime number
Powerful_number
A006327 (Fibonacci(n) - 3. Number of total preorders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. "Sloane's A000045 : Fibonacci numbers"
1000_(number)
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
Product of an integer with itself
thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers). In the real number system, square numbers
Square_number
Natural number
624 14,828,074 = Number of trees with 23 unlabeled nodes 14,930,352 = Fibonacci number 15,240,955 – 15,240,955/12,096,754 ≈ ∛2 15,485,863 = 1,000,000th
10,000,000
7-cube, Rectified 7-cube, 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube 7-orthoplex
List_of_mathematical_shapes
List of mathematical contexts in which exponentiated terms are summed
natural numbers. The successive powers of the golden ratio φ obey the Fibonacci recurrence: φ n + 1 = φ n + φ n − 1 . {\displaystyle \varphi ^{n+1}=\varphi
Sums_of_powers
Type of number introduced by Mike Keith
mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n {\displaystyle n} in a given number
Keith_number
Concept in combinatorics
3-dimensional cube can be partitioned by exactly n planes. The cake number is so called because one may imagine each partition of the cube by a plane as
Cake_number
Triangular array of the binomial coefficients
are left-justified, the diagonal bands (colour-coded below) sum to the Fibonacci numbers. exp ( . . . . . 1 . . . . . 2 . . . . . 3 . . . . . 4 . ) =
Pascal's_triangle
Result of multiplying four instances of a number together
n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n4 as n tesseracted
Fourth_power
Solid with 12 equal pentagonal faces
The problem was solved by Hero of Alexandria, Pappus of Alexandria, and Fibonacci, among others. Apollonius of Perga discovered the curious result that
Regular_dodecahedron
Probabilistic test for the primality of an integer
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in
Lucas_pseudoprime
Square of a triangular number
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n )
Squared_triangular_number
Natural number
points of norm <= 10 in cubic lattice 4177 – prime of the form 2p-1 4181 – Fibonacci number, Markov number 4186 – triangular number 4187 – factor of R13, the
4000_(number)
Natural number
3046 – centered heptagonal number 3052 – decagonal number 3059 – centered cube number 3061 – prime of the form 2p-1 3063 – perfect totient number 3067 –
3000_(number)
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
Arithmetic operation, inverse of nth power
Latin as surdus (meaning "deaf" or "mute"). Gerard of Cremona (c. 1150), Fibonacci (1202), and then Robert Recorde (1551) all used the term to refer to "unresolved
Nth_root
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
Natural number
2580 – Keith number, forms a column on a telephone or PIN pad 2584 – Fibonacci number, sum of the first 37 primes 2592 – 3-smooth number (25×34) 2596
2000_(number)
Natural number
6666 – forty-fourth nonagonal number, and the 11th third-convolution of Fibonacci numbers. In Christian demonology it represents the number of demons in
6000_(number)
Number equal to the sum of its proper divisors
Retrieved 7 December 2018. Cohen, Graeme (1978). "On odd perfect numbers". Fibonacci Quarterly. 16 (6): 523-527. doi:10.1080/00150517.1978.12430277. Suryanarayana
Perfect_number
Numbers in a type of Lucas sequence
named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U n ( P , Q ) {\displaystyle
Jacobsthal_number
Recursive integer sequence
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Catalan_number
Number sequence 3,0,2,3,2,5,5,7,10,...
same relationship to the Padovan sequence as the Lucas numbers do to the Fibonacci sequence. The Perrin numbers are defined by the recurrence relation P
Perrin_number
Result of multiplying six instances of a number
multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube. The sequence of sixth powers of integers are: 0, 1, 64
Sixth_power
Integer having a non-trivial divisor
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Composite_number
Result of multiplying five instances of a number together
multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is: 0, 1, 32, 243, 1024, 3125,
Fifth_power_(algebra)
Set of numbers used in the smoothsort algorithm
Given the close relationship to the famous sequence credited to Leonardo Fibonacci, he may have considered the subject trivial. There is no known nor likely
Leonardo_number
Skyscraper in Tampa, Florida
from 1986 to 1988. Architect Harry Wolf based its measurements on the Fibonacci sequence, in which each number is the sum of the two preceding numbers
Rivergate_Tower
Indian mathematician and astronomer (598–668)
the planets, are discussed in his treatise Khandakhadyaka. Brahmagupta–Fibonacci identity Brahmagupta's formula Brahmagupta theorem Brahmagupta triangle
Brahmagupta
Cambridge University Press, p. 205, ISBN 978-0521686983 Koshy, Thomas (2017). Fibonacci and Lucas Numbers with Applications (2 ed.). John Wiley & Sons. ISBN 9781118742174
List of mathematical constants
List_of_mathematical_constants
Number that represents a hexagon with a dot in the center
numbers are differences of two consecutive cubes, so that the centered hexagonal numbers are the gnomon of the cubes. (This can be seen geometrically from
Centered_hexagonal_number
Ten raised to an integer power
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Power_of_10
Fixed number that has received a name
related to the Fibonacci sequence, related to growth by recursion. Kepler proved that it is the limit of the ratio of consecutive Fibonacci numbers. The
Mathematical_constant
graph Robertson graph Sylvester graph Tutte's fragment Tutte graph Young–Fibonacci graph Wagner graph Wells graph Wiener–Araya graph Windmill graph The strongly
List_of_graphs
Natural number
number 9319 – super-prime 9334 – nonagonal number 9349 – Lucas prime, Fibonacci number 9361 – star number 9371 – Sophie Germain prime 9376 – 1-automorphic
9000_(number)
Number of stacked spheres in a pyramid
a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the
Square_pyramidal_number
Number used for counting
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Natural_number
Number whose sums of distinct divisors represent all smaller numbers
used by Fibonacci in his Liber Abaci (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not
Practical_number
Solid with twenty equal triangular faces
regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges
Regular_icosahedron
Integer filtered out using a sieve similar to that of Eratosthenes
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Lucky_number
Type of figurate number
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Hexagonal_number
Integer divisible by sum of its digits
Curtis; Kennedy, Robert E. (1993), "On consecutive Niven numbers" (PDF), Fibonacci Quarterly, 31 (2): 146–151, doi:10.1080/00150517.1993.12429304, ISSN 0015-0517
Harshad_number
Positive integer that is an integer power of another positive integer
kth power. If k = 2 or k = 3, then n is called a perfect square or perfect cube, respectively. Sometimes 0 and 1 are also considered perfect powers (0k =
Perfect_power
Centered figurate number that counts points in a three-dimensional pattern
A centered cube number is a centered figurate number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical
Centered_cube_number
One of two different regular graphs with 16 vertices
10-regular graph with 80 edges. The 80-edge graph is the dimension-5 halved cube graph; it was called the Clebsch graph by Seidel (1968) because of its relation
Clebsch_graph
American glass sculptor and entrepreneur (born 1970)
(fabricated glass) sculpting process to create his works. His glass Spectrum Cube and Tear Drop sculptures were used in the Marvel film Guardians of the Galaxy
Jack_Storms
Calculating tool
the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20, and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence
Abacus
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
Figurate number
Hypertetrahedral Polytopic Roots by Rob Hubbard, including the generalisation to triangular cube roots, some higher dimensions, and some approximate formulas
Triangular_number
Numbers with a certain property involving recursive summation
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Happy_number
Natural number
can be written as a 2 + b ! {\displaystyle a^{2}+b!} in 3 ways 46368 = Fibonacci number 46656 = 2162 = 363 = 66, 3-smooth number 46657 = Carmichael number
40,000
Natural number
Foundation. Retrieved 2022-06-01. "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer
7000_(number)
Natural number
the sum of five consecutive primes (139 + 149 + 151 + 157 + 163) a q-Fibonacci number for q=3 760 = 23 × 5 × 19. It is a centered triangular number.
700_(number)
Natural number
repdigit in base 4 (22222224), and palindromic in base 8 (252528) 10946 = Fibonacci number, Markov number 10958 = the smallest positive integer that cannot
10,000
triangular numbers is 2 . The reciprocal Fibonacci constant is the sum of the reciprocals of the Fibonacci numbers, which is known to be finite and irrational
List_of_sums_of_reciprocals
Two raised to an integer power
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Power_of_two
Type of Poulet number
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Super-Poulet_number
Polyhedral number representing a tetrahedron
sphere packing as long as n ≤ 4.[dubious – discuss] By analogy with the cube root of x, one can define the (real) tetrahedral root of x as the number
Tetrahedral_number
Sequence of integers
-1}}.} In a similar way to the Fibonacci numbers that can be generalized to a set of polynomials called the Fibonacci polynomials, the Padovan sequence
Padovan_sequence
Odd number with specific properties
Glossary Anatoly S. Izotov (1995). "Note on Sierpinski Numbers" (PDF). Fibonacci Quarterly. 33 (3): 206. Erdős, Paul; Odlyzko, Andrew Michael (May 1, 1979)
Sierpiński_number
Function in algebraic graph theory
time of either formula satisfies the same recurrence relation as the Fibonacci numbers, so in the worst case, the algorithm runs in time within a polynomial
Chromatic_polynomial
Type of composite integer
McDaniel, Wayne (1987). "The existence of infinitely many k-Smith numbers". Fibonacci Quarterly. 25 (1): 76–80. doi:10.1080/00150517.1987.12429731. Zbl 0608
Smith_number
American artist (born 1983)
illustrates Stark's interest in concepts such as, optical illusions, The Fibonacci Sequence, fractals, and Riemannian geometry that explores the theory of
Jen_Stark
Tcheremchantse, S. (2008). "The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian". Commun. Math. Phys. 280 (2): 499–516. arXiv:0705.0338. Bibcode:2008CMaPh
List of fractals by Hausdorff dimension
List_of_fractals_by_Hausdorff_dimension
Figurate number
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Pentagonal_number
Sequence in computer science
processing elements (PEs) are hypothetically arranged in a binary tree (e.g. a Fibonacci Tree) with infix numeration according to their index within the PEs. Communication
Prefix_sum
Numbers parameterizing ways to partition a set
Leyland Loeschian Lucky numbers of Euler Recursively defined numbers Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin Graham Possessing
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
FIBONACCI CUBE
FIBONACCI CUBE
FIBONACCI CUBE
Girl/Female
Indian
Affectionate
Male
Scandinavian
Scandinavian form of Old Norse Rögnvaldr, ROGNVALD means "wise ruler."
Girl/Female
Indian
Good Person
Girl/Female
Christian & English(British/American/Australian)
Virtuous
Boy/Male
Indian
Gold
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Courage; Morale; Patience
Boy/Male
Hindu, Indian
Cool
Boy/Male
English Gaelic Scandinavian
Rules with counsel. Form of Ronald from Reynold.
Girl/Female
Tamil
Harijatha | ஹரிஜாதா
Fair haired
Boy/Male
Indian
Tasty
FIBONACCI CUBE
FIBONACCI CUBE
FIBONACCI CUBE
FIBONACCI CUBE
FIBONACCI CUBE
n.
A solid in the isometric system, bounded by twenty-four equal triangular faces, four corresponding to each face of the cube.
n.
A hydrous arsenate of iron occurring in green or yellowish green cubic crystals; cube ore.
imp. & p. p.
of Cube
a.
A determinate method prescribed for performing any operation and producing a certain result; as, a rule for extracting the cube root.
n.
A cube.
a.
Having half of the similar parts of a crystals, instead of all; consisting of half the planes which full symmetry would require, as when a cube has planes only on half of its eight solid angles, or one plane out of a pair on each of its edges; or as in the case of a tetrahedron, which is hemihedral to an octahedron, it being contained under four of the planes of an octahedron.
v. t.
To raise to the third power; to obtain the cube of.
a.
Subduplicate of the triplicate; -- a term applied to ratios; thus, a and a' are in the sesquiplicate ratio of b and b', when a is to a' as the square root of the cube of b is to the square root of the cube of b', or a:a'::Ãb3:Ãb'3.
n.
The product obtained by taking a number or quantity three times as a factor; as, 4x4=16, and 16x4=64, the cube of 4.
n.
That factor of a quantity which when multiplied into itself will produce that quantity; thus, 3 is a root of 9, because 3 multiplied into itself produces 9; 3 is the cube root of 27.
n.
A liquid or semiliquid preparation extracted (as from capsicum, cubebs, or ginger) by means of ether, and consisting of fixed or volatile oil holding resin in solution.
a.
Of or pertaining to the square root of the cube of a quantity.
n.
The small, spicy berry of a species of pepper (Piper Cubeba; in med., Cubeba officinalis), native in Java and Borneo, but now cultivated in various tropical countries. The dried unripe fruit is much used in medicine as a stimulant and purgative.
n.
Any collection and arrangement in a condensed form of many particulars or values, for ready reference, as of weights, measures, currency, specific gravities, etc.; also, a series of numbers following some law, and expressing particular values corresponding to certain other numbers on which they depend, and by means of which they are taken out for use in computations; as, tables of logarithms, sines, tangents, squares, cubes, etc.; annuity tables; interest tables; astronomical tables, etc.
a.
Pertaining to, or derived from, cubebs; as, cubebic acid (a soft olive-green resin extracted from cubebs).
n.
According to the French notation, which is used on the Continent and in America, the cube of a million, or a unit with eighteen ciphers annexed; according to the English notation, a number produced by involving a million to the fifth power, or a unit with thirty ciphers annexed. See the Note under Numeration.
n.
The product arising from the multiplication of a number into itself; as, a square is the second power, and a cube is third power, of a number.
a.
Expressed by the cube root; -- said especially of ratios.
n.
An instrument of the ancients for finding two mean proportionals between two given lines, required in solving the problem of the duplication of the cube.