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Triangular and Fibonacci Number Patterns Driven by Stress on Core/Shell Microstructures
Science, 2005Fibonacci number patterns and triangular patterns with intrinsic defects occur frequently on nonplanar surfaces in nature, particularly in plants. By controlling the geometry and the stress upon cooling, these patterns can be reproduced on the surface of
Chaorong Li, Xiaona Zhang, Z. Cao
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Bounds on the Fibonacci Number of a Maximal Outerplanar Graph
The Fibonacci quarterly, 1998All graphs in this article are finite, undirected, without loops or multiple edges. Let G be a graph with vertices vl5 v2,..., vn. The complement in G of a subgraph H is the subgraph of G obtained by deleting all edges in H.
A. F. Alameddine
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The Fibonacci Number of Fibonacci Trees and A Related Family of Polynomial Recurrence Systems
The Fibonacci quarterly, 2007Fibonacci trees are special binary trees which are of natural interest in the study of data structures. A Fibonacci tree of order n has the Fibonacci trees of orders n− 1 and n− 2 as left and right subtrees.
S. Wagner
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The Fibonacci Number of Generalized Petersen Graphs
The Fibonacci quarterly, 2006The Fibonacci number F (G) of a graph G is defined as the number of independent vertex subsets of G. It was introduced in a paper of Prodinger and Tichy in 1982. There, they also ask for a formula for the Fibonacci number of a generalized Petersen graph.
Stephan G. Wagner
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IEEE potentials, 1990
Fibonacci numbers are explained, and some of the many manifestations of the Fibonacci series in nature are described. These range from the so-called golden spiral to the Penrose tiling patterns that describe the structure of quasicrystals.
D. R. Mack
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Fibonacci numbers are explained, and some of the many manifestations of the Fibonacci series in nature are described. These range from the so-called golden spiral to the Penrose tiling patterns that describe the structure of quasicrystals.
D. R. Mack
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SOME PROPERTIES OF THE PRODUCT OF (P,Q) – FIBONACCI AND (P,Q) - LUCAS NUMBER
, 2017: Some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q) – Lucas sequence.
A. Suvarnamani
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Fibonacci Number Identities from Algebraic Units
The Fibonacci quarterly, 19811. IHTROVUCTlOhl In several recent papers L. Bernstein [1], [2] introduced a method of operating with units in cubic algebraic number fields to obtain combinatorial identities.
Constantine Kliorys
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The Ring of Fibonacci (Fibonacci “Numbers” with Matrix Subscript)
1991Several authors (e.g., see [8]) have considered the Fibonacci numbers F x where the subscript x is an arbitrary real number and showed that these (complex) numbers enjoy most of the properties of the usual Fibonacci numbers F m (m integral). A quite natural extension of the numbers F x leads to the definition of the Fibonacci numbers F z and Lucas ...
Piero Filipponi +2 more
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Approaches to the Formula for the nth Fibonacci Number
, 1994Russell Jay Hendel, Morris College, Sumter, SC 29150 In this capsule we advocate proving the same theorem in different courses. This helps the undergraduate view mathematics as a unified whole with a uariety of techniques. To illustrate, we review proofs
R. J. Hendel
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Quotients of Fibonacci Numbers
The American Mathematical Monthly, 2016AbstractThere have been many articles in the MONTHLY on quotient sets over the years. We take a first step here into the p-adic setting, which we hope will spur further research.
Florian Luca, Stephan Ramon Garcia
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