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Extending Genetic Algorithms with Biological Life-Cycle Dynamics. [PDF]
Biomimetics (Basel)Felix-Saul JC +3 more
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Designing the Smile in Complete Denture Patient: An Ingenious Approach.
J Pharm Bioallied SciShingane S +5 more
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The Fibonacci Numbers: Exposed
Mathematics Magazine, 2003Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. Indeed, Koshy gushingly refers to them as one of the "two shining stars in the vast array of integer sequences" [16, p. xi]. The second of Koshy's "shining stars" is the Lucas numbers, a close relative of the Fibonacci numbers, about which we will say more ...
Robert Mena, Dan Kalman
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Factorization of Fibonacci Numbers
The Fibonacci Quarterly, 1970The Fibonacci numbers \(F_n\) may be defined by \(F_0 = 0\), \(F_1= 1\), \(F_{n+1}=F_n +F_{n-1}\) for \(n \geq 1\). If \(F_z\) \(z>0\), is the smallest Fibonacci number divisible by the prime \(p\), then \(z =a(p)\) is defined as the entry point (or rank) of \(p\); moreover \(p\) divides \(F_n\) if and only if \(n\) is divisible by \(z(p)\).
Daykin, D. E., Dresel, L. A. G.
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Applications of Fibonacci numbers
The Mathematical Gazette, 1979One card up the sleeve of many a teacher of mathematics involves the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,…, in which each number is the sum of the preceding two. These numbers and the closely related golden ratio (√5 − 1):2 have intriguing geometric and algebraic properties and appear mysteriously in nature ([1], 160-172).
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Fibonacci's Forgotten Number [PDF]
The College Mathematics Journal, 2008 Ezra (Bud) Brown (ezbrown@math.vt.edu) grew up in New Orleans and has degrees from Rice and LSU. He arrived at Virginia Tech shortly after Hurricane Camille, and has been there ever since, with time out for sabbatical visits to Washington, DC (where he has spent his summers since 1993) and Munich.
Ezra Brown, Cornelius Brunson
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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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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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