Results 201 to 210 of about 2,080 (215)
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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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An application of Fibonacci numbers in matrices
Applied Mathematics and Computation, 2004The paper investigates the determinant obtained by \(k\) sequences of the generalized order-\(k\) Fibonacci numbers.
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Applications of Fibonacci Numbers
Mathematics of Computation, 1989Andreas N. Philippou +3 more
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Fibonacci numbers and trigonometry
The Mathematical Gazette, 2004This article started life as an investigation into certain aspects of the Fibonacci numbers, ‘morphed’ seamlessly into the structure of some infinite matrices and finally resolved into a general set of results that link structural aspects of Fibonacci numbers with trigonometric and hyperbolic functions.
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The American Mathematical Monthly, 1961
where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a Pythagorean (number) triple is meant a set of three mutually prime integers u, v, w for which u2+v2 = w2.
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where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a Pythagorean (number) triple is meant a set of three mutually prime integers u, v, w for which u2+v2 = w2.
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Fibonacci Numbers and Geometry
2002Suppose we take a unit segment AB (see Figure 2) and want to break it into two pieces in such a way that the greater part is the mean proportional between the smaller part and the whole segment.
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