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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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1997
Consider the following number trickâtry it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers).
Peter Hilton +2 more
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Consider the following number trickâtry it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers).
Peter Hilton +2 more
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Applications of Fibonacci Numbers
Mathematics of Computation, 1989Andreas N. Philippou +3 more
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1988
The problems discussed in this paper arise from the theory of group presentations. In this section, we give a brief review of this subject, or, at least, those aspects of it which are relevant to the present paper. In the remaining sections we discuss links, occurring in our work over a number of years, between this topic and the Fibonacci and Lucas ...
Colin Campbell +2 more
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The problems discussed in this paper arise from the theory of group presentations. In this section, we give a brief review of this subject, or, at least, those aspects of it which are relevant to the present paper. In the remaining sections we discuss links, occurring in our work over a number of years, between this topic and the Fibonacci and Lucas ...
Colin Campbell +2 more
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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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Trigonometry and Fibonacci numbers
The Mathematical Gazette, 2007This article sets out to explore some of the connections between two seemingly distinct mathematical objects: trigonometric functions and the integer sequences composed of the Fibonacci and Lucas numbers. It establishes that elements of Fibonacci/Lucas sequences obey identities that are closely related to traditional trigonometric identities.
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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. >
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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. >
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Complex Fibonacci Numbers and Fibonacci Quaternions
The American Mathematical Monthly, 1963openaire +2 more sources