From Fibonacci Sequence to the Golden Ratio
نویسندگان
چکیده
منابع مشابه
A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence
In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore, new sequences have been used in order to introduce a new class of series. All properties of the se...
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The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is related to the golden section. The relat...
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We shall refer to A and B as the large and the small Golden Ratios, respectively, and shall in general simply refer to these and their powers collectively as Golden Numbers. Likewise, the ratio between the neighboring Fibonacci Numbers un+i/un will be called the large Fibonacci Ratio. Here, "large" means that the suffices n + 1 > n, without inference to the values of the u s or their ratio. Its...
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A Golden Triangle is a triangle with two of its sides in the ratio (J>:1, where is the Fibonacci Ratio, i.e., (J> = ^(1 + /J) ^ 1.618. Let AABC be a triangle whose sides are a,b, and o and let a/b = k > 1. Bicknell and Hoggatt [1] have shown that (1) a triangle with a side equal to b can be removed from AABC to leave a triangle similar to AABC if and only if k = cj), and (2) a triangle simi...
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A banknote specimen built on Fibonacci principles It is important that a banknote design evokes emotions and is loved by the people while at the same time fulfilling a complex set of functionalities required for all target users including central banks, commercial banks, cash handling professionals and automated systems. It is amid these parameters that the Fibonacci Project has been undertaken...
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ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2013
ISSN: 2314-4629,2314-4785
DOI: 10.1155/2013/204674