Examples of using Fibonacci numbers in English and their translations into Ukrainian
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F How many Fibonacci numbers.
The numbers  in this sequence are called the Fibonacci numbers.
In terms of applications, Fibonacci numbers appear in nature surprisingly often.
The Number  of waves, forming trend coincides with Fibonacci numbers.
Apple used a circle of Fibonacci numbers, combining and cutting the forms to get the Apple logo.
Both numbers  will be Fibonacci numbers.
Those are not Fibonacci numbers, but if you look at them closely, you will see the Fibonacci numbers buried inside of them.
Suppose you wanted to look at adding the squares of the first few Fibonacci numbers.
Another important fact is that the square of any Fibonacci numbers is equal numbers  in the sequence before it, multiplied by the number that appears after him, plus or minus.
Also, the ancient Sumerians knew the golden ratio principle,they used the Fibonacci numbers….
Example of such sets of integers are Fibonacci numbers and perfect numbers. .
In the original version, calculations are more complicated,closely related to the Fibonacci numbers.
Now, it's no surprise that when you add consecutive Fibonacci numbers, you get the next Fibonacci number.
Using this golden ratio as a foundation,we can build an explicit formula for the Fibonacci numbers.
Created the theory of the redundant number  systems based on the generalised Fibonacci numbers(Fibonacci p-codes) and the generalised golden proportions(codes of the golden p-proportion) The principals of the Fibonacci  p-codes and the new computer arithmetic based on them are described in his book- A.P. Stakhov.
Initialize i← Fk, p← Fk-1, q← Fk-2(throughout the algorithm,p and q will be consecutive Fibonacci numbers).
In computer science, the Fibonacci  search technique is a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci  numbers.[1] Compared to binary search where the sorted array is divided into two equal-sized parts, one of which is examined further, Fibonacci  search divides the array into twoparts that have sizes that are consecutive Fibonacci numbers.
Suppose you like to square numbers,  and frankly, who doesn't? (Laughter)Let's look at the squares of the first few Fibonacci numbers.
Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one ormore distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. .
This proof, published by Gabriel Lamé in 1844, represents the beginning of computational complexity theory,and also the first practical application of the Fibonacci numbers.
The obvious reason for the recursive algorithm'slack of speed is that it computes the same Fibonacci numbers over and over and over.
If the Euclidean algorithm requires N steps for a pair of natural numbers  a> b> 0,the smallest values of a and b for which this is true are the Fibonacci numbers FN+2 and FN+1, respectively.
Lyrical arrangements are often given special attention, such as in the lyrics to"Lateralus",wherein the number of syllables per line correspond to an arrangement of the Fibonacci numbers, and"Jambi", in which the metrical foot iamb is used.
Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry,and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks.
If n is not a Fibonacci number, let Fm be the smallest number  in F that is greater than n.
The number  of petals on a flower is typically a Fibonacci number, or the number  of spirals on a sunflower or a pineapple tends to be a Fibonacci number as well.
If to consider together the old and the new branch,in each horizontal plane found a Fibonacci number.
On the other hand, because it's a rectangle, the area is equal to its height times its base, and the height is clearly eight, and the base is five plus eight,which is the next Fibonacci number, 13.
Is the first and second numbers in the Fibonacci sequence.
These numbers are based on the Fibonacci ratio as follows.