Content uploaded by Pedro Hugo García Peláez
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All content in this area was uploaded by Pedro Hugo García Peláez on Mar 11, 2022
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Content uploaded by Pedro Hugo García Peláez
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All content in this area was uploaded by Pedro Hugo García Peláez on Mar 09, 2022
Content may be subject to copyright.
Pedro Hugo Garc´ıa Pel´aez
03/14/2021
The function that return the (n)th number of Fibonacci and Lucas is:
x4
n−3x
2
n+ 1
Where (n) is the (n)th number of Fibonacci and Lucas.
For example for n=7 the roots of the function are:
1
2(29 + 13√5) = 29 + 1
29
2
29+13√5=1
29
In the next graph we can see the form of the function for n=7
1
The Golden Ratio Function
There are an important relation between the tangent lines of (n) and (2n) in the points x and 2x
The root of the quotient between the tangent line of n in the point x and the tangent line of 2n in the
point 2x is equal to x
We can see this with an example:
x = 122.992 ≈ 123