Fibonacci numbers 

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Message boards : Science (nonSETI) : Fibonacci numbers
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Is there an app that will run on my computer that will calculate Fibonacci numbers similar to a Pi program?  
ID: 1207762 ·  
I don't know but Enrico Bombieri of the Princeton Institute for Advanced Study mentions a "Fibonacci quarterly" in an article on Fibonacci included in a book "Fibonacci tra arte e scienza" published by Cassa Di Risparmio di Pisa with Luigi A.Radicati di Brozolo (ed). They should know.  
ID: 1207781 ·  
I think Fibonacci sequences are also involved in some Fractals, particularly the Mandelbrot Set.  
ID: 1207833 ·  
Is there an app that will run on my computer that will calculate Fibonacci numbers similar to a Pi program? Sure. It's pretty easy to make even on your own.  
ID: 1207865 ·  
I think Fibonacci sequences are also involved in some Fractals, particularly the Mandelbrot Set. Yeah they pop up all over in mathematics. Phi (the golden ratio) comes immediately to mind. ____________  
ID: 1207880 ·  
Another number, a ratio kept popping into my mind as I wrote the previous post that featured the golden ratio of 1.618. The number was 1.4. It turns out that there is another “golden” ration based on 1.414, which is the square root of 2, which also happens to be the length of the diagonal of a square with sides of length 1.  
ID: 1207911 ·  
There is a "Binet" formula and also a generating function where you round to get the answer. Do a Google and you can get to other generating sites as well. If you are interested in Fibonacci numbers, the golden ration and hidden structure in Mathematics, contact me via private message and I will send you a paper that I wrote a few years back on the subject.  
ID: 1207930 ·  
If you average the ratios of adjacent Fibonacci numbers: 1,1,2,3,5,8,13,21... with Lucas number ratios: 2,1,3,4.7,11,18,29... you can approach Phi, to any desired level of accuracy, in fewer steps than using either alone. Michael  
ID: 1207989 ·  
(1 + sqrt(5)) / 2  
ID: 1208115 ·  
a:=1;  
ID: 1208119 ·  
a:=1;  
ID: 1208120 ·  
If you average the ratios of adjacent Fibonacci numbers: 1,1,2,3,5,8,13,21... with === actually you can start with any numberssay two arbitrary three digit numbers. Add them together and then add this sum to the 2nd number and then continue on by adding this sum to the previous one and so on. You will soon approach PHI at the tenth number if you take the ratio of the tenth to the ninth. This ratio will be at least 1.61 and possibly you could round it to 1.618. Try it for yourselfmakes a good magic trick.  
ID: 1208125 ·  
Nice respondence to Fibonacci numbers thanks.  
ID: 1208175 ·  
the : means a variable in computer languages.  
ID: 1208220 ·  
Is there an app that will run on my computer that will calculate Fibonacci numbers similar to a Pi program? They're 'organic' ratios, rather than absolute numbers. just use the golden ratio ;) See any Fibonacci expansion contours or Golden Ratios in the speakers I made when I was 17? and here's some fibonacci sequences to play on them :D 'BT's Fibonacci Sequence' ____________ "It is not the strongest of the species that survives, nor the most intelligent that survives. It is the one that is the most adaptable to change." Charles Darwin  
ID: 1208227 ·  
Nice respondence to Fibonacci numbers thanks. On the software I was using, well known constants such as Pi cannot be redefined. If I type "evalf(Pi);", it returns 10 digits (or whatever I set it for) of 3.141592654... . If I want to define Sarge's constant as 2.176218, i could use SC:=2.176218. So, indeed, the colon before the equals sign indicates I am defining something the software package does not already know to be equal.  
ID: 1208274 ·  
Pi is an infinite series. The nth Fibonacci number has a closed form equation. What's interesting is that the equation has irrational numbers in it yet gives a whole number (rational)  
ID: 1208313 ·  
I was watching the Science channel on TV and the show was about alien contact and they were discussing seti and the aliens would communicate through math and it would probally be Fibonacci numbers. So I had a program that will run Pi numers to when ever I stop the program so I was wondering about Fibonacci numbers. So I thought I would make this posting and see what the seti crunchers would say.  
ID: 1208334 ·  
Pi is an infinite series. The nth Fibonacci number has a closed form equation. What's interesting is that the equation has irrational numbers in it yet gives a whole number (rational) That is one definition of Pi. One could also define it as 4 * integral(sqrt(1  x^2),0 .. 1,dx). So many ways to start.  
ID: 1208349 ·  
You also need to look at Lucas Numbers,  
ID: 1208403 ·  
Message boards : Science (nonSETI) : Fibonacci numbers
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