1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Accuracy, Fibonacci + Golden Ratio

  1. Aug 10, 2008 #1
    I have been curious about this for a while...

    I'm interested to know if there is any easy way to tell the accuracy of the (n+1)th on the nth term of the Fibonacci series in relation to the golden ratio.

    I know that as n tends to infinity the ratio tends to the Golden Ratio "Phi" - but is there a way to tell, say, to how many decimal places the 32nd on the 31st term is close to Phi?
     
  2. jcsd
  3. Aug 10, 2008 #2
    We can do even better, and give Binet's closed-form expression for the [itex]n^{th}[/itex] Fibonacci number in terms of the golden ratio [itex]\phi[/itex]:

    [tex]F(n) = \frac{\phi^n - (1 - \phi)^n}{\sqrt{5}} [/tex]

    Sorry to give away so much, but mathematics is large enough :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Accuracy, Fibonacci + Golden Ratio
  1. The golden ratio (Replies: 11)

  2. Golden Ratio (Replies: 11)

  3. Golden Ratio (Replies: 2)

  4. The Golden Ratio? (Replies: 3)

Loading...