Comments on: Fibonacci numbers at work

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By: paul

paul — Thu, 12 Mar 2009 20:38:56 +0000

Thanks,

I will definitely check the Sobol sequence.

By: John

John — Thu, 12 Mar 2009 20:26:19 +0000

Paul, I have only seen Fibonacci points defined for 2D. For 3D, you could use a quasi-random sequence such as the Sobol sequence. Numerical Recipes has a description of these sequences.

By: paul

paul — Thu, 12 Mar 2009 20:09:44 +0000

Interesting post.
It is possible to generate a Fibonacci sequence for a 3D function ?
I was thinking as something like:

j/Fk(1,Fk-1,Fk-2)

Thanks.

By: Jonathan Hogg

Jonathan Hogg — Sat, 03 May 2008 04:12:44 +0000

There really is something about seeing the old-school examples pop up in the real world…I think it speaks volumes about the way we are all, at some level, verschulert to the point that even the most avid learner starts to believe that the things of education are part of a mythical world only loosely related to reality.

By: jimcp

jimcp — Thu, 24 Apr 2008 20:33:47 +0000

Never seen the formula written like ((GoldenRatio)^n – (-GoldenRatio)^-n)/Sqrt[5] as you do, but it is correct and I liked it ( but mathematicians should be conservative to preserve past work ).

The most efficient way of calculating the Fibonacci numbers I have found thus far is f(n_):=Floor[(GoldenRatio)^n/Sqrt[5]+0.5]. (Using Mathematica syntax)

I like your blog and have added it to Math Blogs on http://mathematics-diary.blogspot.com/

By: Thomas Guest

Thomas Guest — Thu, 24 Apr 2008 12:50:22 +0000

One interesting thing about these classic sequences is that they grow very quickly. So if you’re programming in C++ with fixed width integers, int Fibonacci(int) might as well use a simple lookup table. For a 4 byte int, you’d need fewer than 50 entries. And int Factorial(int) would only need 13 entries! Of course you’d still use a program to calculate these entries.