Talk:Fibonacci sequence/Archive 2

Archive 1

Archive 2

Archive 3

Archive 4

Gopala / Hemachandra

I've removed the clause from the introduction that says that the numbers are also called the "Gopala-Hemachandra numbers". The page already mentions that Fibonacci was anticipated by Gopala and Hemachandra, and I find no evidence that the numbers are actually called the "Gopala-Hemachandra numbers".

I'm also going to redirect the Gopala-Hemachandra numbers article to this one, since the two phrases mean the same thing and that article contains nothing that isn't already in this one.

-- Dominus 14:16, 11 Nov 2004 (UTC)

Addendum: even the external research paper linked to from the Gopala-Hemachandra numbers page does not refer to the numbers as the "Gopala-Hemachandra numbers". It says "The numbers in the sequence are called Fibonacci numbers." The phrase "Gopala-Hemachandra numbers" does not appear in that paper.

-- Dominus 14:18, 11 Nov 2004 (UTC)

i agree that the internal reaseach paper linked to from the page definatley does not refer to the numbers as gopala-hemachandra numbers.i have checked twice over and it does not apper in the paper. —Preceding unsigned comment added by 213.1.35.46 (talk) 14:35, 25 September 2007 (UTC)

I note we still have a page Gopala-Hemachandra number (no s at the end) which is not a redirect. I've now redirected it to here. --Salix alba (talk) 14:53, 25 September 2007 (UTC)

Bartok

From the "Application" section: "It is commonly thought that the first movement of Béla Bartók's Music for Strings, Percussion, and Celesta was structured using Fibonacci numbers."

Well maybe it is commonly thought, but that doesn't mean it is true. Until someone can come up with an explanation on why that movement has 88 bars and not 89 as the Fibonacci sequence would suggest, I would like to see this part removed from the article. NguyenVanThoc 22:41, 30 November 2007 (UTC)

Formula

While these nifty bignum formulas are nice and all, I think it would be very nice to have the actual formula for calculating them. The math isn't that hard to do by hand, because of cancelling pieces. I think that the article needs it because it is the non recursive form of it.

See the Closed Form Expression, which translates to:

$F\left(n\right)=({1 \over {\sqrt {5}}})(({1+{\sqrt {5}} \over 2})^{n}-({1-{\sqrt {5}} \over 2})^{n}))$

Courtesy of Posamentier and Lehmann -Dagordon01 16:40, 1 December 2007 (UTC)

Formula of finding fibonacci number

lets say a = sqrt(5), then: F(n) = ((a+1)^(n+1)-(a-1))/(2^(n+1)*a)

See the discussion above about "Formula" and the reference to Posamentier and Lehmann -Dagordon01 16:52, 1 December 2007 (UTC)

Popular Culture

This section is VERY vague. Should some examples be given? —Preceding unsigned comment added by BrettxPW (talk • contribs) 20:52, 10 December 2007 (UTC)

Identity for doubling n

I added the actual identity for doubling n. I think the formula for F_{2n+k) needs a reference or something since I have never seen that before. The reference provided right below that does NOT contain that identity and indeed contains an identity that is completely wrong: F_2n=F_{n}^2+F_{n-1}^2. I believe that reference should be removed. I also don't see how it reduces to the F_2n formula when k = 0. Also, it should definitely not say for all integers k and n because it doesn't make sense if n<0 or k<3. (SlaterDeterminant (talk) 16:44, 3 January 2008 (UTC))

I fixed the formula that you added for F_2n. The F_2n+k formula looks fine to me - it is just a special case of Formula 47 from the MathWorld page. When k=0 you have F_k=0, F_k-1=1 and F_k-2=-1, so you get F_2n = 2F_n+1F_n - F_n² as expected. Gandalf61 (talk) 17:17, 3 January 2008 (UTC)