Talk:Negafibonacci

how many negafibonacci numbers are required for the unique sum? just 2? i'm having trouble finding 2 that add up to 12. some one more expert please make this section clear.Essap 18:10, 7 May 2007 (UTC)essap[reply]

never mind that last comment, i know what the article is trying to say. i will make it more clear and add another example or two. i want to keep the dispute tag because the article has no sources. i know that positive integers can be uniquely expressed as sums of fibonacci numbers, but is it also true that any interger can be uniquely expressed as sums of negafibonacci numbers? maybe i should put an expert tag on this too...Essap 22:19, 7 May 2007 (UTC)essap[reply]

There is a lecture being given by Donald Knuth on August 4. I will fill in more after that. He says:

All integers can be represented uniquely as a sum of zero or more “negative” Fibonacci numbers F −1 = 1, F−2 = −1, F−3 = 2, F−4 = −3, . . . , provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles, where each triangle has one
90◦ angle, one 45◦ angle, and one 36◦ angle.

RayKiddy 18:30, 21 July 2007 (UTC)[reply]

I've changed the primary definition. There are a few different definitions available; I prefer this one, because it seems more natural (to me) to extend the Fibonacci sequence "backwards" than to multiply it by an alternating sign. At least it makes the notation look more sensible!

Some sources should still be found, and I'd like to see something here about Knuth's use of the negaFibonacci representations as "coordinates" in the tiled hyperbolic plane. Regardless, I think I'll remove the stub tag.... Jaswenso 14:18, 4 September 2007 (UTC)[reply]

It now seems to me that there is not much more to say here. Web search and a search of math reviews suggest that so far, Knuth isn't publishing anything about his coordinatization of the hyperbolic plane. Absent a reference on that topic, maybe we've covered the state of knowledge on this topic. Unless there's some objection, I'll remove the expert tag. First, though, maybe we should consider merging this page with NegaFibonacci_coding. Thoughts? Jaswenso (talk) 09:04, 18 December 2008 (UTC)[reply]

Anti-Fibonacci Numbers

Err, didnt we delete an article on this not too long ago? Except it was called "Anti-Fibonacci Numbers" instead of "Negafibonacci"? And yet nobody is asking for this to be deleted? *confused* There are articles on AT&T research that still link to the old Anti-Fibonacci page. 69.205.63.181 (talk) 22:16, 5 February 2009 (UTC)[reply]

Anti-Fibonacci number was deleted at Wikipedia:Articles for deletion/Anti-Fibonacci number. The deleted article was unsourced and started:

The anti-Fibonacci numbers comprise a sequence closely related to the Fibonacci sequence. It satisfies the following recursion formula:
$f(k+2)=f(k)-f(k+1)\,.$

The anti-Fibonacci sequence begins

$1,0,1,-1,2,-3,5,-8,\dots \,$

This is not exactly the same as Negafibonacci numbers and there is a reference to the very notable Donald Knuth. But you are free to suggest deletion. PrimeHunter (talk) 00:31, 6 February 2009 (UTC)[reply]

Recurrence Relation

I don't quite see why the formula here should differ from that in Fibonacci_number - That formula,

F_{n}=F_{n-1}+F_{n-2},\!\,

and the base cases

F_{0}=0\quad {\text{and}}\quad F_{1}=1.

already adequately define these "negafibonacci" numbers. Article should be deleted, and the section on "Integer Representation" should be moved into Fibonacci_number. —Preceding unsigned comment added by 130.216.1.16 (talk) 09:23, 20 May 2009 (UTC)[reply]