Talk:Negafibonacci

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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

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

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)

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)