Talk:Fibonacci sequence

Fibonacci Approximation Function

A function that approximates the Fibonacci sequence is the following: y = (0.003)x^6 - (0.0064)x^5 + (0.0701)x^4 - (0.3435)x^3 + (1.0052)x^2 -(0.6578)x + 0.9895

Try and plot it on Octave or in any other software.

~_Roberto::Barone_~ 95.234.175.68 (talk) 15:14, 18 September 2023 (UTC)

It is possible to come up with many polynomials that accurately approximate a few of the Fibonacci numbers. (See polynomial fitting, generally.) However, regardless of the polynomial p(x), it is the case that

$$\lim _{x\rightarrow +\infty }{\frac {p(x)}{\phi ^{x}}}=0\,,$$

and thus the polynomial will fall woefully short of the Fibonacci sequence for large enough values of x. —Quantling (talk | contribs) 15:38, 18 September 2023 (UTC)

Thanks for your reply.

I know... Mine was just an approximate attempt for the sequence.

~_Roberto::Barone_~ 95.234.175.68 (talk) 16:01, 18 September 2023 (UTC)

Pictures in article

The first two pictures in the article illustrate some features of the squares of Fibonacci numbers. Don't we have any pictures to illustrate the actual Fibonacci numbers instead of their squares? Eddi (Talk) 16:32, 2 October 2023 (UTC)

With the addition of some thickened / darkened lines, the first picture could emphasize non-squares. The lines that I would thicken are

• the topmost line, of length 34,
• the rightmost line, of length 21,
• the line from the lower right corner, going left for a length of 13,
• from there going up for a length of 8,
• from there going right for a length of 5,
• then down 3,
• then left 2,
• then up 1, and
• then right 1.

—Quantling (talk | contribs) 20:41, 2 October 2023 (UTC)

The areas of the squares in the figure are squares of Fibonacci numbers, but the properties illustrated are not particularly areal. --JBL (talk) 17:05, 3 October 2023 (UTC)

It's a fair point that these images show more or less the same thing twice, and one of the two could be substituted with another type of image without losing much. –jacobolus (t) 17:13, 3 October 2023 (UTC)

Sure, I agree. --JBL (talk) 20:33, 3 October 2023 (UTC)

Intro paragraph

There is not only one Fibonacci sequence. The sequence 2,5,7,12,19,... is a Fibonacci sequence. So I do not see why the introduction should refer to "the" Fibonacci sequence. Shouldn't it describe "a" Fibonacci sequence?

Also, it is not true that every number of a Fibonacci sequence is the sum of the two predecessors (as explained in the introduction paragraph) since the first two numbers in a sequence do not have two predecessors. Shouldn't the language be made precise?

I attempted to correct these two issues back in October 2023, but Jaybee didn't like my edits and reverted them, saying that I should not have done so. Why? Majfoster (talk) 06:37, 7 December 2023 (UTC)

First, because Wikipedia articles must be based on the consensus of mainstream published sources, not on the idiosyncratic views of individual editors. Second, because this article is about the usual Fibonacci sequence, not other sequences defined from the same recurrence. We have a separate article for that: Generalizations of Fibonacci numbers. —David Eppstein (talk) 07:27, 7 December 2023 (UTC)

Thank you for the feedback. I see now there is another page for the generalized sequence. I should have done my due diligence to see if it existed before making a fuss. Majfoster (talk) 16:44, 7 December 2023 (UTC)

I agree that starting with other than 0, 1 should be in the other article.

I've boldly made an edit to reflect the other point you make; the lead sentence now reads "In mathematics, the Fibonacci sequence is a sequence starting with 0 and 1 in which each subsequent number is the sum of the two preceding ones." For the very first sentence that may be too much information, but let's see what other editors think. —Quantling (talk | contribs) 15:08, 7 December 2023 (UTC)

Excellent, I am am satisfied! Majfoster (talk) 16:45, 7 December 2023 (UTC)

Fibonacci numbers vs. Fibonacci sequence

We bothered to change the name of the article from Fibonacci numbers to Fibonacci sequence. However, much of the text still says things like "The Fibonacci numbers are" rather than "The Fibonacci sequence is". I realize that there are some instances where we really do mean the former, and I realize that there are some instances where changing the former to the latter would be a word salad, and I realize that we don't have to be pedantic about every occurrence ... but might it be worthwhile to change many of instances of the "Fibonacci numbers" to "Fibonacci sequence"? Or, putting it another way, if I do that, am I likely to get instantly reverted? Thanks —Quantling (talk | contribs) 14:39, 2 February 2024 (UTC)

No big deal indeed, so no problem with me. Afaiac, go ahead . - DVdm (talk) 15:41, 2 February 2024 (UTC)

However, the article title and your personal preferences are not good reasons for the change, and, per MOS:VAR, you must provide stronger reasons.

Also, the two phrases are not always equivalent. For example, in the last but one paragraph of the lead, the examples given are related to the first numbers of the sequence only, not to the whole sequence. So, I would oppose strongly to the change in this paragraph. In the last paragraph of the lead, this is different, as the Fibonacci numbers are not individually related to the golden ratio; this is the sequence that is related to it. So, in this case, I would strongly support the change. D.Lazard (talk) 16:30, 2 February 2024 (UTC)

I agree. Of course we can only make changes where it makes sense. - DVdm (talk) 16:41, 2 February 2024 (UTC)

Fibonacci numbers are not individually related to the golden ratio

This claim seems too broad and pretty pedantic. For example, powers of the golden ratio when written as "golden integers" of the form $a+b\varphi$ have "individual Fibonacci numbers" as their coefficients, as described in Fibonacci sequence § Decomposition of powers. –jacobolus (t) 17:30, 2 February 2024 (UTC)

Of course, I would not have used this sentence in the article. However, to establish the expression of the powers of the golden ratio, one needs the recurrence relation, and thus the defition of the sequence. The fact is that it is better to use "sequence" when all numbers are considered together. So "sequence" is better in the first sentence (before the colon) and the last sentence of the last paragraph of the lead; "numbers" is better in the remainder of this paragraph. D.Lazard (talk) 17:55, 2 February 2024 (UTC)

possibly problematic picture placement

Before my edit, my phone (at least in portrait page orientation instead of landscape) displayed the yellow "tiles" image after the phrase "the sequence begins" but before the actual sequence of "0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...", making the page easy to misread as saying "Starting from 0 and 1, the sequence begins 21, 13, 3, 2, ..."

If a reason exists why the opening sequence of numbers should start a new line, please move the picture to prevent the article from displaying in such a confusing, misleading way, realizing that the display is prone to change based on what device a reader uses and if the user tilts the device this way or that (and possibly also depending on what browser and zoom settings are in use).

Thanks. --173.67.42.107 (talk) 08:23, 29 May 2024 (UTC)

The sequence is displayed on its own line for emphasis. For a better fix of your problem, I moved the image down. D.Lazard (talk) 08:59, 29 May 2024 (UTC)