Talk:Reciprocal Fibonacci constant

Nonperiodicity of continued fraction represetantion

Gandalf61 had removed recently added assertion about nonperiodicity of continued fraction representation of ψ. The truth is, yes, the assertion was really unsourced and interesting question remains - is ψ a quadratic irrational? Similar is with Apéry's constant ζ(3) - there are also no sources about this, or perhaps I've missed something. Series of both constants have infinitely many terms. --xJaM (talk) 14:06, 15 January 2008 (UTC)

No closed-form formula?

The claim in this article that there is no closed-form representation of the reciprocal sum seems to be contradicted by Wolfram's website. One should be more specific when making this claim; does it mean that the series has no closed form representation? Does it mean that the number itself is non-algebraic? If it's the former then it's wrong, since Wolfram's website solves the series and cites papers over 20 years old which had the original solution in them. 76.111.56.192 (talk) 22:16, 20 February 2010 (UTC)

The expression on MathWorld involves Jacobi's elliptic functions, which usually aren't allowed to count as closed-form expressions. It does show that our article could use expansion, though. —David Eppstein (talk) 22:23, 20 February 2010 (UTC)

There IS a closed form!

The already referenced http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html gives several closed expressions in terms of θ₂ and the first derivative of the rather well-known [function]. I have written and tested the simplest Mathworld formula in gosper.org/recipfib.pdf. [[1]] repeats the erroneous no closed form claim. I think disqualifying θ₂ and Γ_q as non-closed forms is almost as retrogressive as disqualifying complex numbers as non-numeric. Is there really a Wikipedia standard for closed form?--Bill Gosper (talk) 07:41, 29 August 2014 (UTC)

Style

@Quantling:

• The temporal and causal senses of "since" are distinct: "since cheese is made of milk..." does not imply that there was a time when cheese was not made of milk. Using "because" rather than "since" is simply a stylistic preference.
• Similarly for the preference for "proved" over "proven". The OED says (s.v. 'prove', verb, II.4) "In this sense [sc. 'to demonstrate the truth of'] the past participle proven ... is often used."

But I will not revert because the modified text is unobjectionable. --Macrakis (talk) 15:01, 19 August 2024 (UTC)

Agreed, these are stylistic distinctions. It is my upbringing as a mathematician (and what I perceive as the majority opinion in that realm) that leads me to "proved" meaning "showed that it was mathematically true" and "proven" meaning "showed that it was dependable"; though I acknowledge that these words are interchanged by many authors. My avoidance of "since" in the present context is based upon a copy editor who kept correcting my usage of the term. Since that time and because of these reasons — see what I did there? — my personal preferences are for, well, my personal preferences. Thank you for tolerating my quirks. —Quantling (talk | contribs) 15:18, 19 August 2024 (UTC)

A different copy editor in my life taught me to use "that" for clauses that are essential to identifying the noun, and a comma followed by "which" for clauses that are informational. (With exceptions, e.g., to avoid word repetition within a sentence.) So I like "Because the ratio of successive terms tends to the reciprocal of the golden ratio, which is less than 1, the ratio test shows that the sum converges."

However, I'd change "Bill Gosper derived an accelerated series which provides O(k²) digits." If there are also accelerated series with other than O(k²) digits then I'd write "that" instead of "which" because this clause distinguishes the accelerated series from the others. If there is only one relevant accelerated series then I'd put a comma before "which" because the clause is not essential to distinguishing the noun, but is providing additional information about the accelerated series. Would changing that be going too far with my English pedantics / quirkiness? (I understand that this may be predominantly an American English thing, and I understand that that introduces complications in the context of Wikipedia.) —Quantling (talk | contribs) 15:32, 19 August 2024 (UTC)

Grammarians differ on the correct use of "that/which":

... for "polished" prose, many American style guides, such as the 16th edition of The Chicago Manual of Style, recommend generally avoiding which in restrictive relative clauses. This prescriptive "rule" was proposed as early as 1851 by Goold Brown. It was championed in 1926 by H. W. Fowler, who said: "If writers would agree to regard that as the defining [restrictive] relative pronoun, and which as the non-defining, there would be much gain both in lucidity and in ease. There are some who follow this principle now, but it would be idle to pretend that it is the practice either of most or of the best writers." Linguists, according to Stanford linguist Arnold Zwicky, generally regard the proposed rule on not using which in restrictive relative clauses as "a really silly idea". (from English relative clauses)

but certainly I agree that a comma would make it non-restrictive. In this particular case, the distinction isn't even necessary. Note above that even Fowler is just suggesting that rule and observes that the best writers don't necessarily follow it. --Macrakis (talk) 16:49, 19 August 2024 (UTC)