Content deleted Content added
MiszaBot I (talk | contribs) m Archiving 2 thread(s) from Talk:Fibonacci number. |
MiszaBot I (talk | contribs) m Archiving 2 thread(s) from Talk:Fibonacci number. |
||
Line 706:
:The quoted caption at [[Fibonacci number#Relation to the golden ratio]] looks right to me. 1 / (1/φ) = φ (this holds for any non-zero number and not just φ). And more generally, (1/φ<sup>''n''</sup>) / (1/φ<sup>''n+1''</sup>) = φ (also holds for all non-zero numbers). In addition, φ has the special property 1/φ = φ−1. [[User:PrimeHunter|PrimeHunter]] ([[User talk:PrimeHunter|talk]]) 01:15, 2 May 2011 (UTC)
== "Gopala-Hemachandra Numbers" ==
My remarks on [[Talk:Gopala–Hemachandra number]] seem to be relevant, so I am copying them here. I said:
:There does not seem to be any source for the main claim of this article, namely that "A Gopala–Hemachandra number is a term in a sequence of the form …." The sources cited in the article do ''not'' state this. I cannot find any indication that anyone actually uses the term "Gopala–Hemachandra number" in this way, or indeed for anything else.
:I am not disputing that Gopala and Hemchandra dicussed the Fibonacci series before Fibonacci did; I agree that that is well-established. My only complaint is with the claim that the term "Gopala–Hemachandra number" is a recognized term.
:Two of the cited sources refer to "Gopala–Hemachandra codes". I don't think these two sources are enough to establish that the term is widely used. One of the two sources cited for this is self-published, and does not meet Wikipedia's standards for [[WP:RELIABLE|reliable sources]]. —[[User:Dominus|Mark Dominus]] ([[User talk:Dominus|talk]]) 15:13, 28 March 2011 (UTC)
The J.H. Thomas source does use "Gopala-Hemachandra sequence" to refer to a general sequence that obeys the recursion {{mvar|a{{su|b={{mvar|n}}}}}} = {{mvar|a{{su|b={{mvar|n}}-2}}}} + {{mvar|a{{su|b={{mvar|n}}-1}}}}, but it is self-published. I have not seen the Basu-Prasad paper yet; I have written to Professor Basu asking for a copy, but she has not yet replied. But even if it does use "Gopala-Hemachandra sequence" or "Gopala-Hemachandra number", it's only a single paper; the term is clearly not in widespread use, and I think it is inappropriate to add it to this article as if it were a common phrase. —[[User:Dominus|Mark Dominus]] ([[User talk:Dominus|talk]]) 16:00, 29 March 2011 (UTC)
:Just about everyone in the world says "Fibonacci number". I hate it when people claim we can't use the standard terminology for some newly discovered historical reason. The result, when the new name is used, is that finding literature becomes substantially and unnecessarily more difficult. Attempts at changing names happen regularly, usually when a different European mathematician is claimed to precede the one whose name is used. Often, the justification for the claim is rather unclear, and usually it does not change existing terminology. Thank goodness. Changing very well-established terminology ought to be done only for very good reasons. [[User:Zaslav|Zaslav]] ([[User talk:Zaslav|talk]]) 06:26, 28 June 2011 (UTC)
::Anyway the standard here is to name things what they are named, not what they should be named. See also [[Stigler's law of eponymy]]. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 06:43, 28 June 2011 (UTC)
== How a bit of information on the complex plane? ==
If you use the equations on this page for i, what is the i<sup>th</sup> Fibonacci number? [[User:Robo37|Robo37]] ([[User talk:Robo37|talk]]) 09:43, 6 July 2011 (UTC)
:I think it's 0.221247712 + 0.299699204i. Do you think this should be included in the artical?
::Can you show the details of your calculation ? [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 13:09, 8 July 2011 (UTC)
:::The details of my calculation?... I entered (((1+sqrt 5)/2)^i-(-(1+sqrt 5)/2))^i)/sqrt 5 into Google calculator... I am no mathematician, sorry, but maybe if you can look into how Google calculator got to this you might be able to change that into some king of closed solution involving e and/or pi. [[User:Robo37|Robo37]] ([[User talk:Robo37|talk]]) 13:38, 11 July 2011 (UTC)
::::Oops, wrong formular. The i<sup>th</sup> Fibonacci number is ''0.379294534 + 0.215939518 i'', which I got by ((1+sqrt 5)/2)^i-((-1)^i/((1+sqrt 5)/2)^i)))/sqrt 5.
| |||