Talk:Silver ratio

message: Hello. I do not know what actually is the definition of silver ratio, but 
1.414... = Sqrt[2]
and
2.414... = 1 + Sqrt[2] 
Thus NOT
1.414... = 1 + Sqrt[2]  Wrong!
So, although I do not know the accurate answer, neither does this article give any such.
As a practical note, a rectangle with proportions 1:2.41 is quite elongated. So, if you asked me, I would guess that the answer is 1:1.41 . However, as I've already noted, I don't know. 
80.221.61.8 16:26, 13 April 2006 (UTC)
replies: text: Oh for heaven's sake, it was just vandalism. See? Next time try fixing it. I'm removing the tag. Melchoir 23:38, 2 June 2006 (UTC)
thread_title:  Serious errors 

message: I think that the silver means in general deserve their own article...does anyone else agree? Carifio24 22:59, 25 December 2006 (UTC)
thread_title: Separate silver means article

message: Two opposite edges of a regular octagon form a silver rectangle (the long type of silver rectangle), obviously enough, and this seems interesting and relevant enough to mention. But does anyone know of a reference for this fact? I couldn't find anything searching for the terms "silver rectangle" and "octagon" together in Google or Google Scholar, and I don't want to mention this in the article if it's WP:OR. —David Eppstein 05:51, 30 January 2007 (UTC)
thread_title:  Silver rectangle in an octagon 

message: Does anyone know this ratios name in danish?--83.72.7.63 18:31, 14 March 2007 (UTC)
thread_title:  In danish 

message: I made the connection to the article on exact trigonometric ratios because sqrt{2} + 1 = cot 22.5. Through some algebraic manipulation, I am sure other connections can be made. --Opinionhead 14:20, 16 October 2007 (UTC)
thread_title:  Trigonometric Ratios 

message: Hi
There is material in several sections (Pell number , square triangular number) that could be made more consistent. I might actually get to it. For now I put in a rough but not too rough start. If my learned fellow WIkipedians agree to let it stay (more or less) then I will move the current first line down to a new section computation and pursue further ideas. Before putting in more work I want to see how this sits with folks.--Gentlemath (talk) 08:23, 20 February 2009 (UTC)
thread_title:  New Start, more to come 

message: Based upon a discussion at Wikipedia talk:WikiProject Mathematics#"Infoboxes" on number articles, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August ☎ 15:52, 18 October 2009 (UTC)
thread_title: Removal of infobox

message: As I was looking through the main page under the PROPERTIES section of Silver means I noted the following curious observation- under odd numbered powers of S_m^n in the equations, if one sums the leftmost numerical units (taking 1 as default when nothing is listed) of each contribution, the result is every other Lucas number. 
That is:
:: \!\ S_m^3 = S_{(1m^3 + 3m)}    1+3=4
:: \!\ S_m^5 = S_{(1m^5 + 5m^3 + 5m)}    1+5+5=11
:: \!\ S_m^7 = S_{(1m^7 + 7m^5 + 14m^3 + 7m)}    1+7+14+7=29
:: \!\ S_m^9 = S_{(1m^9 + 9m^7 + 27m^5 + 30m^3 + 9m)}    1+9+27+30+9=76
:: \!\ S_m^{11} = S_{(1m^{11} + 11m^9 + 44m^7 + 77m^5 + 55m^3 + 11m)}.    1+11+44+77+55+11=199
This matrix of equations of itself seems very similar in spirit to the Pascal Triangle, and given that a sister of Pascal with sides 2,1 generates the Lucas series, by summing samplings across every other diagonal (just as the Fibonacci series does in the classical Pascal with 1,1 sides), even more interesting. The sides of these Pascal sisters provides the 'seeds' of these Fib-like series, which may appear as contiguous numbers anywhere in the series. Thus a connection may be made between Pascal systems, and the metal means. And to think I hated math in school....  — Preceding unsigned comment added by 96.234.78.93 (talk) 05:01, 13 October 2011 (UTC)
thread_title:  PROPERTIES 

message: Hi all,
I think the notation for silver means should be changed to φn.
\begin{align}
\phi_n = \frac{n + \sqrt{n^2 + 4}}{2} \\
\text{so}\quad \phi_1 = \frac{1 + \sqrt{5}}{2} = \phi \\
\end{align}
This could thus be generalized to all real numbers and even complex numbers.
Thanks,
The Doctahedron, 16:08, 25 December 2011 (UTC)
replies: text: Since Vera de Spinadel has published such a sequence of silver means, this suggestion has been incorporated into the article.Rgdboer (talk) 22:26, 10 August 2013 (UTC)
thread_title:  Metallic ratios 

message: The silver ratio √2+1 on the real projective line (or the real axis or the imaginary axis on the complex projective line a.k.a. Riemann sphere) is halfway between 1 and ∞ (infinity pole). Its reciprocal √2−1 is halfway between 0 (zero pole) and 1. Those are straightforward consequences of the stereographic projection, cot(45°/2) and cot(135°/2) respectively.  — Preceding unsigned comment added by 85.65.95.79 (talk) 12:01, 3 June 2018 (UTC)
thread_title:  Projective lines