Talk:Golden ratio

message: The reference to "Zometoy" is erroneous; the actual product is "Zometool". 2603:8080:4E05:7812:0:0:0:BA4 (talk) 12:44, 8 July 2023 (UTC)
replies: text: "Zometoy" was Steve Baer's original (very low production) toy made of wooden dowels and drilled (?) nodes. Take a close look at the picture. Zometool was a later company by Marc Pelletier and Paul Hildebrandt which took the same concept and figured out how to make a better version of it out of injection molded plastic. For some about the history, see http://people.tamu.edu/~ergun/hyperseeing/2018/06/FASE/buehler2018.pdf –jacobolus (t) 15:38, 8 July 2023 (UTC)
thread_title:  Reference to "Zometoy" product 

message: It is probably quite, but not sufficiently, well known, that the continued fraction expression, Ø = 1+1/(1+   1/(1+1/(1+1/(1+1/( ... infinitely, is easy to evaluate as a short algebraic expression.  The part to the right of the gap has value Ø, so we can curtail the expression to Ø = 1+1/(1+Ø); multiply to a quadratic ... .
That may be worth mentioning. 94.30.84.71 (talk) 13:47, 7 November 2023 (UTC)
replies: text: Or not worth mentioning. JRSpriggs (talk) 00:56, 8 November 2023 (UTC)

text: When the article says  that is the converse of your statement. But notice that each step in going from one form to the other is reversible, so these are essentially the same idea. If you like you can write this explicitly as \varphi = 1 + \cfrac{1}{1 + \cfrac{1}{1 + \ddots}} \iff \varphi = 1 + \frac1\varphi. (Under the assumption that \varphi > 0.) I think the version in the article is fine though. –jacobolus (t) 01:01, 8 November 2023 (UTC)
thread_title:  Summing the Contained Fraction 

message: In "Golden ratio conjugate and powers" equation ending -0.618033 needs to have an ellipsis added -0.618033... 2605:A601:A962:AC00:549:D9C7:F671:4843 (talk) 04:24, 8 January 2024 (UTC)
replies: text: I did not found any such equation without an ellipsis. Possibly, a horizontal scroll was needed for seeing the ellipsis. D.Lazard (talk) 09:13, 8 January 2024 (UTC)
thread_title:  Semi-protected edit request on 8 January 2024 

message: The golden ratio can be calculated from "(1+√5)/2." Using the positive value for √5 gives 1.6180. Using the negative value for √5 gives the negative of the reciprocal of 1.6180, -0.6180. Is this just a coincidence? Does this have any significance? 2601:18E:C700:4B7F:9592:6C05:1FCC:C6FA (talk) 16:52, 20 February 2024 (UTC)
replies: text: It is not a coincidence. These are the roots of a quadratic equation. The sum of the roots is 1 which is the negative of the linear term's coefficient. The product of the roots is −1 which is the constant term. So the equation is x2 −x −1 = 0. Just what we need. JRSpriggs (talk) 02:19, 21 February 2024 (UTC)

text: To put it another way, the golden number is the unique number with this "coincidence"; that is what makes it special.  Kinda like asking whether it is a coincidence that the Equator is the one latitude where the duration of daylight never varies. —Tamfang (talk) 17:16, 27 March 2024 (UTC)
thread_title:  Negative Reciprocal of Golden Ratio 

message: Please, let you add a link to q:Golden ratio at the bottom of the WP article 2.196.177.65 (talk) 11:44, 15 May 2024 (UTC)
replies: text: This appears to be a backdoor method of reinstating extremely dubious claims about the widespread use of the Golden ratio in classical art and architecture, unsupported by modern scholarship and correctly eradicated from this article. —David Eppstein (talk) 17:33, 15 May 2024 (UTC)
replies: text: The page q:Golden ratio is very strange. That page should probably be deleted, unless someone plans to fill it with proper quotations. I was expecting it to have stuff like Kepler "Geometry has two great treasures [...]" etc., but instead it seems to be some incoherent book excerpts. It's not clear what the point is, but it seems like an abuse of Wikiquote. –jacobolus (t) 19:20, 15 May 2024 (UTC)
thread_title:  Link to Wikiquote