# Talk:Golden ratio

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## Golden ratio

I would enjoy discussing your entry under the section "Golden triangle" as I suspect that the statement is false or at the minimum needs clarification. The entry reads: ￼ I'd love to see a proof that the triangles so described are similar.

Most literature describes a golden triangle as an isosceles triangle whose ratio of the common side to the distinct side is equal to the golden ratio φ.

Following the figure in your section the side CB is identical to the same side in the original triangle thus forcing all corresponding sides to be proportional in the ratio of 1:1. But the triangles are not congruent as Euclid's Proposition 3 in book VI asserts that XB = AX*CB/AC for any triangle whose angle is so bisected. To recapitulate: I'd love to see a proof that the triangles so described are similar. Frank Gordon (talk) 02:15, 30 November 2015 (UTC)

I'm not quite sure what you're asking or not clear about, but there are 2 "types" of golden rectangles (ABX-like and BCX-like) and golden triangles of different types are not similar, only golden triangles of the same type are similar. So ABX and BCX are not similar but ABC and BCX are similar.--Kmhkmh (talk) 02:43, 30 November 2015 (UTC)

ABX is a straight line! — Preceding unsigned comment added by Frank Gordon (talkcontribs) 22:03, 7 December 2015 (UTC)

"1 cubit = 7 palms and 1 palm = 4 digits. The theory is that the Great Pyramid is based on the application of a gradient of 5.5 sekeds" Pi square root matches the seked which is what they actually used, THERES NO EVIDENCE THEY KNEW ABOUT PI, the earliest recorded egyptian pi was in 1850BC and it was (16/9)2 . Maybe they liked 22/7 or maybe its was magic for sight of any of the millions of ref on google for 3.14 or rather 3.16 which is what they thought? What ever baseless claim people make it was not the egyptians using Pi and this should be stated instead of baseless speculation that contradicts the evidence!--Thelawlollol (talk) 04:26, 18 June 2016 (UTC)

## Quadratic Formula for the Golden Ratio

In the page, it is stated that:

>>> Using the quadratic formula, two solutions are obtained: >>> φ = 1+(sqrt(5)/2 = 1.6180339887 >>> and >>> φ = 1-(sqrt(5)/2 = -0.6180339887 >>> >>> Because φ is the ratio between positive or negative quantities φ is necessarily positive:

I believe the two solutions should have been:

φ = (sqrt(5)+1)/2 = 1.6180339887 and φ = (sqrt(5)-1)/2 = 0.6180339887.

It is common to state φ = 1.6180339887, but I think it is not incorrect to put it as 0.6180339887, depending on whether you are viewing the ratio from the angle of [ b/a = (a+b)/b ] or [ a/b = b/(a+b) ]; "a" being the shorter side of the rectangle. My humble opinion.

Best regards

Robinkklam (talk) 02:21, 6 June 2016 (UTC)

${\displaystyle 1-\varphi }$ (the negative number) is a solution of the defining quadratic equation ${\displaystyle x^{2}-x-1}$. ${\displaystyle \varphi -1}$ (the positive number) is not. Try using a calculator to plug these numbers into the equation and see for yourself. —David Eppstein (talk) 02:43, 6 June 2016 (UTC)

Yes. I did make a wrong turn in my calculation. Thank you for your note. — Preceding unsigned comment added by Robinkklam (talkcontribs) 07:53, 6 June 2016 (UTC)

## Semi-protected edit request on 27 June 2016-Golden Ratio-applications in nature.

Presence of Golden Ratio in Nature-

1)In a honeycomb the female honeybees always outnumber male honeybees and the ratio in which they do so is the Golden Ratio(1.618:1).

2)Sunflower seeds grow in opposing spirals and the ratio of by adjacent diameters is always The Golden Ratio.

3)The nautilus-a cephalopod mollusc pumps gas into its chambered shell to adjust its bouyancy and the ratio of each spiral's diameter to next is Golden Ratio.

Namami2011 (talk) 09:36, 27 June 2016 (UTC)

A typical honey bee colony includes on the order of 50 000 individuals. In winter, there may be no drones at all. In summer, there may be several hundred drones per colony. The summertime ratio is on the order of 100:1, two orders of magnitude away from the golden ratio. Just plain Bill (talk) 11:39, 27 June 2016 (UTC)
Also, be careful when using the word "always". You would have to prove that it is true for every flower, every individual, every species. It may be true that patterns "tend" to the golden ratio, but when you deal something that can be numbered, at best you get a fraction, which cannot be a rational number like the golden ratio. Dhrm77 (talk) 12:45, 27 June 2016 (UTC)
I'm closing this edit request as it is clear that there is no consensus for it. In addition to the above objections, the nautilis shell, while being shaped like a log-spiral, has a different aspect ration than the golden spiral. —David Eppstein (talk) 17:02, 27 June 2016 (UTC)
Right, because none of these things is true. Dicklyon (talk) 21:24, 2 July 2016 (UTC)

## Edit request for end of "Decimal expansion" section.

The computation result in the last paragraph is seriously out of date. Replace the last paragraph with:

The decimal expansion of the golden ratio φ () has been calculated to an accuracy of two trillion (2×1012 = 2,000,000,000,000) digits.[1]

71.41.210.146 (talk) 13:57, 2 July 2016 (UTC)

Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format.  B E C K Y S A Y L E 14:52, 6 July 2016 (UTC)
I want X = the last paragraph of the "Golden Ratio#Decimal expansion" section, which currently reads:
The golden ratio φ has been calculated to an accuracy of several millions of decimal digits . Alexis Irlande performed computations and verification of the first 17,000,000,000 digits.[2]
replaced by Y = the text I supplied above:
The decimal expansion of the golden ratio φ () has been calculated to an accuracy of two trillion (2×1012 = 2,000,000,000,000) digits.[3]
Sorry, I didn't quote the text to change, but I thought I specified it clearly enough. 71.41.210.146 (talk) 01:46, 7 July 2016 (UTC)
Done - the heading "Decimal Digits: 1,000,000,000,000" confused me initially - Arjayay (talk) 08:22, 7 July 2016 (UTC)
Is there some particular reason for electing the series ${\displaystyle {\frac {13}{8}}-\sum _{n\geq 0}{\frac {(-1)^{n}(2n+1)!}{n!(n+2)!4^{2n+3}}}}$ as a relevant example of a series converging to ${\displaystyle \varphi }$? Its convergence is not so fast, and the series representation ${\displaystyle 1-\sum _{n\geq 1}{\frac {(-1)^{n}}{F_{n}F_{n+1}}}}$ that comes from the continued fraction is better-looking and has a similar convergence speed. 131.114.104.188 (talk) 11:14, 11 November 2016 (UTC)Jack D'Aurizio