Talk:Golden ratio

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Golden ratio[edit]

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)

Golden ratio, exterior division?[edit]

Wy not in english wikipedia? See this in German Wikipedia: exterior division (German) --Petrus3743 (talk) 13:16, 15 January 2016 (UTC)

Yes check.svg Done Petrus3743 (talk) 14:07, 8 February 2016 (UTC)

The Golden ratio has the simplest of all periodic continued fractions[edit]

The Golden ratio has the simplest of all Category:Periodic continued fractions, all 1's, the period length being 1. All Category:Quadratic irrational numbers have an [eventually] periodic continued fraction, the period length could be any finite length, including 1. (Category:Rational numbers all have a finite continued fraction, which is a special case of [eventually] periodic continued fraction, i.e. all 0's, the period length being 1.) — TentaclesTalk or mailto:Tentacles 22:46, 21 April 2016 (UTC)

In other words, the set of [eventually] constant sequences is the subset of the [eventually] periodic sequences for which the period is 1. — TentaclesTalk or mailto:Tentacles 22:56, 21 April 2016 (UTC)

Quadratic Formula for the Golden Ratio[edit]

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)

(the negative number) is a solution of the defining quadratic equation . (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.[edit]

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.[edit]

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 (OEISA001622) 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)

Red question icon with gradient background.svg 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)
@Becky Sayles: 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 OEISA001622. 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 (OEISA001622) 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)
Yes check.svg Done - the heading "Decimal Digits: 1,000,000,000,000" confused me initially - Arjayay (talk) 08:22, 7 July 2016 (UTC)
Yes, your description did not specify adequately. In the future it may be helpful to follow instructions more carefully as they are written to avoid these types of common mistakes. In particular, the phrase "last paragraph" may be ambiguous as to its meaning given that an editor may recognize it to be the sentences after a break in the source, or some other number of sentences in the apparent text depending on the width of the screen they are using at the time and possibly settings affecting the appearance and indentation. Additionally your identification of the section within the heading, as opposed to the body of your request, makes it more difficult than is necessary to locate the text addressed. One of the purposes behind protecting pages is to reduce the number of inappropriate edits. The process has evolved over time and requires specification in a particular format based on the experience that edit requests without take significantly longer to be read and are much less likely to be accepted. The time and effort editors spend to make edit requests becomes wasted, and the progress of the encyclopedia is slower. If you feel that there is a better way to handle edit requests or something that could make the instructions easier to follow, discussion at Wikipedia talk:Protection policy may be helpful.  B E C K Y S A Y L E 13:33, 7 July 2016 (UTC)
@Becky Sayles: Thank you!
As for "RTFM"... I have to laugh. I created that template and I wrote those instructions, so please forgive me if I thought I understood them pretty well. :-) I think the problem was simply that putting essential information only in the section heading was a bad idea; I realize in hindsight that the natural thing to do is to ignore the boiler plate in the message box and above and only read carefully the request after the prominent message box. (It's a lot less prominent in the edit box.)
I apologize for that, but I think I really did follow the letter of the instructions. I just showed that you can follow the letter and still do a really bad job. (https://i203.photobucket.com/albums/aa310/brykoe/CalvinHobbes-1.jpg comes to mind.) Sorry for taking up up your time. 71.41.210.146 (talk) 15:15, 7 July 2016 (UTC)

References

  1. ^ Yee, Alexander J. (17 August 2015). "Golden Ratio". numberword.org.  Independent computations done by Ron Watkins and Dustin Kirkland.
  2. ^ The golden number to 17 000 000 000 digits. Universidad Nacional de Colombia. 2008. Archived from the original on 6 January 2010. 
  3. ^ Yee, Alexander J. (17 August 2015). "Golden Ratio". numberword.org.  Independent computations done by Ron Watkins and Dustin Kirkland.