Talk:Golden ratio

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"Reasons for the occurrence of phi in nature"

I have seen very elegant arguments for why it is advantageous for some plants to incorporate the golden ratio into the distribution of their leaves or seeds. It is based on the fact that phi is the "most irrational" number in the sense that it is the most difficult to approximate with a ratio of integers (an approximation up to a certain precision requires a large denominator). I am not familiar enough with the argument to write it myself, but if someone else is, I think it would definitely be worthwhile.

More generally, a precise statement (and possibly a proof) of the fact that phi is the "most irrational" is lacking from this article. —Preceding unsigned comment added by 68.89.174.144 (talk) 04:29, 6 June 2008 (UTC)

I'll be happy to write it if you'll tell me your source. Dicklyon (talk) 21:53, 6 June 2008 (UTC)

See eg Atela et al (2008) A Dynamical System for Plant Pattern Formation: A Rigorous Analysis, Journal of Nonlinear Science, Volume 12, Number 6 / March 2008, pages 641-676.

This particular model and its explanation goes back to papers Stéphane Douady and Yves Couder on spiral phyllotaxis, from 1991 onwards. But see the article Phyllotaxis at Mathworld for discussion and observeration of the phenomenon going back much earlier, including papers by Coxeter. Jheald (talk) 15:11, 21 July 2008 (UTC)

(sin 30) / (sin 18) = Golden number

I found this out using a calculator. Maybe it could be added to the article. —Preceding unsigned comment added by 74.58.215.201 (talk) 20:47, 28 June 2008 (UTC)

It already says that $\varphi ={1 \over 2}\csc 18^{\circ }$, which is exactly the same, since $\sin 30^{\circ }={1 \over 2}$. -- Dominus (talk) 21:02, 28 June 2008 (UTC)

More generally, things you find out using a calculator are not encyclopedic, per WP:RS and WP:NOR. Dicklyon (talk) 21:04, 28 June 2008 (UTC)

A calculator isn't a reliable source? KenFehling (talk) 07:13, 21 July 2008 (UTC)

That's like putting your own chemistry researches on here and claiming a test tube is a reliable source. Reyk _YO! 07:44, 29 July 2008 (UTC)

That's not really the same at all. The results of a calculator are verifiable by anyone. In fact, this very article and many math related articles have computations that someone did with a calculator. KenFehling (talk) 19:19, 29 July 2008 (UTC)

If the calculations and examples are used to illustrate a known fact, then that's fine. For instance look at the example section in Engel expansion. I picked the number 1.175 because it would illustrate the algorithm concisely, and I did those calculations with the aid of a calculator. But that's not original research because I didn't invent the algorithm and I'm concerned only with explaining an already known fact. If I'd just been fiddling around with my calculator one day, found something interesting and decided to put it up on Wikipedia going, "Look what I've found out!", then that would be OR. The fact that anyone with a calculator could check to see if I'm right is immaterial. Reyk _YO! 22:16, 29 July 2008 (UTC)

Right. I agree completely with what you said. I think we were just divided by semantics. KenFehling (talk) 23:37, 29 July 2008 (UTC)

A good properly functioning calculator is NOT a reliable source for something like this, but anyone can do this sort of calculation on paper in a minute and that seems like a reliable source. Calculators approximate, and knowing how and when such approximations appreciably affect the bottom line requires keeping your brain in gear. Talking students out of gullibly believing their calculators is a substantial challenge. (Talking them out of using a calculator as an anesthetic device is another challenge, but not the same one.) Michael Hardy (talk) 22:56, 29 July 2008 (UTC)

PS: See also exact trigonometric constants. Michael Hardy (talk) 22:58, 29 July 2008 (UTC)

on Further Reading

I moved a number of this items to refs, since they usefully support some points in the article. It's not clear what the remaining 6 are good for, or why we'd want a further reading section in addition to all the cited reading. Some are not very accessible. I bought a copy of Doczi, and it doesn't have much useful (lots of fanciful stuff about spirals that someone might find interesting, but most of it not very connected to the golden ratio). The Walser book looks pretty ([1]), but I haven't spotted a great place to cite it.

So should we remove these, if they're not sources that support the article? Or if someone has a copy of some that arent' online, can we add something that they support? Dicklyon (talk) 05:13, 24 August 2008 (UTC)

Per WP:MOS, the Further Reading section is intended for additional books on a topic that are not cited in the article as sources. I think we would need a rationale to remove an entry that fits this definition. Also, I see no need to make an extra effort to cite something that is now in Further Reading. The only one that I have read is Huntley, which is a pretty good overall treatment by a mathematician (I don't have it; I got it from a local library). Finell (Talk) 03:06, 26 August 2008 (UTC)

That the Parthenon uses Golden Ratio is now contested?

I recently saw a Nova program on the current Greek reconstruction of the Parthenon. The program implied that the Parthenon did not use the Golden ratio anywhere, and that the theory that it did was a creation of renaissance thought, not careful measurement. —Preceding unsigned comment added by 71.104.240.132 (talk) 03:56, 4 September 2008 (UTC)

There is no evidence the Greeks used golden ratio in art or architecture (they favoured rational proportions). I don't know who first cooked up the theory that they did, but I doubt it goes as far back as the rennaisance - I think it is after Fechner's psychophysics (which was about 1890, as far as I recall). The golden ratio myth is based on speculation and secondary popular modern sources. (Please prove me wrong, if you can!)--Noe (talk) 06:37, 4 September 2008 (UTC)

The earliest such claim I've seen is this guy in 1912. And he clearly doesn't know what he's talking about (see this note 2 on p.22). Dicklyon (talk) 07:18, 4 September 2008 (UTC)

I just noticed that he attributes some of the Parthenon proportioning to Jay Hambidge, though not necessarily the divine section aspects; here is more on that guy and the Parthenon. Dicklyon (talk) 07:31, 4 September 2008 (UTC)

Difference?

I've seen stuff that tells me 1.618 is the golden ratio, but I've seen peole call the Golden ratio 0.618 as well. What is the difference? and can anyone tell me anymore natural stuff that is based on the goloden ratio? Thanks a lot.Ericrules2363 (talk) 03:04, 2 October 2008 (UTC)Ericrules2363

The difference? 1.618 − 0.618 = 1. Fredrik Johansson 05:54, 2 October 2008 (UTC)

Phi, phi, pho, fum, I smell a troll... Dicklyon (talk) 05:58, 2 October 2008 (UTC)