Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

While reading many sources and watching many video's about nature and physics I wonder if the golden ratio is really that often occurring in nature and physics ? If I look on the Wikipedia pages I see both arguments for it in sea shells and similarly it seems debunked on other pages. I believe it occurs in some animals and plants and buildings but I really wonder :

1) Is it true that golden spirals dominate the majority of logarithmic spirals in both hurricanes and spinning galaxies ? And that most hurricanes and spinning galaxies are logarithmic spirals ?

2) Is it true that the golden ratio recently occured as an important constant in investigations of relativity and quantum mechanics ?

The list of things associated with the golden ratio is unmeasurably large , it goes from black holes to evolution, pyramids, religion, chemistry and even finance and aliens.

And also it is sold as both a part of education and as 'hidden secret'. Even worse , it does not play a superimportant role in math apart from continued fractions and a few other subjects imho.

I remain very skeptical about the golden ratio in 'science' especially nonmathematical, physics and biology.

And thus I finally want the truth about it. And if it turns out to be mainly nonsense , I think we should give the golden ratio a more realistic place in both media and especially publications and education. I think it is becoming harmful. It might even give the impression towards some people that they know a bit of math and biology !?

To me it appears as a dangerous concept ! Maybe this should go to chat.

But at least I asked 2 clear questions.

share|improve this question
I presume you've seen this? –  J. M. Sep 10 '12 at 16:41
See also maa.org/devlin/devlin_06_04.html –  Robert Israel Sep 10 '12 at 16:47
@J.M No i havent. Should i ? –  mick Sep 10 '12 at 16:55
Thanks Robert Israel. –  mick Sep 10 '12 at 16:57
This could possibly be cross-posted on Skeptics. –  zzzzBov Sep 10 '12 at 21:12

3 Answers 3

up vote 7 down vote accepted

The golden ratio appears as a solution to a quadratic. It is therefore important in applications where that quadratic appears. It can also be considered to be important in applications where that quadratic appears approximately.

There is otherwise, however, no underlying physical reason as to why it should or should not appear. The ratio is merely a convenient approximation to physical scaling in many systems. However, so too is 8/5=1.6. These physical systems have mathematical properties that can lead to structures that lead to things like logarithmic spirals, and these models are based on underlying physics, but rarely do they exactly equal $\phi$.

As with many things in popular science, it has been spectacularized by unsavvy media and educators trying to make something seem "special," whereas the truly special aspects of the mathematics and the sciences are usually much more complex -- and much more interesting.

share|improve this answer
Thats what i thought. So are you saying the answer to both questions is no ? Thanks for your quick reply. Dont you think we should do something about the problem ? –  mick Sep 10 '12 at 16:42
Among all the problems with popular journalism and public education, I think this particular issue ranks fairly low on the list. –  Arkamis Sep 10 '12 at 16:49
We have bigger fish to fry (math-wise, at least) than correcting false impressions on $\phi$, @mick... –  J. M. Sep 10 '12 at 16:50
What are the biggest fish J.M ? –  mick Sep 10 '12 at 16:53
@mick I cannot definitively say "no" to your second question. It is entirely possible that someone recently developed an astrophysical model in which $x^2-x-1$ appears, and of which I am unaware (astrophysics is of nothing more than casual interest to me). –  Arkamis Sep 10 '12 at 16:54

My answer:

Biology (phyllotaxis), yes.

sunflower image

Physics, no.

Art, no.

Hidden Secret, no.

Mathematics, yes.

share|improve this answer
I don't see $\phi$... –  Fabian Sep 10 '12 at 19:28
@Fabian: See http://en.wikipedia.org/wiki/Sunflower#Description. –  ruakh Sep 10 '12 at 20:47
Can you expand on that? If your “no” is in answer to the question in the title, then why not? –  Konrad Rudolph Sep 10 '12 at 21:17

I think claims that the golden-ratio is found in nature are exaggerated.

However undeserved its recognition on the street may be, though, it is still a useful number that does pop up here and there, due to its nifty scaling-invariance property.

One instance is golden-section search, a numerical method for optimisation of a function of one variable, in which the golden number naturally arises.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.