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I have recently read about the numerous occurrences of the golden ratio and Fibonacci numbers in nature. I have read that it occurs in everything from shells to plants and that the rectangle that is most aesthetically pleasing has its sides in this ratio aswell. Are these just coincidences or is there a reason that it occurs so often?

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closed as primarily opinion-based by user491874, Xander Henderson, Sahiba Arora, Dietrich Burde, Did Jan 15 '18 at 22:47

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ The occurrences of the golden ratio in nature are often coincidences, or people imposing such a ratio where it doesn't actually exist. It is pure numerological hogwash. As to the Fibonacci sequence showing up in nature, Vi Hart has a good explanation of why me might expect the Fibonacci numbers to show up in plant morphology (the second video in the series, in particular, I think is where it is addressed). Though, again, I think it is mostly people fishing for significance. $\endgroup$ – Xander Henderson Jan 15 '18 at 19:55
  • $\begingroup$ At any rate, I've voted to close this question as "Primarily Opinion Based." $\endgroup$ – Xander Henderson Jan 15 '18 at 19:56
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    $\begingroup$ The true reason is that people want to see it in nature. vimeo.com/88132964 $\endgroup$ – Yves Daoust Jan 15 '18 at 19:58
  • $\begingroup$ I strongly suggest you to read the book The Mathematics of Harmony. I am sure you can find interesting answers for your question. $\endgroup$ – Amin235 Jan 15 '18 at 20:42
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Take ten random numbers in range $[0,1]$, such as ten measurements on the human body or on the Parthenon.

Like

$$0.699, 0.637, 0.407, 0.599, 0.024, 0.998, 0.425, 0.248, 0.460, 0.616.$$

Form all pairwise ratios and look for $\phi$:

$$1.000, 1.724, 0.011, 1.475, 1.067, 1.103, 1.416, 1.101, 0.702, 0.077\\ 0.580, 1.000, 0.007, 0.856, 0.619, 0.640, 0.821, 0.639, 0.407, 0.045\\ 87.766, 151.292, 1.000, 129.477, 93.606, 96.849, 124.241, 96.613, 61.643, 6.801\\ 0.678, 1.168, 0.008, 1.000, 0.723, 0.748, 0.960, 0.746, 0.476, 0.053\\ 0.938, \color{red}{1.616}, 0.011, 1.383, 1.000, 1.035, 1.327, 1.032, 0.659, 0.073\\ 0.906, 1.562, 0.010, 1.337, 0.967, 1.000, 1.283, 0.998, 0.636, 0.070\\ 0.706, 1.218, 0.008, 1.042, 0.753, 0.780, 1.000, 0.778, 0.496, 0.055\\ 0.908, 1.566, 0.010, 1.340, 0.969, 1.002, 1.286, 1.000, 0.638, 0.070\\ 1.424, 2.454, 0.016, 2.100, 1.519, 1.571, 2.015, 1.567, 1.000, 0.110\\ 12.905, 22.246, 0.147, 19.039, 13.764, 14.241, 18.269, 14.206, 9.064, 1.000 $$

It's there !

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  • $\begingroup$ So its not actually anything special just people trying to see something that isnt there? $\endgroup$ – A.Darwish Jan 15 '18 at 20:42
  • $\begingroup$ @A.Darwish: that's my opnion. $\endgroup$ – Yves Daoust Jan 15 '18 at 20:55

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