Physics equations with the mathematical constant Phi?

[ole cram]

TL;DR

Does the math constant Phi (Φ = 1.618) or its inverse appear in "fundamental" physics formulae?

I know Phi appears often when modelling exponential growth and, probably because of that, also in Biology/Ecology. But does it appear spontaneously in the mathematical description of some fundamental physics phenomenon at all? (As does Pi, the ubiquitous irrational number)
Hope I'm posting on the right forum. Thanks in advance

 

[Keith_McClary]

Some discussions:
https://www.google.com/search?channel=fs&client=ubuntu&q=Golden+ratio+physics

 

[Mark44]

I know Phi appears often when modelling exponential growth and, probably because of that, also in Biology/Ecology.

As far as I recall, phi doesn't play a role in exponential growth, but it does play a role in such things as the Fibonacci sequence and the spiral arrangement of the scales on pine cones, the florets on a sunflower, and other examples - https://awkwardbotany.com/2019/12/25/pine-cones-and-the-fibonacci-sequence/.

 

[Vanadium 50]

Any time the number 5 comes up you can replace it by (2Φ-1)².

 

[PeterDonis]

Moderator's note: An unacceptable reference has been deleted.