Physics equations with the mathematical constant Phi?

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Discussion Overview

The discussion revolves around the presence and significance of the mathematical constant Phi (Φ) in physics equations, particularly whether it appears in fundamental physics phenomena similar to the way Pi does. Participants explore its connections to exponential growth, biology, and mathematical sequences.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that Phi appears frequently in modeling exponential growth and in biological contexts.
  • Another participant challenges this by stating that Phi does not play a role in exponential growth but is associated with the Fibonacci sequence and natural patterns like the arrangement of scales on pine cones and sunflower florets.
  • A different claim proposes that any instance of the number 5 can be expressed as (2Φ-1)², implying a mathematical relationship involving Phi.
  • A participant provides a link to external discussions about the golden ratio in physics, indicating interest in broader exploration of the topic.

Areas of Agreement / Disagreement

Participants express differing views on the role of Phi in exponential growth and its relevance to physics, indicating that multiple competing perspectives exist without a consensus.

Contextual Notes

Some claims rely on specific interpretations of mathematical relationships and definitions of growth, which may not be universally accepted or applicable in all contexts.

ole cram
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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
 
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ole cram said:
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/.
 
Any time the number 5 comes up you can replace it by (2Φ-1)2.
 
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