Has number phi ever popped up in modern or classical physics

In summary, the divine proportion, Phi, has been mentioned in modern and classical physics. It has ties to the Fibonacci series and has been appearing in quantum equations.
  • #1
Matrixman13
32
0
I was wondering if the number phi (1.618) has ever popped up in modern or classical physics. thanks in advance
 
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  • #2
I have been looking into the divine proportion and so i was wondering if phi has ever showed up in physics...just a clarification.
 
  • #3
I have heard of it coming up in biology, but not in physics. Take that for what it's worth.
 
  • #4
1/G=G-1 only place i ever saw it was when i wrote root finding algorithm. Golden section converges faster than interval halving with same amount of work ... but not as fast as Newton's method (Newton's sometimes don't converge as often).
Plant ratios : oak 2/5 (rev/leafs) elm 1/2 beech 1/3 some trees 3/8 some bushes 5/13 pinecones and common teasel and sunflower 21 curves crossing 34 curves ... 34-55, 55-89, dahlia 8 ray 13 ragwort 21 oxeye daisy. That's all i have. It's geometric and biological somehow.

Best
 
Last edited:
  • #5
well I am doing my maths coursework and its to do with the phi function, you look at the factors of a numbers (eg. 7) and look at the factors below it (1,2,3,4,5,6,7) and any of the factors which are in the factors of 7 you don't include (excluding 1, that would defeat the whole object). Not sure if it has any relevence to the Phi number though.../me gets out his coursework...
 
  • #6
Thinking about it a little more: i never heard of the golden ratio having a name.
It's just the limit of the ratio of two terms in the Fibonacci series : 1 2 3 5 8 13 21 ...

[tex]
\frac{{\sqrt 5 - 1}}{2} = .618...
[/tex]

The nth term (n large) is given by :

[itex]
\[
\frac{1}{{\sqrt 5 }}\left( {\left[ {\frac{{1 + \sqrt 5 }}{2}} \right]^{n + 1} - \left[ {\frac{{1 - \sqrt 5 }}{2}} \right]^{n + 1} } \right)
\]
[/itex]

Best
 
  • #7
Well, pi can be expressed in terms of the sum of the arctangents of a bunch of Fibonacci numbers. Does that count?
 
  • #8
well i know what it is,I just wanted to know if it was in physics cause i know it's in biology a lot.
 
  • #9
I've never come across it in physics. Well, if you had something that was a solution of the required quadratic, it could be a multiple of phi, but that doesn't really mean anything special.
 
  • #10
I have done some research, and I found this site
http://www.tshankha.com/phi.htm

It apparently shows that phi has been appearing in quantum equations.

I'm only 14...so i don't really know what the math means.
could someone please explain what's going on in this site
thanx
 
Last edited by a moderator:
  • #11
or maybe not

k...can someone atleast comment on the site
 
  • #12
I remember Loren Booda's physics website makes mention of Fibonacci numbers, which of course is a topic that has ties to the Golden section. Maybe he will enlighten us.
 

Related to Has number phi ever popped up in modern or classical physics

1. What is number phi and how is it related to mathematics and physics?

Number phi, also known as the golden ratio, is a mathematical constant that has been studied and admired for centuries due to its unique properties and aesthetic appeal. It is approximately equal to 1.6180339887 and can be found in many natural and man-made structures. In physics, number phi has been linked to various phenomena such as quantum mechanics and fractal geometry.

2. Has number phi been observed or measured in any physical experiments?

While there have been numerous claims about the presence of number phi in various physical systems, there is no concrete evidence to support these claims. Some studies have suggested that number phi may appear in quantum systems, but these findings have not been replicated or widely accepted by the scientific community.

3. Is there a mathematical formula or equation that incorporates number phi in physics?

To date, there is no established formula or equation in physics that explicitly includes number phi. However, there have been attempts to incorporate number phi into certain aspects of physics, such as in the study of wave-particle duality. These attempts are still largely theoretical and require further research and validation.

4. Are there any ongoing research or studies about the role of number phi in physics?

Yes, there are ongoing research and studies about the potential role of number phi in different branches of physics. Some scientists are exploring the connections between number phi and chaos theory, while others are investigating its potential applications in quantum computing. However, these studies are still in their early stages and require more evidence and experimentation.

5. Can number phi be used to explain or solve any current scientific problems?

At this time, number phi has not been proven to have any significant impact on current scientific problems or theories. While its presence in various systems and its correlations with certain phenomena are intriguing, there is not enough evidence to suggest that it can be used to explain or solve existing scientific problems. Further research and experimentation are needed for a better understanding of the potential applications of number phi in physics.

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