Phi

[Matrixman13]

I was wondering if the number phi (1.618) has ever popped up in modern or classical physics. thanks in advance

[Matrixman13]

I have been looking into the divine proportion and so i was wondering if phi has ever showed up in physics.....just a clarification.

[Janitor]

I have heard of it coming up in biology, but not in physics. Take that for what it's worth.

[flexten]

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

[Lokolo]

well im doin 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...

[flexten]

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 ...


\frac{{\sqrt 5 - 1}}{2} = .618...


The nth term (n large) is given by :


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


Best

[Dburghoff]

Well, pi can be expressed in terms of the sum of the arctangents of a bunch of Fibonacci numbers. Does that count?

[Matrixman13]

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.

[Gokul43201]

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.

[Matrixman13]

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 dont really know what the math means.
could someone please explain whats going on in this site
thanx

[Matrixman13]

or maybe not

k....can someone atleast comment on the site

[Janitor]

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.