Wow, good work! but there are still plenty of examples in nature where the fibonacci sequence does occur in the leaf patterns on plants. Very recently, there has been some beautiful theory explaining the appearance of the fibonacci sequence as a consequence of the balance of mechanical forces during the growth and development of plants

Here's a great talk on this at the Kavli institute http://online.itp.ucsb.edu/online/pattern_c03/shipman/

See also this pop article in Physical Review Focus http://focus.aps.org/story/v13/st18

And I also recall this Science paper from 2005 -- this is a truly amazing experimental test of these ideas - this group created micron sized silver particles enclosed in a glass shell and observed the emergence of fibonacci patterns as the particles were cooled. Warning! hardcore mechanics knowledge needed: http://www.sciencemag.org/cgi/content/abstract/309/5736/909?...

Interesting. I never questioned this but I also never tried to prove it. I wonder how this all started, and how it became commonly accepted as a truth.

When something works as an approachable example for a (potentially) difficult concept, it tends to get spread around, regardless of whether it's actually true or not.

Similarly, the Inuit don't actually have several words for snow. (http://en.wikipedia.org/wiki/Eskimo_words_for_snow)

and light doesn't travel in a straight line (it radiates in all directions)

I only found about that one recently

Photons radiate in all directions, but doesn't every photon go in a straight line?

As I understand it, photons can meander in any direction at any time but due to the way probabilities cancel each other out, they tend to move in a straight line when not in the vicinity of other particles.

However, because EM diffraction is observable at macroscopic scales, the "straight line" thing really is confusing. Growing up, I always wondered how radio waves transmitted through walls and assumed they just went through them when in fact they go around.

Oh, that's really interesting... I didn't know that (I know very little about physics, I'm more of the mathematician kind).

I thought nothing went in a straight line and everything moved in a wave-like motion.

I don't think the wave is related to 3d movement in the case of light... it's not that the photon is going up and down all the time.

I think this explaination is right:

"In electromagnetic wave, it is the electric and magnetic field vector (or amplitude) that is oscillating." (not the position)

from here: http://www.physicsforums.com/archive/index.php/t-186751.html

Annoyingly, before me and my cofounder were hung up on precisely this question. We said "I know we've heard this a lot, but I can't think of any natural reason why the golden ratio would be favored in nature." We thought for a while, and gave up.

We should have just looked at the data. stupid, stupid, stupid...

My Science Fair project when I was 11 was about the Fibonacci sequence. That kinda stuff is all over the place due to the golden number.

i am interested in spirals and generating them with recursion, i got some new ideas thanks to this.

Er, did you read the article?