Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]

[pokerfan]

6. Did you watch the first video in the series?

There's also more here on Wolfram Mathworld. Not so much the article itself but a whole bunch of references: http://mathworld.wolfram.com/Phyllotaxis.html

I don't think it's so much a matter of it having to be this way because, as you noted, a 180 degree spacing could work more or less as the third leaf doesn't completely shade the first lead as it's further up the stem. It's just that some arrangements are more efficient than others and natural selection has a way of rewarding the most successful.

It's not entirely unlike the life cycle of the Cicada (http://en.wikipedia.org/wiki/Cicada#Life_cycle) being on 13 or 17 year cycles, both prime numbers. A sort of natural Archimedes sieve which generates prime numbers.