Doodling in Math - Spirals, Fibonacci and Plants - 2

This girl is so cool I may soon have to create a tag on this blog just for her awesomeness. Last time we saw her, she gave us a nice introduction to how the Fibonacci sequence can give rise to the kinds and numbers of spirals we find in many plants.

Now, talking about plants, and considering the question of the most efficient leave arrangement for them to maximize sunlight for photosynthesis (aka, plant nom-noms), we stumble upon something incredible (that we've also seen before in this stunning animation): an irrational number, but not just any irrational number: the golden ratio!

Over the past two millenia, there's been speculation as to why one of the crazy commands in Pythagoras' nutty religion was to stay away from beans (and the fact that Pythagoras was willing to let himself get killed rather than cross through a field full of these plants).

You see where I'm going, right? I'm going to have to look up their leave distribution, but is it just possible the father of rational mathematics realized bean leaves follow this "irrational" formation and hence refused, as a matter of mathematical principle, to have anything to do with them???