Bounded-Error Log

theoretical and applied randomness by betaveros

Φllotaxy

2013-04-04 (101 words) filed under Math, School

This is beautiful. Why do they have to make it sound all mysterious and difficult? That’s (the reciprocal of) the golden ratio, by the way.

[Textbook]

Transcript since the resolution is far from awesome: “Most angiosperms have alternate phyllotaxy, with leaves arranged in an ascending spiral around the stem, each successive leaf emerging 137.5° from the site of the previous one. Why 137.5°? Mathematical analyses suggest that this angle minimizes shading of the lower leaves by those above.”

\[\frac{137.5^\circ}{360^\circ} = 0.3819\ldots = 1 - 0.6180\ldots = 1 - \frac{1}{\phi} = \phi^{-2}\]

edit: Go figure, the angle itself is called the golden angle.

(note: the commenting setup here is experimental and I may not check my comments often; if you want to tell me something instead of the world, email me!)