new leaves developing in some fraction - such as 2/5, 3/5, 3/8 or 8/13 - of a spiral. Eureka, the numbers in those fractions are fibonacci numbers!
You can determine the fraction on your dormant stem by finding a bud directly above another one, then counting the number of full circles the stem went through to get there while generating buds in between. So if the stems made three full circles to get a bud back where it started and generated eight buds getting there, the fraction is 3/8, with each bud 3/8 of a turn off its neighbor upstairs or downstairs. Different plants have favored fractions, but they evidently don't read the books because I just computed fractions of 1/3 and 3/8 on a single apple stem, which is supposed to have a fraction of 2/5. All are fractions with fibonacci numbers, at least.
NUMBERS AND ART
I haven't forgotten about the artists. It turns out there are certain proportions we humans generally find pleasing: the rectangular proportions of a painting, for example, or the placement of a focal point in a painting.
In a painting, for example, the Golden Cut states that the ratio of the distance of the focal point from the closer side to the farther side of a painting is the same as the ratio of the distance from the farther side to the painting's whole width. A pleasing ratio, it turns out, is 0.618... or, if you want to use the inverse, 1.618... . Enter fibonacci: Divide any fibonacci number by the fibonacci number before or after it and you get 0.618... or 1.618..., not exactly at first, but closer and closer the higher the fibonacci number you start with. Try it.