The Golden Ratio (GR) is defined by dividing a line into two parts, where the ratio of the length of the entire line to the longer division is equal to the ratio of the longer division to the shorter. That ratio is approximately 1.618, and some claim it's the most aesthetically pleasing ratio to the human eye. (The GR is related to the Fibonacci sequence, in which the next number in the sequence is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, 21, and so on.)
This article by Keith Devlin
sets out to disprove that the GR has been used in art and architecture, but what I found most interesting was the discussion about how GR appears in the natural world:
Finally, if you take a close look at the way leaves are located on the stems of trees and plants, you will see that they are located on a spiral that winds around the stem. Starting at one leaf, count how many complete turns of the spiral it takes before you find a second leaf directly above the first. Let P be that number. Also count the number of leaves you encounter (excluding the first one itself). That gives you another number Q. The quotient P/Q is called the divergence of the plant. (The divergence is characteristic for any particular species.) If you calculate the divergence for different species of plants, you find that both the numerator and the denominator are usually Fibonacci numbers. In particular, 1/2, 1/3, 2/5, 3/8, 5/13, and 8/21 are all common divergence ratios. For instance, common grasses have a divergence of 1/2, sedges have 1/3, many fruit trees (including the apple) have a divergence of 2/5, plantains have 3/8, and leeks come in at 5/13.
For instance, in the case of leaves, each new leaf is added so that it least obscures the leaves already below and is least obscured by any future leaves above it. Hence the leaves spiral around the stem. For seeds in the seedhead of a flower, Nature wants to pack in as many seeds as possible, and the way to do this is to add new seeds in a spiral fashion.
Cool.