Researchers are beginning to understand why some plants have beautiful repeating spiral patterns to their structures that incorporate the so-called golden angle (approx 137.5 degrees). Math buffs, artists, and mystics will appreciate that the golden angle is related to the golden ratio, also known as the "divine proportion," that frequently appears in aesthetically-pleasing forms. From Science News (photo by Scott Hotton):
Plants with spiral patterns related to the golden angle also display another curious mathematical property. The seeds of a flower head form interlocking spirals in both clockwise and counterclockwise directions. The number of clockwise spirals differs from the number of counterclockwise spirals, and these two numbers are called the plant's parastichy numbers (pronounced pi-RAS-tik-ee or PEHR-us-tik-ee).Link
These numbers have a remarkable consistency. They are almost always two consecutive Fibonacci numbers, which are another one of nature's mathematical favorites. The Fibonacci numbers form the sequence 1, 1, 2, 3, 5, 8, 13, 21 . . . , in which each number is the sum of the previous two...
Initially, researchers thought these patterns might provide an evolutionary advantage by somehow promoting plants' survival. But more recently, they have come to believe that the answer lies in the biochemistry of plants as they develop new leaves, flowers, or other structures.