Geeky Fun at Christmas
The seeds of a sunflower, the spines of a cactus, and the bracts of a pine cone all grow in whirling spiral patterns. Remarkable for their complexity and beauty, they also show consistent mathematical patterns that scientists have been striving to understand.
A surprising number of plants have spiral patterns in which each leaf, seed, or other structure follows the next at a particular angle called the golden angle. The golden angle is about 137.5. Two radii of a circle C form the golden angle if they divide the circle into two areas A and B so that A/B = B/C.
The golden angle is closely related to the golden ratio, which the ancient Greeks studied extensively and some have believed to have divine, aesthetic or mystical properties.
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).
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.
The Fibonacci numbers tend to crop up wherever the golden ratio appears, because the ratio between two consecutive Fibonacci numbers happens to be close to the golden ratio. The larger the two Fibonacci numbers, the closer their ratio to the golden ratio. But this relationship doesn't fully explain why parastichy numbers end up being consecutive Fibonacci numbers.
Scientists have puzzled over this pattern of plant growth for hundreds of years....
As you struggle to engage in the tedium of Christmas behold the sprout stalk or the festive pine cones and observe and wonder, let others debate Vince, Dave and Nick, let your mind be on higher things.