Currently in Atherton, flowers are blooming like crazy. It seems as if everywhere one looks, bunches of beautiful, colorful flowers meet one’s eyes. While flowers are nice to look at, people often forget or fail to realize that mathematics are at work in the growth of flowers. This week, we wanted to introduce just a few mathematical concepts that govern flowers. More on this complex and curious topic can be found here.
Many flowers and plants, such as the sunflower, display spiral patterns in which each leaf, seed, or petal follows the next at a particular angle. This angle, which is approximately 137.5º, is called the golden angle. This angle either has been or will be covered in geometry class, but to summarize, 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.
Plants with spiral patterns related to the golden angle also display another fascinating 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; these two distinct numbers are called the plant’s parastichy numbers.
These parastichy numbers actually have an extraordinary consistency: they are almost always two consecutive Fibonacci numbers, which your child either already has learned or will learn in school. 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.
We hope that this little snippet of the mathematics behind flowers was interesting! There is much more to read up on this topic, so if your child is interested, any one of Atherton’s libraries is sure to have books with more information. Hopefully, this post will drive you to pay just a little closer attention to the beautiful flora we have here in Atherton! For more fun ways to learn math, visit The Mathnasium of Palo Alto-Menlo Park.