Plant Angles

Although the butterflies are the stars of the show in the Texas Discovery Gardens, they’re not the only interesting and beautiful things you’ll see there. There’s also a breathtaking array of different plant species, some of which you’re not likely to see in everyday life. There’s a wide enough range of species that you can go on a mission to uncover a secret that underlies many plants around the globe.

Your mission, should you choose to accept it, is to measure the angle between successive leaves around the stalk of different plants. There are lots of different plants to try. To clarify the mission, you’re not looking for the angle between branches or between a leaf and a branch. Instead, you should try to look straight down the stalks of various plants, and measure the angle between the directions that two successive leaves stick out radially from the axis of the stalk. I’ve marked the different kinds of angles in these photos from the Center, so you can better see what is meant.

When you’ve taken a number of measurements, what do you notice? Are any angles more common than others?

You should observe that angles around 137 or 138 degrees are the most common. Why that number? Is there anything special about that angle?

It turns out there is! What are the leaves there for? To catch sunlight for photosynthesis, which feeds the plant. Imagine that the angle between successive leaves was 90 degrees, a right angle. Then there would be just four orderly rows of leaves, stacked up right on top of each other, and they would block each other from the sun. So that would be an extremely bad angle. 90 degrees being bad suggests the question of whether there is a best angle, where the leaves on average overlap the least? And indeed there is. Using some geometry and other math, you can prove that there is an ideal, least-overlap angle, and that that angle is between 137 and 138 degrees. So the plants have naturally evolved to “discover” that ideal angle. This is a case of a basic mathematical principle dictating the structure of millions of life forms on earth. And the story gets even more interesting — it turns out that angle is closely related to the Fibonacci numbers (1,1,2,3,5,8,13, and so on, where each number is the sum of the previous two) and so can help explain why when you pick up a pineapple or sunflower or pinecone, there are usually a Fibonacci number of spirals to its seeds.