Nature’s Secrets

Yes, plants can do mathematics

February 3, 2013 

Meg Lowman, an N.C. State University professor and forest canopy expert, directs the N.C. Museum of Natural Sciencesa¢,Ǩ,Ñ¢ Nature Research Center.

Math phobes are wrong! Mathematics is just a language, and language is only a habit of thought.

E.O. Wilson

“The Creation” (2006)

If you lie down at the base of a tree and look up, you will notice that the angulation of the branches is extraordinarily regular. Some, such as Norfolk Island pine, are fairly circular; some, such as maples, are gentle spirals. Unique shapes such as the umbrella tree’s follow a mathematical code that results in an arc-shaped canopy. Other plant parts exhibit a similar pattern of spiral phyllotaxis (the technical term for the arrangement of plant architecture) – pine cones, sunflower heads, arrangement of leaves on stems, and even bud scales. Nature is one big mathematical exercise!

Did you know that the angle between successive elements of most plant spirals equals the golden angle of approximately 137.51 degrees that was first studied by the ancient Greeks? Botanists originally thought that plant growth shapes were determined by sunlight, and that leaf and branch angulation was nature’s way of maximizing sunlight to all parts of one plant. But recently, scientists have discovered that this spiral phyllotaxis is also a byproduct of the biochemistry of plant growth.

Another amazing factoid for math lovers is the inclusion of the Fibonacci numbers in plant growth. As leaves or branches grow spirally along a main axis, their placement forms an interlocking spiral clockwise, and counterclockwise arms. But the number of clockwise arms never equals the number of counterclockwise arms. Instead, the sequence is identical to the Fibonacci sequence, where every sequential number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc). And scientists now recognize that these mathematical angles are somehow linked to the biochemistry of plant growth.

Francis Hallé, a botanist from the Institut de Botanique in Montpelier, France, traveled around the world mapping plant mathematics. He found that most trees have a repeated architecture – “reiteration” – whereby units of architecture are repeated as plants grow. Hallé found 24 models of tree growth throughout forests of the world. For example, the growth pattern of Norfolk Island pine represents an extremely different model from mangroves.

Why do botanists bother to map plant phyllotaxis? The answer is linked to economics and health, as well as agriculture. Such computer-generated information may give us clues to plant growth and provide important links between nutrition, biochemistry, metabolism and architecture. Perhaps someday a homeowner can order up a forest of 15-foot high, 45-degree angulated branching red rose hedges with dinner-plate-size flowers. Or perhaps a new variety of rice with reinforced stalk structures will triple the harvest, reducing starvation in developing countries.

Meg Lowman, an N.C. State University professor and forest canopy expert, directs the N.C. Museum of Natural Sciences’ Nature Research Center. Online:

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