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Published: Thursday, March 7, 2013, 12:01 a.m.

# Pine cones offer fascinating lesson

• Associated Press / Lee Reich

It's easier to see the Fibonacci number sequence in nature if you tip a spruce (or pine) cone with marker pens.

What do pine cones and math have in common?
A 13th century Italian mathematician named Leonardo of Pisa, better known by his pen name, Fibonacci, came up with a number sequence that keeps popping up throughout the plant kingdom.
A Fibonacci sequence is simple enough to generate: Starting with the number 1, you merely add the previous two numbers in the sequence to generate the next one. So the sequence, early on, is 1, 2, 3, 5, 8, 13, 21 and so on.
To see how it works in nature, go outside and find an intact pine cone. Look carefully and you'll notice that the bracts that make up the cone are arranged in a spiral.
Actually two spirals, running in opposite directions, with one rising steeply and the other gradually from the cone's base to its tip.
Count the number of spirals in each direction -- a job made easier by dabbing the bracts along one line of each spiral with a colored marker. The number of spirals in either direction is a fibonacci number.
I just counted 5 parallel spirals going in one direction and 8 parallel spirals going in the opposite direction on a Norway spruce cone.
Or you might examine a pineapple. Focus on one of the hexagonal scales near the fruit's midriff and you can pick out three spirals, each aligned to a different pair of opposing sides of the hexagon.
One set rises gradually, another moderately and the third steeply. Count the number of spirals and you'll find eight gradual, 13 moderate and 21 steeply rising ones. Fibonacci numbers again.
Scales and bracts are modified leaves, and the spiral arrangements in pine cones and pineapples reflect the spiral growth habit of stems. To confirm this, bring in a leafless stem from some tree or shrub and look at its buds, where leaves were attached.
The buds range up the stem in a spiral pattern, which kept each leaf out of the shadow of leaves just above it. The amount of spiraling varies from plant to plant, with new leaves developing in some fraction -- such as 2/5, 3/5, 3/8 or 8/13 -- of a spiral. Eureka: The numbers in those fractions are Fibonacci numbers.
Learn more
•For a good visual explanation of Fibonacci in nature, go to tinyurl.com/af75uea.
For more about basic Fibonacci, try the books "Fascinating Fibonaccis: Mystery and Magic in Numbers" and Trudi Hammel Garland's "Fibonacci Fun: Fascinating Activities with Intriguing Numbers."
For a visual of how nature influences art go to the Viewing Mound at the Evergreen Arboretum & Gardens, 145 Alverson Blvd., Everett, where you can see the metal sculpture "Fibonacci," a water feature inspired by the Italian mathematician. From the Viewing Mound, you can catch a sweeping view of the arboretum grounds.
Story tags » Gardening

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