Scientists Say: Fibonacci sequence

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Fibonacci sequence, (noun, “Fib-oh-NAH-chi SEE-kwints”)

A Fibonacci sequence is a pattern of numbers. Each number in the sequence is the sum of the previous two numbers.

The following set is a Fibonacci sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34…

Adding the first two numbers — 0 and 1 — gives the third number, 1. Adding the next two numbers —1 and 1 — gives the fourth number, 2. The numbers could go on forever.

This simple pattern appears often in nature. For instance, Fibonacci numbers occur frequently in the body plans of living things. An easy place to see this is in plants.

Plants may not know math. But flowers often have petal numbers that follow the Fibonacci sequence. Lilies and irises often have three petals. Hibiscus flowers come with five petals. Daisies tend to sport 21 petals. These numbers all occur on a Fibonacci sequence starting with 0 and 1.

These numbers also appear in nature’s spiraling structures. Turn a pine cone upside down and look at the scales. The scales grow in a spiral that starts from the bottom of the pine cone. You can count the number of spirals that emerge toward the left and toward the right. Usually, the spiral numbers are Fibonacci numbers. For example, a small pine cone has three spirals going toward the left and five toward the right.

Sunflower seeds and petals also grow in spirals from the flower’s center. These spiral numbers are nearly always Fibonacci numbers.

This pattern can also appear as a ratio. If you take two neighboring numbers of the sequence and divide them, you get a ratio. For instance, 13 divided by 8 equals 1.625. And 21 divided by 13 equals 1.615.

The further along the sequence you go, the closer that ratio gets to the “golden ratio.” The golden ratio is about 1.618. (We cannot write it out completely because it is an irrational number. That is, the numbers after the decimal go on forever.) The consistency of this ratio means that the numbers of a Fibonacci sequence fit inside one another in a very regular way.

That consistency means spirals built from Fibonacci patterns can pack together without wasting space. Leaves or petals fill up space evenly and with little overlap. That lets each leaf or petal get the most sunlight.

Scientists are working to figure out why this pattern shows up so often in nature. One idea is that as a living thing makes new cells, those new cells will pack together in the most efficient way possible. That tends to fill space in a Fibonacci pattern.