Spiral Arms

1. A Consequential Countdown

Spiral Arms

It's not unusual to find spirals in nature—in the shapes of nautilus shells, among some kinds of spiderwebs, and in the arms of many galaxies.

This cross section of a chambered nautilus shell reveals a spiral pattern.

Plants often feature spirals, too. Pineapples and pine cones have rows of diamond-shaped markings, or scales, which spiral around clockwise and counterclockwise.

The surface of a pineapple features scales that appear to form sets of spirals. USDA ARS

If you count the number of spirals of scales, you are likely to find 8, 13, or 21, all Fibonacci numbers.

In the head of a sunflower, the tiny florets that turn into seeds are typically arranged in two intersecting families of spirals, one winding clockwise and the other winding counterclockwise.

The head of a sunflower (above) displays two intersecting families of spirals, as shown in the diagram (below) of a typical seed arrangement.

Count the number of spirals (clockwise versus counterclockwise) of florets (or seeds) and you may find 34, 55, 89, or 144—all Fibonacci numbers, of course.

TRY IT!

Count the number of spirals of scales or florets to look for Fibonacci numbers.

Scales on the bottom of a pine cone form parts of spirals.

Spirals among the florets of a daisy-like flower.

Floret spirals at the center of certain types of daisies feature the numbers 21 and 34. You can look for similar patterns on broccoli or cauliflower.

Scientists have long wondered why Fibonacci numbers (see "A Special Sequence") come up in plants (see Nature's Numbers"). The answer may have something to do with the way plants grow, especially the way petals or buds space themselves to gather the most sunlight and nutrients as they get bigger.

Wherever you look, nature certainly has a way with numbers.

Answers:

Counting spirals of scales or florets can be very tricky, and the answers depend on whether you count along an edge or further toward the center. Sometimes the spirals are hard to see, and it's difficult to tell where each one starts and ends. As a result, different people can come up with different answers, and the numbers you get are often not Fibonacci numbers.

The lesson is to be wary of claims that anyone makes about the occurrence of Fibonacci numbers without seeing the evidence or checking for yourself.

See also "Golden Blossoms, Pi Flowers" and "Fermat's Natural Spirals."

For detailed information on counting spirals, see "How to Count the Spirals"(National Museum of Mathematics).

NEXT: The Golden Ratio