Moment of Science: Fibonacci and the “Golden Ratio”

Time for some simple mathematics that span across the scientific world. This week, we’re exploring just some examples of the “golden ratio”.

* Fibonacci, or “Leonardo of Pisa,” wasn’t the first to come up with the numbers, but he did popularize them. The “Fibonacci sequence” involves each number being the sum of the two previous ones: 1+1=2, 2+1=3, 3+2=5 and so on. This sequence pops up incredibly often in mathematics, and you’ll often see it expressed as a spiral, with the square sides adding up in the same way with each quarter-turn. If you go far enough down the line and start to divide each number by the one before it, you end up with this ratio: 1.618 (and a lot of extra small numbers to follow, so we’ll just keep it there). That’s the “golden ratio”, or “phi” as the Greek symbol and while it’s not the exact same as a Fibonacci spiral, it’s very close.

* Enough of getting bogged down in the numbers, here’s where you can find it in practice all around you. Flower heads like sunflowers closely follow that rule, with the seeds spiraling out in familiar fashion, likely to maximize area for growth and sunlight. The number of petals is also often a Fibonacci number: 3 for lilies, 5 for buttercups, even 21 for black-eyed Susans. (Note that some flower petals are actually “sepals,” and don’t count toward that figure.) Pinecones and pineapples generally follow the golden rule as well, along with cauliflower. On a larger scale, tree branches also tend to split from each trunk or branch in a Fibonacci sequence, too.

* Snail and nautilus shells are a common example, as is one of our inner ear bones called the “cochlea,” but those are technically a little off of the golden ratio. Hurricanes and spiral galaxies are again close, but not quite there.

* From spirals to faces, both human and nonhuman, eyes, ears, mouth and nose all closely follow that golden ratio for being spaced apart, and that’s something “that other Leonardo” picked up on nicely in his artwork. Upon closer inspection, the length between finger sections also starts looking awfully familiar, as do the body sections of ants and some other insects.

* You can’t even escape Fibonacci on the molecular level. To get a full double-helix of DNA, those molecules are 34 angstroms long by 21 wide -- both numbers being part of the sequence. (An angstrom is a hundred millionth of a centimeter, by the way.)

* Some of these may be a case of “look hard enough and you’ll find what you want to find,” like elephant trunks, octopus tentacles, the Great Pyramids of Giza, but there’s a reason those numbers keep intertwining with scientific discoveries, a ratio that shows up in more places than we may ever realize.

See a spelling or grammar error in our story? Please include the title when you click here to report it.