There is an order in nature and a harmony in the universe that might not be readily apparent. What initially looks to be the product of utter chaos, such as a hurricane, or simply a random conglomeration, such as the hundreds of seeds packed into the head of a sunflower, actually fits neatly into a mathematical formula — the Fibonacci Sequence.

The Fibonacci Sequence is a numerical pattern in which the next number in a recurring series is produced by adding the previous two numbers together. The sequence reads as: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.

In the natural world, it can be expressed in the petals or leaves on many plants, in the structure of pineapples and artichokes, and in the shell of a nautilus, as well in as galaxies in space, and in hurricanes over the ocean. Fibonacci numbers also are used in computer science and in finance to determine the interval when an asset’s price will cease to climb and start to lose value.

The Fibonacci Sequence is named for Leonardo Pisano Bigollo, an Italian mathematician born late in the 12th century in the Republic of Pisa. He was also known as Leonardo of Pisa or by his nickname Fibonacci, which translates generally to “son of Bonacci.” His father was a merchant who had been appointed to assist the group of Pisan traders working in the ports of North Africa in what is today Algeria. While there, Fibonacci studied under a master mathematician. He also traveled a great deal, visiting Egypt, Greece, Sicily, and Syria, where he further cultivated his use of math and his interest in numbers.

Fibonacci is widely recognized as one of the leading mathematicians of the Middle Ages. He is credited with introducing the Latin-speaking part of the world to more extensive mathematical formulas, and he was invited to appear before the Holy Roman emperor Frederick II. Fibonacci’s numerical pattern is believed to have been first identified in ancient India and used there in the study of poetic meter.

Dan Reich, associate professor emeritus in the department of mathematics at Temple University, writes that the Fibonacci Sequence exposes a pattern that is likely much more important than what the Italian mathematician originally imagined.

“It can be used to model or describe an amazing variety of phenomena, in mathematics and science, art, and nature,” Mr. Reich wrote in a paper titled “The Fibonacci Sequence, Spirals and the Golden Mean.”

“The mathematical ideas the Fibonacci Sequence leads to ... have long been appreciated for their charm and beauty,” Mr. Reich said, “but no one can really explain why they are echoed so clearly in the world of art and nature.”

The Fibonacci Sequence, also referred to as the Fibonacci Series, is nature’s numbering system. Nikhat Parveen, a biochemist at the University of Georgia, says this mathematical order — the Fibonacci numbers — is hidden in the “seeming randomness” of the natural world.

“They appear everywhere in nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pine cone, or the scales of a pineapple,” she writes. “The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.”

The Fibonacci order Parveen cites is evident in a lily’s three petals, while buttercups have five, and some daisies have 21 or 34 — all Fibonacci numbers. The order is also observed in the fruit of bananas (three sections) and apples (five sections), and in the way the branches on a tree and the leaves on each branch are configured.

“In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one,” she said.

In animals, the Fibonacci Sequence is observed in snails and in the chambered shell of the nautilus, which is a logarithmic spiral, or in a starfish with its five arms. A human being has five digits on each hand, eight fingers total, and one thumb on each hand — all numbers that appear in the Fibonacci Sequence.

Galaxies such as the Milky Way have spiral arms that follow the Fibonacci pattern, as do hurricanes. Their shape is remarkably similar to that of the nautilus, which is illustrated in a figure called the Golden Rectangle, formed by the proportional stacking of the first eight numbers that follow zero in the sequence.

“Its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the universe,” writes George Dvorsky, a Canadian bioethicist and futurist.

Contact Blade outdoors editor Matt Markey at mmarkey@theblade.com or 419-724-6068.

First Published July 29, 2018, 8:26 p.m.