What is Fibonacci Sequence

What is the Fibonacci sequence and where does it derive from? Why do we find it everywhere around us, from nature to art?

Despite the popular belief that mathematics isn’t related to religion, there is plenty of evidence throughout the history that suggests otherwise. If you don’t believe me, just take a look at this Pythagorean prayer:

“Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all.”

This tradition of sacred numbers was very much alive in the medieval Christian teachings, and each number from 0 to 10 had it its meaning. We owe it to the Ancient Greeks and the influence their philosophers had on the medieval Europe. That is how the belief that numbers have some mystical meaning became embedded in the fabric of the society we live in today.

As the matter of fact, almost all known cultures related numbers with their beliefs. Does Kabbalah ring a bell? One thing is in common for all of these religious teachings is that they all try to explain the universe we live in and to find answers to the problems that troubled humankind throughout the centuries. That is why the discovery of Fibonacci’s sequence isn’t an isolated incident in the history of mathematics, but rather a result of efforts that started more than a thousand years earlier.

Who is Fibonacci?

Leonardo, before Leonardo is perhaps the best description of this genius mathematician whose name is much better known than his work. His real name was Leonardo Pisano Bigollo and he is considered to be one of the most talented European mathematicians from the medieval period. The native of Pisa got his nickname Fibonacci in the 19th century, seven centuries after his death. He lived from 1170 to 1250 during a period in which science wasn’t exactly popular and people often chose to believe in superstitions.

He wrote two books that became influential long after his death. Liber Abaci or (Book of Calculation) introduced the Hindu-Arabic numbers to the Western world, but most importantly, it is the first book in Europe that explains what is known today as the Fibonacci sequence. He didn’t discover the sequence because the Indian mathematicians had been aware of it long before Leonardo of Pisa.

Fibonacci simply introduced one of the most mysterious and intriguing mathematical problems to the Western civilization. He explained it in a rather unorthodox way by using an example of the growth of a rabbit population. In the sequence, each number is equal to the sum of the previous two numbers.

Fibonacci's rabbit analogy

Diagram of Fibonacci’s rabbit analogy

The Fibonacci sequence shouldn’t be confused with Fibonacci spiral, although they are closely related. The Fibonacci spiral uses Φ (phi) or the golden ratio as its basis, and it is this spiral that can be spotted in nature as well as in art.

Patterns in nature

Observation is one of the earliest scientific methods humans applied when approaching the issues they didn’t understand. Fibonacci’s spiral can be easily spotted on pine cones, seashells, sunflowers, flower petals and countless other life forms.

Nobody really knows how and why these patterns occur. The most reasonable explanation would be that the leaves of a flower follow the sun and grow on the part of the flower that has both the most growth hormone and the most sunlight. This sounds convincing but falls short of  explaining the sea life forms, for example.

Symmetry is another way to try to explain a mystery that troubled many generations of scientists, philosophers, and mystics. Why are these patterns so common in nature? We might know what symmetry is, but nobody really knows why it happens. It seems quite possible that the Indian mathematicians, as well as Fibonacci, simply observed the nature and identified a phenomenon for which they found a mathematical explanation.

Pine cone spiral & Visualization

Pine cone spiral & Visualization of a pine cone spiral

Fibonacci and art

Art imitates life, at least it strived to imitate life during the Renaissance period when the Fibonacci spiral was first used in painting. To paint means to organize the pictorial space and this space is often rectangular. That is why the Fibonacci sequence found its way into the world of art. The use of simple shapes, such as circles, squares, and rectangles throughout the history of painting had a rather functional purpose, it allowed the spectator to see the picture faster and without difficulty.

The Renaissance period is very important for the story of the deification of the Fibonacci sequence. It was during this time that intellectuals sought to find perfection and associated anything that they considered to be perfect with the almighty creator of the universe. That is why Leonardo da Vinci often refers to the golden ratio as to the Divine proportion.

Western art in the subsequent centuries looked up to the Renaissance masters, which explains why almost all paintings that use perspective composition also utilize the Fibonacci spiral. Painting isn’t the only art that uses the laws of the Fibonacci’s sequence, but the reasons for using it in architecture or music are fairly similar to the reasons of the painters.

Madonna del Parto, (Madonna of the Meadow) Giovani Bellini

Madonna del Parto (Madonna of the Meadow), Giovani Bellini, 1505

Fibonacci and Pop culture

Up to the present day, both scientists and artists are frequently referring to Fibonacci in their work. His sequence has become an integral part of our culture and yet, we don’t fully understand it. We can’t explain why these patterns occur, and we are even having difficulties explaining what the numbers are. Nevertheless, if you pick up a book like Da Vinci’s Code, you will find quite a lot about Fibonacci and his numbers, but these references don’t get us any closer to understanding why nature chose this sequence to make some of its most beautiful creations. We can only marvel at them or think they are God’s way of communicating with us, but we don’t have the capacity to comprehend its meaning or its significance.

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Zeljko D.

Zeljko D.

Željko D. is an art historian and an artist. He balances between his work as a writer and a photographer. He is probably at his best when he combines words and images. Željko is known for his passion for underground art. He has collaborated with a number of respected art institutions and likes to share creative energy with others. His view may be avant-garde but deep down he is a book-loving guy who enjoys researching and constantly discovers new things.