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The Fibonacci Sequence - An Integer Sequence Appearing in Nature

Updated on May 24, 2016

the Fibonacci Sequence

Algorithmic Spiral of a Sea Shell
Algorithmic Spiral of a Sea Shell
Fibonacci Sequence
Fibonacci Sequence

The Fibonacci Sequence - An Intricate Mathematical Design of Nature

The Fibonacci Sequence is a sequence of numbers that appears all over nature whether the student of math recognizes it, or not. It’s a perfect example of the relevancy of math in our daily lives, and the mysteries of its presence. In learning to recognize and appreciate this reality by studying math, the student has a broader perspective on nature and a better chance at understanding it’s mysteries.

Nature is full of many intricate mathematical designs, some of which appear in direct proportion to the Fibonacci Sequence, thereby leaving a curious student to wonder about the possible meaning behind such manifestations, and potentially draw the necessary connections in order to arrive at some kind revelation. Whether or not some kind of meaning or revelation is ever reached is uncertain, but the student will never have a chance at this kind of serendipity unless he/she first learns to see and recognize math as it exists in our daily lives.

Everybody knows what a sunflower is but how many people have stopped to investigate the arrangement of the individual florets in one of its heads, as they form mathematical spirals. As in some species, there are twenty-one spirals in the clockwise direction and thirty-four in the counter-clockwise direction, (while the precise numbers depend on the species of sunflower), but 21 and 34, or 34 and 55, or 55 and 89, or even 89 and 144 -these are all numbers in the Fibonacci Sequence. They are not random and do not appear haphazardly.

Everybody has seen the black and white keys on a piano but who has stopped and realized that the Fibonacci sequence can be found in an octave on the keyboard itself. An octave contains two black keys in once cluster and three black keys in another cluster, for a total of five black keys. A keyboard also has eight white keys, for a total of thirteen keys. These particular numbers in that order are precisely the third through the seventh terms of the Fibonacci Sequence. Sure, maybe the person who invented the piano could have been aware of the Fibonacci Sequence and invented this system of keys accordingly; possible, but I don’t think so, but even if so, why?

Plants are unaware of the Fibonacci Sequence yet they just grow in the most efficient ways, and it just so happens that the most efficient way also involves this same numbering sequence. Many plants show the Fibonacci Sequence in the arrangement of their leaves around the stem. Some pine cones and fir cones also produce their spirals in this same format. Some succulents and coniferous trees also show these numbers in the bumps on their trunks. And these same numbers appear in the rings on trunks of palm trees. So what’s going on, why is this occurring all over the place?

In the case of leaf arrangement, or phyllo taxis, some of these mathematical arrangements may be related to the efficiency of maximizing the space for each leaf in order to increase the average amount of sunlight falling on each leaf. By securing even a tiny advantage such as this, over many generations, a plant ensures the efficiency of its own survival and propagation. For example, in the case of densely packed leaves in cabbages and succulents, this correct mathematical arrangement may prove crucial for the availability of space between leaves.

Although our daily lives and nature itself can often appear totally random and meaningless, an observant student may recognize a semblance of harmony in this mathematical order involving the Fibonacci sequence. Phyllo taxis is the study of the ordered position of leaves on a stem. On some plants, the leaves are staggered in a spiral pattern in order to ensure maximum exposure to sunlight. And so, if the Golden Ratio is applied to a circle, we can see how it is that a plant exhibits the Fibonacci sequence.

Moving on to animals, this same Fibonacci Sequence can be found in sea shells, dolphins and starfish. Golden proportions can be found in the sea shell of a chambered Nautilus; the spiral that appears on the outside is not random, it is a logarithmic spiral. The fins and tail and eyes of a dolphin fall at the Golden Ratio along the sections of its body. A starfish has five arms; the number five is the fifth number in the Fibonacci Sequence. Some of which may sound random at first, but if one looks closer, than not so much. These golden proportions are often referred to as the Golden Mean -which are mysterious numbers that seem to arise out of the basic structure of our cosmos -like the number phi which appears clearly and regularly in things that grow and unfold in steps, obviously including living things like plants and animals as I have discussed.

And when it comes to the Fibonacci Sequence, humans are no exception as they exhibit Fibonacci characteristics as well. The Golden Ratio is seen in the sections of our fingers; and we have eight fingers in total, five digits on each hand, three bones in each finger, two bones in one thumb and one thumb on each hand, and the ratio between our forearms and our hands is also the Golden Ratio. The face of the Fibonacci Sequence can be seen as appearing again and again in nature, even if all we choose to do is look down at our hands.

What does all of this mean? It would seem incredibly coincidental at best if there were no meaning to be found at all in this mathematical order. To say it is pure coincidence that this Fibonacci Sequence appears all over nature, would be a really easy way to dismiss a very intriguing mystery. But still, some may find this to be their best way of dealing with yet another question that seems to have no answer and they may be fine with it. But just as the number phi appears in so many places in so many natural ways, I think the mystery of this mathematical order is worth delving into, just as I think math is a subject that is not only indispensably practical and useful, but intriguing for the philosophical meaning it seems to possess, and I have a sneaking suspicion that I am not alone in my interest to not only use it, but pursue the mysteries it seems to possess.

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