Who or What is a Fibonacci?
Up until today, I had no real understanding of Fibonacci and his mathematical prowess. I also didn't realize how much his teaching has and will continue to influence my life magically. To give you the best understanding of just how magical this math is, you have to go back to the creation of the numeric system we use today.
Fibonacci, or Leonardo Bigollo Pisano ("Leonardo the Traveller from Pisa"), was an insightful mathematician from Italy around the 12th century. He wrote a book called Liber Abaci (Book of Calculation) that changed how Europeans did their math calculations forever. Up until Liber Abaci Europeans, used the Roman Numeral system as their only method of calculation. It was cumbersome and quite limited when you started getting into large numbers. Fortunately for the Europeans, Fibonacci translated the Hindu–Arabic numeral system based on glyphs. Today we know those glyphs as, 0,1,2,3,4,5,6,7,8,9. This is the Fibonacci Sequence (hereto known as the symbol F).
The Fibonacci Spiral
Pay attention here, this is very important. The new system of symbols (glyphs) used to represent the system are in principle, independent of the system itself. Yes, this is the part I used to glaze over when I was in math class too. Let me make it easier for you to get the meaning here and why it is so important to you.
Each glyph or number in our case is part of a ten-digit system (0-9) that works together to solve complex problems. However, here is the key, each number is independent of the system as a whole. The number can stand on its own.
The "magic" that Fibonacci reminds us of is the truth that all things are a part of a system but can also operate independently of that system for the own best and highest good. For example, people can identify their age with a number or multiple numbers. No math is required until you say that person will be 55 years old in 2021. What year was he/she born? 55 - 2021 = 1966. Now large numbers are being used together as a system to answer a specific question.
Carl Sagan Knew it Too
I know you're impressed with my math skills, but what does Fibonacci have to do with the magic of life? Hang in there, and I'll reveal that to you soon.
Math is everywhere, and it is the universal language we can all agree on.
Carl Sagan knew this very well when he put together a record that contained a collection of artifacts and attached it to Voyager One in 1977. He curated the record selections of sounds and music from Earth as well as greetings in 55 languages. But the disk also contains encoded photos seeking to teach aliens the mathematics and or the measurements — needed to understand the human race and their place in the universe.
That is why Fibonacci is so important in our lives. His math is indeed universal and can act as a primer for other civilizations to communicate with us on our level of understanding.
If You Look, You Will See
Applications of Fibonacci numbers are everywhere and include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems.
Fibonacci numbers also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, and an uncurling fern. See the photo below for the perfect or identical progression of the fern leaf. Start with #1 and look at #2 to see the leaf and go to #4 to see the leaf's leaf. And if we take a microscope you'll see it again and again.
In this paragraph, I will need you, the reader, to take the knowledge you have regarding the sequence of numbers (F) and show you the magic they contain. To do this, I will teach you about the Golden Ratio (hereto known as the symbol φ), and how it fits in with Fibonacci's mathematics?
Remember the Golden Ratio
The Golden ratio, also known as the golden section, golden mean, or divine proportion, is the definitive proof that the Universe has a blueprint for life. Simply put, φ is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment. I will give you examples of this math later in the article to make it easier to understand. But suffice to say, it describes predictable patterns for everything from atoms to stars in the sky based on the ratio of 1.618 (φ). It is derived from the Fibonacci Sequence (see chart below). These two terms are often used interchangeably to describe the same idea regarding nature and how it maintains balance or symmetry in its infinite design.
Certainly, each of these math equations will work independently of each other, but we need to tie these two theories together to help you see what is possible. Remember Fibonacci gave us successive numbers starting with 0 and 1, each new number in the sequence is simply the sum of the two before it. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377... The following are examples of successive pairs: 1+2=3, 2+3=5, and 5+8=13, and so on.
The Golden Ratio is φ
The Golden Ratio is 1.618 (φ), and if you divide each successive pair of numbers in the sequence like the larger number 5 divided by smaller number 3, you get 1.666…, and 8, divided by 5, you get 1.60., A perfect or Godlike or Golden ratio or balance has now been proven.
Did You Know You Were Perfect?
Here comes the beautiful or magical part. Take the human body, for example, if you divide the length from your head to toe by the length from your bellybutton to toe, you will find the answer tending to φ or 1.6. You can repeat this test by dividing the length from the top of the head to the shoulder and then the length from the top of the head to your chin. You will get φ again!
Why do We Love Flowers So Much?
Now let's look at nature. A sunflower grows in opposing spirals, the ratio of its rotation’s diameter to the next is 1.618. φ again!
The ratio between the margin of a leaf to its veins(some plants) also gives φ.
The ratio between the margin of a leaf to its veins(some plants) also gives φ.
We can look to subatomic structures of human DNA and get the same φ. If you look at a cross-sectional view from the top of the DNA double helix forms a decagon. A decagon is two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon. The ratio of the diagonal of a pentagon to its side is φ to 1.
The Universe is Perfect Too
Now let's move our focus from the Micro to the Macro and investigate or solar system. If we take into account the average of the mean orbital distances of each successive planet as it relates to the one before it, it tends to equal φ. This also works with the planets themselves. If you look at the rings of Saturn, you see that there is a ring that is quite a bit denser than the other ring's surrounding it. Miraculously this inner ring exhibits the same golden section proportion as the brighter outer ring i.e. φ
Even the most cynical among us can not dispute that life all around us is always in order and perfectly in balance. In theory, this should remind us that we are in order and balance too. Nothing is wrong. From our DNA to our bodies and out to the far reaches of space, we are all in alignment. I gave you the math so that you could see for yourself that all is good and precise. What you do with this information is up to you, but the one thing you can't do is forget that it exists. Fibonacci had no intention of showing us the perfection of ourselves and the universe, but that is exactly what he did. I'd say that was φ!
