The wonder of the Fibonacci Sequence
Before I begin, I want to clarify that I am far from a mathematical marvel and this is not a mathematical analysis which will push you into greater depression than math in school ever will. Because this a topic I am passionate about, and don't want to bore you, I decided to present it in the simplest way I can manage.
In 1202, an Italian mathematician called Leonardo Fibonacci published Liber Abaci, or in english: Book of Calculation, in which he first introduced to the world a sequence of numbers, which held incredible meaning. Back then, the sequence posed as a solution to a problem involving the growth of a population of rabbits, but what Sir Fibonacci didn't know was the fact that the later named Fibonacci sequence approaches the golden ratio asymptotically (so defined, that the ratio becomes increasingly exact as a variable approaches a limit, usually infinity).
FIBONACCI SEQUENCE
1 1 2 3 5 8 13 21 34 55 ...
In this sequence, each number is a sum of the previous 2 numbers, which serves as a basis for the creation of the Fibonacci spiral, which is in perfect golden ratio, and will soon blow your mind.
Each number presents a side length of a square. If we draw said squares next to eachother according to the sequence, we may notice that they are connected, that, as in the sequence, the previous two squares form the side of the next square, which is the same length as the number in the sequence.
If we draw an arch through all of the squares, they all connect into a large spiral that continues to infinity.
This spiral should be familiar to all of you, because I'm sure everybody has seen a photograph of spiral stairs. Here comes the fun part. The Fibonacci spiral has in the past gotten the name God's Fingerprint, because of one simple reason; it is everywhere. And by everywhere I mean everywhere. Have you seen a sunflower? Right there. There's more! Seashells, flower petals, pinecones, pineapples, fingers, animal bodies and, most fascinating of all: Hurricanes, DNA molecules and even in outer space - GALAXIES! Really makes you feel small doesn't it?
This, dear readers, is the wonder of the Fibonacci sequence and the Golden Ratio. Artists of all sorts (musicians too) devoted their lives to this; placing, painting everything in their works in the golden ratio, honouring God, for the world is his creation and he had left a piece of himself behind for man to find.
I think a lot about the universe, and am fascinated by how very little we actually know about it. When I first heard about it, I was left speechless, and had to take a moment to myself to really let the realisation hit me. How absolutely incredible is it, that one simple spiral, created from the simplest sequence, is present everywhere? We always hear about certain theories that seem to be accurate, but soon turn out to not be applicable to everything, which consequently makes them lose importance. However, the Fibonacci sequence along with the spiral is applicable to everything, and I must admit, I find it to be the most beautiful thing in the world.
x, Valens
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