0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765...

Have you ever seen this progression of numbers? 

Perhaps you have, perhaps you haven't. This is called the Fibonacci Sequence.
It's not too difficult to replicate, either. Each number is the sum of the two preceding numbers, starting with 0 and 1.

What's so special about this famous sequence? When a number of this sequence is divided by the previous Fibonacci number, it results in a number that becomes closer and closer to approximately 1.618 as the sequence continues, without ever actually hitting that precise number. 

Allow me to introduce you to Phi (φ).

Phi is the twenty-first letter of the Greek alphabet, and is used in the Greek numeric system as 500 (φ') and 500,000 (,φ).
For our intents and purposes, Phi (not to be confused with Pi because the pronunciation is similar) is a mathematical symbol used for one plus the square root of five, all over two.
...which equals approximately 1.6180339887. The same number that the Fibonacci Sequence is linked with.

The Golden Ratio. Known to different people sometimes as the golden mean or the golden proportion, Phi is just another name for the famous Golden Ratio.

So, we have a string of numbers and some particularly well-christened letter. What is the significance of it all, and why is it so important?

The Golden Ratio has been inspiration for a lot of the world's music, art, and architecture. You may have heard of the first people to use it, the Egyptians in building the Pyramids. This ratio has been found multiple times in nature, so many times that people have believed this ratio to be one of the building blocks upon which the world was formed. Many artists and musicians have used the Golden ratio in their paintings and compositions.

For example. Did you know that the number of female to male bees have an uneven ratio? After studying their genetics and ancestry, it's been found that the number of female bees divided by the male bees is approximately 1.618 because of the way the generations progress, with some variation.

Leonardo De Vinci has a famous piece of art, called the Ventruvian Man, displaying his knowledge of the human body. Several different proportions of the human body approximate the Golden Ratio. When measured, the distance from one's head to foot, divided by the belly-button to foot approximates Phi, as does a person's base arm (without measuring the hand) divided by the lower arm. The lower arm divided by the hand also follows this. There are many other instances similar to this in the human body that are said to equal the "Divine Proportion".

The shells of mollusks that use chambers also equal the divine proportion- dividing the farthest outside section by the next equals Phi, and this can be done to each section consecutively to the middle. Sunflowers, with their rings of seeds, also exhibit the ratio. Dividing the diameter of one of the seeds on the farthest outside of a sunflower by a seed from the next also equals the proportion.

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Some of these things have been disputed and people argue that the proportions are not perfect enough to be considered widely-known. However, I thought that Phi, the Golden Ratio, and the Fibonacci Sequence are interesting enough, regardless.