The Golden Ratio, also known as the Fibonacci Sequence, what is it and why does it seem to be everywhere in our world? Just a simple trip to your backyard can reveal an amazing display of nature, beauty and design. And why is it that so many things in nature are divided into numbers of three, five, eight, thirteen, twenty-one, and with the same proportions of the Golden Ratio, even the design and the proportions of insects such as bees and spiders reveals a hidden code that seems to permeate our world. So I hope you will enjoy this presentation where I hope to share the amazing abundance of the order that is within nature called the Fibonacci Sequence and the Golden Ratio. So what is the Golden Ratio and who is this Fibonacci guy? Well Leonardo Fibonacci was an Italian mathematician who was often credited with this amazing mathematical formula. However, it's recorded that when he was asked where it came from, he replied, it's been around forever, and many believe that it came from the numerical sequences that are found in the breeding of rabbits. But regardless of who discovered it, it is an inherent principle in all of nature. So let's do a little example to further describe what these numbers are and how you can calculate them. I find it's best to simply start with the numbers. Basically, just take the first two numbers in our numeric system. Add those two numbers together to get the sequence. The next number would be one. And then you continue in the succession of adding two numbers, the previous two numbers, one and one equals two, two and one equals three, three and two equals five. And this pattern can continue to infinity. Okay, so what does this mean? It's not just a fun little number game. The hidden beauty and order in the Fibonacci Sequence can be seen when we put it to a visual application. Many are familiar with the typical Nautilus shell or golden spiral. So let's do a little example. All you need really is a piece of paper, something to mark with and a ruler. Basically, make a one inch by one inch square and put a one inch by one inch square adjacent to it. Then we will continue to add squares to the previous squares. Now, right now, I'm just speeding this up and you can see what I'm doing. But it doesn't really start to sink in until we start observing the relationships between the squares. There begins to emerge a pattern, a relationship known as the golden ratio. As artists, we realize that there is a certain inherent beauty in relationships of this nature. We typically call it the rule of thirds. Watch as I highlight certain areas or segments of this Fibonacci sequence example. You'll begin to notice that there is a pattern that continues throughout of the ratio of approximately one third to two thirds. The exact proportion is one to one point six. And the golden spiral that is also found so much in nature can also be drawn within the diagram. So what does this all mean? Why is this pattern everywhere in nature? What does that mean to us as artists? Of course, as artists, we are examiners and interpreters of nature. So it only benefits us to learn the rules of nature and why there is an inherent beauty and order to it. For example, a landscape artist would benefit greatly from learning the rules of how trees grow and how they too exemplify and display the Fibonacci sequence in the order of their branches and the multiplicables of their growth. Not only will it benefit the artist to understand these rules, but recreating them effectively can also increase the chances that our artwork will embody the characteristics of nature that we are also naturally drawn to. So I encourage you to examine and explore these relationships that are found everywhere, not just on earth, but even in the heavens in the way that hurricanes and storms often form. And yes, this pattern can be seen in the very fabric of life. We can even examine this numeric sequence and occurrence on a more personal level within our own bodies. For example, look at the 1 to 1.6 ratio of the human arm. The divisions from the shoulder to the elbow and the elbow to the end of the tips of the finger is a perfect 1 to 1.6 ratio. Breaking it down even further, the divisions from the elbow to the wrist and the wrist to the tips of the fingers is also a perfect 1 to 1.6 ratio. And by now, you've probably guessed it. Yes, this continues on into the hand and even into the fingers. As a matter of fact, the human body is a bountiful display of the Fibonacci sequence ever wonder why your front teeth are larger than the rest or why your ear is shaped in the way that it is. Perhaps it is because the pattern of the Fibonacci sequence is encoded in our very DNA. So I hope I've encouraged you to become students of this grand design and have a childlike enthusiasm in wondering why this code is found in music, in architecture, and of course, in the beautiful artworks of the masters and many amazing artists up to day. So in conclusion, Fibonacci may get the glory for this golden, very special ratio that exists in all of our universe, but truly it points to a grand design. And yes, a grand designer. I hope you enjoyed this special Monet Cafe presentation. Please subscribe, like this video. Feel free to make comments. And as always, happy painting.