This is Gareth Manfredgraf with Restore the Planet, and today I'm here to share with you about the Fibonacci sequence and spiral. The Fibonacci sequence is a series of numbers that go from 1 to 1 to 2 to 3 to 5 to 8 and then to 13 and 21, and on and on. In fact, it will continue like that forever. You might wonder, is this some sort of arcane mathematics that doesn't make any sense? Absolutely not. This number sequence is very easy to understand. You simply add back the last two numbers. For example, we start with 1, the smallest total unit that we can have. There's nothing before 1, so we simply have to duplicate it. So we get another 1, but the next time we perform this process, we get 1 and 1, which makes 2. To perform this process again, you'll have to add 2 and 1 to produce 3, then 2 and 3 to produce 5, then 3 and 5 to make 8 and 8 and 5 to make 13. And so on, unto infinity, nature uses this extraordinarily simple number sequence to construct so many of her forms. Everything from galaxies to sunflowers, and now I'm going to show you how this number sequence translates into actual physical geometry. If you're just starting out, it's best to begin with a surface like graph paper, meaning that it's easiest if you draw on something that has evenly and symmetrically placed square units of measurement that are all of the same size. To make it simple, we'll have one of these units represent 1, and we'll trace it out in red. Then we need another 1 unit, so we'll draw that one next to the first one. Then on the top, or in this case the bottom, we can draw a line connecting both of the 2 squares that we made. We can then duplicate that line 3 more times and produce a perfect square. Then we can duplicate that process as many times as we like, or as many times as the canvas that we're using will allow. You can see the 5 square is 5 units by 5 units, the 8 square is 8 units by 8 units, and so on. Now I'm going to show you how to add the more feminine curving lines. There are various ways that I've seen different artists do this, but I'm going to show you the method that I like the best because I feel that it most closely matches nature. This method allows you to use circles to construct the spiral. To begin with, draw a perfect cross whose every arm is the exact length of the square that you're working in. The center of this cross should be placed furthest from where the spiral will end up being. Now all you've got to do is draw a perfect circle, which by virtue of its size and positioning is cut into 4 equal pieces by the cross. This means that the square that you're working on should take up one quarter of the circle that you're using to produce a spiral within it. Now all we've got to do is erase the other 3 quarters that we don't need, but in this case either side is the same so we can simply add back in one quarter. Now all we've got to do is repeat this process again and again until all of the zero curvature scaffolding for a Fibonacci spiral is filled. And as you can see in its completed form it very closely matches the twisting motions of a galaxy. Thanks so much for watching and wanting to understand our universe. Have by far the absolute best day ever!