Now we move on to the golden ratio, and I find that this is the one, people love to hate on this on the internet, but I think it's really tremendously valuable, and I think a lot of the reasons that people like to jump on over is because they don't quite get that it's very wide-ranging in its ability to be applied. So classic thinkers, from Plato to Pythagoras to Kepler believed that geometry is a powerful underpinning of the cosmos, and Plato supposedly even said, "God geometrizes continually." Da Vinci had an obsession with proportions, which we're gonna take a look at in a couple of minutes. He would create large areas of his work around the exact proportions of the golden ratio. It's also called the golden mean by some people. So did Salvador Dali, if you ever go to the Dali Museum in Florida, it's actually, the building is built around the golden ratio. There's a giant spiral in the middle, and there's a spiral staircase built around the golden ratio, and it says so on the buildin...
g. It was so fundamental to his work, and a lot of artists have used it over time, but it's a little bit complex, so we're gonna break it down. The right version is kind of a golden ratio, golden rectangle version, and the left is your golden spiral, but they're the same general concept. So what it does is it describes an aesthetically pleasing proportion where the largest shape is divided by a perfect square, and the resulting rectangle is in exact proportion to the original one, and this goes all the way down the drain. I'm gonna show you a graphic on this is just second. You can show this as a spiral, because you're basically just connecting the dots of the shape. Now, the ratio/rectangle works really well as an alternative to the rule of thirds. So we're not actually gonna dig into it really at all, because it's the same stuff as the rule of thirds. You use it flat, you can use it to organize facial features, it's the same things, it's just the lines are spaced slightly differently. But we are gonna dig into the spiral, because the spiral is a bit more unique in terms of how we look at it in relation to all of the other compositional devices, because it is a fantastic way to show depth and to organize depth. It doesn't have to be, you can use it very flat, but it's great for depth, meaning, establishing a foreground, a midground, and a background, or a foreground and background, but it's really, really quite effective. And so this is what they look like. Basically, if we take a look at this right slide over here, we have the rectangle, we divide a perfect square, and then the resulting rectangle is the exact proportion to the original rectangle, and then we divide another square, and we have the proportion, and another square, another square, another square, another, and basically, that's your down the drain. And so the spiral starts in one corner, and it draws your eye completely through the image. And it can be up, down, left, right, mirrored, both ways, it works in a lot of different varieties. But you'll kinda see how this line corresponds to this line, and if we were to flip the thing, you'd have a line here, and this line corresponds to this line, and again, if we were to flip it, that's basically where it comes from. 'Kay? This is also based off, like, a good way to illustrate, not based off of, it's a good way to illustrate this, is the Fibonacci sequence where the previous two numbers are, you add the previous two numbers to get the next number, and so forth, and so on. It's basically this, right? It's how we illustrate that concept. There is a lot of math behind this. I'm not gonna get into it too, too much, but basically, the math creates this number called phi, P-H-I, which is kinda similar to pi in that it just keeps going. We round phi to 1.618, and basically, what that means is after you do all this formulaic math, since the square is a one-to-one, right, one and one, if this means one, then this is 1.618. That's actually what the numbers behind this is all trying to get across. But that's not necessarily here or there, that's just where it comes from. Now, we're gonna talk about the spiral. And so, as we said, when a curve is drawn along the outer edge of the perfect square's intersection, we get the spiral, which is a different way to illustrate the golden ratio. Now, take a look and see if you can spot how the eye is drawn through the image. So we can hopefully see it first, the image is kinda drawn in, separated into two halves. You have the music studio on the left and the subject on the right. Now, if you actually, because our eye is drawn to areas of contrast and brightness, we actually see this contrasty reflection in the top left-hand corner, right? And so our eye is drawn there, but because it's a little bit fainter than this, we know that this is the subject. But still, our eye can be drawn around there. So we start up here, and we have this little, the speaker. We're drawn to the shiny bit of the bag. We come around, hits here, comes back around, and it ends here, and it looks like this, okay? And again, it's not necessarily about doing this stuff consciously, sometimes it's about doing it innately, but sometimes it is conscious. This is a stairway at the Vatican. 'Kay, again, guides, doesn't have to adhere to it completely, but it does follow the general flow. One of my favorite ways to really explain this, 'cause I find that people have the most trouble with the golden spiral, more than anything else. It's just very difficult for people to find it beyond something that seems very literal, and I think one of the strongest, most effective ways to explain it, is in an over-the-shoulder shot, which we are very familiar with in TV and film. We see this all the time. This is not my photo. This is an amazing stock photo. But anyway, so spiral, right? Large object, our eye is drawn to it, but it's out of focus, so we know it's not the point of the image. But you'll actually see, goes up here, follows around to the shoulder, comes back around, and ends up on our face. And even if it's not following this exact thing to a T, the idea is still there, and we're establishing foreground, midground, background. 'Kay? This is The Inspiration of Saint Matthew by Caravaggio, it's one of my favorite paintings. You can see the inspiration of the spiral within this composition. This is The Sacrament of the Last Supper by Salvador Dali, which is an amazing example of the spiral. He was very, very precise with his use of this stuff. The golden ratio is not limited to rectangles and squares, it works on triangles, pyramids, other geometric forms, like the pyramids of Egypt, Stonehenge, Angkor Wat in Cambodia, the Parthenon, Notre-Dame, Mona Lisa, all feature the golden ratio or the golden mean in some capacity. I encourage you to go look it up and find examples of this, they are everywhere. The ratio is found in proportions of the human body, it's found in seashells, it's found in hurricanes. They discovered this a very long time ago and implemented it into art and architecture for thousands of years. So take a look at Da Vinci's Vitruvian Man, right? Vitruvian Man on the left, Mona Lisa's face on the right. The belly button, right, divides the lower half from the top half, we can also see the ratio of movement, how it affects movement, how it shapes the movement. On the Mona Lisa, center of the face, eyes, nose, mouth, and then when you layer this on top, you can actually see, again, the shape the other way. On the Vitruvian Man, divides him right at the arms, right across the chest, again, right at the belly button again. And the Mona Lisa, middle of the nose, center of the face, eyes, mouth. These proportions are everywhere. Parthenon, right? I have drawn in the roof. But. Uses the ratio to subdivide, and actually goes even further, like, you can break it apart by columns and everything else. But you've got the big line here. You've got the roof line, and the roof. It's very, very cool. This is the one that takes the most time and practice to really see, but as soon as it clicks, you're just like, "Ah." Clears up everything.