簡單瞭解黃金比例

Hey guys, welcome back to ours4all channel. My name is Anastasia. And today I want to touch base on something that's really cool. So have you ever heard about those artists, myself included, architects, photographers, always chasing the perfect composition to try and present their work in the most pleasing way to the viewer's eye. Well, truth is, artists have been focusing on this for centuries. And a solution was eventually created by a series of mathematicians who figured out a way of life, so to speak. So if you're a beginner artist or you're an art lover who wants to know what's this golden ratio fuss is all about, this video is for you. The golden ratio in itself is 1 to 1.618. The ancient Greek mathematicians were always fascinated by this ratio because it appeared in so many things in life. Today majority think of Fibonacci aka Leonardo of Pisa as the one who gave a sequence of numbers which contribute to the golden ratio. Side note, there's evidence that shows that other mathematicians in India found the sequence centuries before Fibonacci. But Fibonacci is our guy and eventually this sequence was named in his honor. So the sequence begins with 1. Then we add the preceding number, which is 1 as well. And we get the sum of 2. 2 is the next number in the sequence. Now to 2 we add the preceding number 1 and we get a 3. Same thing. To 3 we add the preceding number of 2 and we get a 5. And that's our sequence. That goes on and on following the number of 8, 13, 21, 34, 55, 89, 144 and so on. And the further down the sequence goes, if we take 144 and divide it by 89, we get 1.6179 etc. or 1.618. So that's our magic number. That's our golden ratio. Nearly two centuries later after Fibonacci, Leonardo da Vinci has illustrated a book which was written by a mathematician, Luca Pacioli, where we see the famous Leonardo's painting of the Vitruvian Man. And in that painting we see the golden ratio itself. In a way that's where the name the golden ratio has come to light. So if you think about it, let me explain how it looks like in life on the Vitruvian Man that Leonardo da Vinci has drawn. So if you take your hand, we'll say this is 1. Now if we look at the forearm, the forearm is 1.618 times bigger than the hand. If we look at the humerus, it's the same idea. The humerus is 1, whereas the forearm plus the hand is 1.618 times bigger than the humerus. You basically can see the sequence all over. It's anatomy of the ear. It's in our heartbeat. It's even in the little plants that we have at home. So look at this little plant. So if we look right in the middle, let's start with this guy. So this guy is 1.618 times bigger than the smaller one. And it keeps going and going. If you look at sunflower seeds, it's the same situation. We see this ratio 1 to 1.618 everywhere. Eventually,this ratio also translates into a spiral, which we call the golden spiral. So the golden ratio can also be found in our heartbeat. And in fact,it can be found in music written by Mozart and Bach as well. So it's very,very neat. In fact,our own DNA has the spiral,golden spiral as well. Now let's focus back on visual artists. Here's how this ratio can be broken down. And here are some few tips where you can start as an artist using this ratio or ratios that are similar to it. At first,we start with the golden rectangle. Once we divide this golden rectangle into a square, we now see another golden rectangle, which is smaller. But it's also a golden rectangle, which you can later on divide into another square, yielding a smaller golden rectangle. And it keeps going and going. So that's the premise of it. Now once we have that golden rectangle, and we have the broken down squares and rectangles, we can go ahead and draw the spiral within it. And the spiral shows up in famous pieces of art. For example,this Vermeer's painting of the lady with the pearl earring. The end of the spiral ends in her gaze. And as you can see,the spiral also leads into her eyes. So it's a very powerful painting that we know and love. And we love looking at it. So this golden spiral may explain why. Or if we even look at Mona Lisa, the golden spiral also gets into the pupils of her eyes, focusing our attention on that smile that no one can explain to this day why we love it so much. Or the Michelangelo's famous painting, where the touch comes right into the center of where the division between the square and the new golden rectangle begins. Or of course the Hokusai's great wave. It literally emanates the spiral itself. If you're interested in further mathematical formulas and the exact explanation of how the spiral came to be, my fellow YouTubers are incredible. And there's so much information about the golden spiral over there and the golden ratio. So you can definitely look that up and get a more detailed mathematical explanation. Now,if you're starting out artist, here are a few ways to start building your composition eventually leading into the golden ratio compositions. Just a side note. It's never a rule that you have to use the golden ratio. It's just another tool in your art toolkit that you can pull out and use whenever you see fit. The first thing that you can do as a starting out artist is grab your page and divide it into a tic-tac-toe style. So you go and draw those nine squares and basically where those four points interact, those are your key points that you want to keep on the page. We know this trick as a rule of thirds. A lot of painters and artists use this. It's the easiest way to get your composition going to make the composition look pleasing to the eye. Basically what you're going to focus on is creating your key areas of interest in these four points. In one of those four points, two, three or all of them. Like in this drawing that I have of plumeria flowers. Now,once you've done a few of those compositions using the rule of third, there's another next level step that you can do which is the rule of 5-8. So when you look at the Fibonacci sequence, 5 and 8 both appear in there. When you divide 8 by 5, you get 0.625. Now,0.625 is just a smidge different from 0.618, but it's still good to use. So what you're going to do is you're going to grab your page. You're going to measure out whatever the width is and you're going to multiply it by 0.625. Doing that will create one line. Boom. Once you do that again, you're going to measure out the same number by 0.625 and you're going to draw the next line. Then you're going to measure out the height and you're going to do the same thing. Multiply by 0.625 from the top. It's going to create one line going down this way and the same thing from the bottom. Once you've got those, you see a slightly different definition where the square is slightly closer to each other and the other lines are slightly more vertical or rectangular looking. So that's the rule of 5-8. You can go ahead and place your subjects there or you can play how you divide the page regarding on that. So if you look at Mona Lisa's painting, you can see it right there as well. And of course later on, you can start playing with the spiral and see what you can create there. Now I'm still working towards that end. It's not easy. It's quite tough. But it's definitely something that make your art piece look more appealing to the viewer's eye. But again, it's just a tool in your huge toolkit. So there you have it. There's your golden ratio. I hope this video helped a little bit explain what it is. On that note, thank you so much for watching. Hit like and subscribe. And I'll see you guys soon. Bye.