In this video, I'm going to explore the relationship between a square and the golden ratio. The key to unlocking the golden ratio from the square is to bisect one of the edges, I'll bisect CD, and that creates this new point E. Now I'm going to draw a circle centered at E, and the radius is going to go up here to A or B. That actually is enough to encode the golden ratio. We just need to know how to unlock it. The way you do that is by extending CD. We have a new point over here F. This actually creates a golden ratio right here.

So that the whole segment CF is to CD and CD is to d f. We can take this further and create a golden rectangle By making a parallel line to BD through F, and a parallel line to c f through B, that creates a new point over here, G. And that also encodes a new Golden Ratio right up here. This is a golden rectangle. So rectangle a GCF is a golden rectangle, which has the proportions of one to five. It turns out this rectangle, b, g, d f, is also a golden rectangle. It has the same proportion, although it's smaller and turned in 90 degrees. And similarly, over here, we have another golden rectangle that we can sketch in.

So you see the square encodes three golden rectangles right off the bat. actually four, if you think about HB ID, a GCF, and then the other two smaller golden rectangles on the sides. And you can look at this diagram and realize that it's only half of the story. So if I draw another square and extend the lines, we have additional golden rectangles down here and here. And of course, two more going across the other way. So the square is very intimately connected with the golden ratio through this circle that has a radius like that.

Going from the midpoint of one of the edges of the original square to the opposite corner.