This chapter is about the golden ratio, which is sometimes called the Golden section or the divine proportion. And in this video, I'd like to show you how you can derive this geometrically from the vesica viscous form. So let's start by drawing a circle on this horizontal line. And then another circle from the intersection point on the line back to the center. A label these points of intersection A through D. Now I'll draw another circle from A to C. And then I'll draw a line segment from the bottom of the vesica or almond shape up to this intersection point, which I'll label as you enough and that diagonal line cuts the horizontal line at G. And so this point G is the point which cuts the segment BC, precisely at the golden ratio or golden section. I'm going to cover that in this for emphasis.
And then I'll take a screen capture so that I can draw on this. So to understand the golden ratio algebraically that is in terms of ratios. I'll just describe that to you. So the whole is to the larger as the larger is to the smaller a whole SBC. That is to the larger in exactly the same proportion as that larger is to the smaller both of these ratios are equal and You might ask what are they equal to? Well, they're equal to the golden ratio, which is symbolized by the Greek letter phi.
And that's approximately equal to 1.618. I say approximately because this is an irrational number that keeps going on forever. So there are more digits if you'd like to know them. And it goes on forever. So I'll show you as far as I've memorized. I'll go back.
And so far we've made this diagram, but it's a symmetrical. I'll draw another circle from D to B. And then I'll draw in a segment from E up to this point, which I'll label as each. That creates a point of intersection called And that also creates a golden ratio except now the larger and the smaller segments are reversed. So, now BC is to IC as I see is to be i. So, for any given segment that you have, you can divided at two points, two unique points, which form this golden ratio or golden proportion, golden section.
We can also do this in another way, if we draw a circle from C to A and from B to D that creates two additional circles each with the same radii is the other larger circles. Then I can draw in a segment from E right up through the middle and I'd like to label that point j This point k, where the line intersects with the original vesica circles which I'm going to decorate in black. And I'll also decorate this new golden ratio which we now have here. So, this golden ratio the whole j E is to K e as k e is to j k that forms the golden ratio. You can also draw a line down below, Jo label and color and that forms another Golden Ratio. But this time the whole is KL so KL is to ke as ke is to El.
So, now we have these two different ways of seeing how the golden ratio emerges during directly out of this foundation geometry