The Golden Ratio isn't only constructible from a vesicle discuss. In fact, it's interrelated with lots of different kinds of geometries. So in this video, I'd like to show you how it emerges from an equal lateral triangle. To construct that triangle, I'm going to draw a circle on this vertical line and two additional circles like that. Now I can draw in the equal lateral triangle by connecting these intersection points. To emphasize that, I'm going to change the color of the triangle lines to black and also color in the circumcircle surrounding that in black.

Next, let's bisect each one of the edges. Another way of thinking of that is I've identified the midpoints And now I will connect those midpoints with lines. You can think of this as a kind of recursion within where we have these segments which I could sketch in in black. So we have the triangle within. And now we actually have all we need to construct six golden ratios. I'm going to draw those in in red.

Also, I'll use a thicker line and a thicker.so. The first Golden Ratio I'd like to draw your attention to is right here. Chart label A, B and C. So segment A B is cut at C. And this forms a golden ratio. So a B is to CB CB is to AC Also we have the same type of ratio over here. So CD is to CB as CB is to BD. So we have a corresponding Golden Ratio on the right.

And you guessed it, we have golden ratios going this way. Two of them and this way, bringing the total up to six different golden ratios that emerge directly out of the relationship that a circle has, with its inscribed equal lateral triangle.