The pentagram is actually built on the golden ratio. I'm going to draw a Pentagon. And we'll just straighten that out. And then I'll inscribe a pentagram within it. This edge is in the golden ratio with respect to this edge. I'll just undo a couple of times.

In fact, this segment is cut at the Golden Ratio By this point, and similarly on the other side. So each edge of the pentagram defines two different golden ratios. So that's a total of 10 Golden ratios just from the edges. Of course we can also inscribe a pentagram Within, and it would code encode another 10 different golden ratios, such as this one, and the one on the other side. You can even draw circles connecting these dots. And that defines new points which can be used to create additional pentagrams.

I'll just erase the circles now. And so these additional pentagrams March outward along the arms. So for example, I could draw in these circles, and then draw in another pentagram over here. And then I'll erase these circles. And you get the idea that we could make ever smaller pentagrams reaching out along that arm, and of course, each pentagram is another temple to the golden ratio in a sense The Pentagon and the pentagrams within are just replete with golden ratios more than any other form. The pentagram is a study in the golden ratio