That's all Euclid did. Buckminster Fuller, too. Start with a circle, move the compass point to a point on the circle, draw an arc that intersects the circle again. Move the point to one of those intersections. Keep doing that until you've divided the circle into six segments. Keep doing things like that and the relationships inherent in geometry is exposed itself to the careful eye. And those ratios, and constants, and designs are comfortable to our minds because they are all around us. The beauty of the Archemedes Spiral, or the Golden Mean, is nothing magical, it appears all the time in nature. Fractals occur in nature, but have only recently been understood, largely because computers can do all the tesselations and geometric operations on a massive scale, but we have always seen them and found them compelling.

My point is: there is no mystery there beyond the elegance of geometry itself. The makers don't have to be all that brilliant. Give a bunch of tenth-graders the simple tools of geometric construction (that the Egyptians used to build their pyramids, Romans their aquaducts....) and a big canvas to play on, and I'll bet they can create designs that produce the relations the article describes. Inscribing circles inside and outside of a triangle! Who could have possibly thought of that? Oh, wait, when I draw a triangle in AutoCad, I'm given the choice: is the triangle inside or outside a circle of a given radius?

Euclid started with the simple shapes and built a science. He focused mainly on squares and circles. Bucky started with triangles and created a whole new branch of that science just by playing with triangles, dividing them, re-arranging them, seeing what they could do. Both of them saw the beauty of geometry and what it reveals about the universe we inhabit. But those relationships were there before these people described them. Bucky was adamant about this: all of his inventions were discoveries hidden in nature itself.

I've been encouraging you to think more about how one could create the designs using simple geometric relationships. I believe it would help your investigations. I'm sure you've taken a straight edge, a compass, and a good sharp pencil and used them to recreate the designs you've seen on a piece of paper. That should be one of the first things done in any serious investigation of these art forms. Ask yourself, "how would I make that?". Don't assume it can't be done, figure out how it can be done.

Don't ever underestimate the creative ability of the human brain.

Just my opinion.

(I've some ideas on how to do the wheat in the cone shape, but that will have to wait for a later posting and a couple of small experiments.)