I was able to generate two circles (step 1 - as you may discern the 1 and the label 'circle(s)' in the picture); step 2, I made the small square (labelled 'square 2'); step 3, i made the triangle by describing two angles equal using the base of the square to the center of the first circle; step 4, i did the parallel lines; step 5, the hexagon; and, finally, step 6, the ratio of the golden mean by surpassing the hexagon's inferior to include a small hat to cap the structure above.
What do you think that final step also generated?
I kid you not. I can demonstrate it again in person (or, I'll make a powerpoint presentation and post it here where you can watch the steps). I really did make this beautiful geometric structure. And all in one sitting in the crapper. It was G*d's glory I saw and now I'm frightened.
I was quite possibility wrong about generating the pentagon in the above construct. but the other geometric shapes are really there. i've been attempting to derive it but how it would arise naturally is kind of putting up a fight. my apologies.
I just realized the impossibility of generating the right intersections for a regular pentagon using only one compass. One needs at least two compasses (compii?) because the initial point of the pentagon starts outside the center of the circle and finding it requires adjusting to at least one other radius to generate the starting point.