howto3

Represented in red, you can see in this cut and taped together version the beginning formation of the equiangular spiral that I will compare to the accute angled spiral in the next section. The equiangular spiral is equivalent to the exponential expansion rate of Pythagorean triangles. Thus, the equiangular spiral is equivalent to pi, since pi is equivalent to the exponential expansion rate of Pythagorean triangles.

However, as you can see, the letters along the alignments of green arrows do not all match each other in the cardinal quadrants. There is still one more step of topological transformation to complete before we see the final phase of this model comparing the pi exponential expansion rate with the Fibonnaci rate of expansion.

To complete the final step in creating the phi/pi model in three dimensions, and thus combining the equiangular spiral of the Pythagorean exponential expansion rate with the accute angled expansion rate associated with Fibonnaci's sequence, we only have to fold and paste the model four times, connecting the letters of each increments three green arrows with the same lettered arrows of the increments smaller and larger than it. The result of this is that now the red outlined Pythagorean (or pi) spiral is complemented by the three necessary directions (the green arrows) to form the accute, or triangular, Fibonnaci (or phi) spiral.