As Above so Below
The Gnomic World is a magical world, a cornucopia of Elementals, bound-ed by Fiveness. The "active ingredient" to produce Phi is the square root of five. Phi and the square root of Two produce the Five Platonic Volumes, which are all that is needed to produce all the crystallographic forms, which in turn govern the shapes of all Atomic, Crystalline, Molecular, and Chemical Bonds, and so forth from there .
The shape and form of Five. Just as the Bell Curve is the Distributive law, Phi is the Proportionate Law. The Bell Curve governs statistical operations in the digital world, and Phi governs proportion in the Geometrical World.
We know Phi as the Golden Section, Golden Mean, Extreme and Mean, Mean and Extremes; "the Lesser Extreme is to the Mean, as the Mean is to the Greater Extreme." It is the only proportionate ratio that can be stated only in terms of itself. It is also a particularly pleasing proportion, which is good because it appears everywhere, in both Nature and Math.
The original gnomon was the upright staff that casts the tangential shadow that marks the length of the hypotenuse, it becomes Gnomic as the self-iterative symbol for all right (Pythagorean) triangles, and it became Gnomon as the caster of the time shadow on all sundials everywhere.
The symbol of this 5 world of both geometry and mathematics is the Pentacle, which is composed of five self-similar Phi relationships, which can be drawn in a single motion.