Sacred Geometries
(This is an excerpt from a University Of Metaphysical Sciences course at www.umsonline.org,
please feel free to visit the school website)
Sacred geometries are resonant structures, harmonic patterns (which may be received by senses and transmitted to the lower-mind for interpretation). Geometric forms which, unless given life, are fixed and static. It is the inherent properties of the golden spiral that compel all sacred geometric forms to implode or transcend. The golden spiral is an inherent component within both angular and spherical geometry. Masculinity is represented by straight lines, femininity by curved lines, their points of meeting being spatial points for mapping the field. The golden spiral is the force creating the vortex-field in sacred geometrical forms through which all harmonic patterns transcend form and move into quantum coherence/fluidity. The sacred aspect of geometry is the relationship between form and vibration.
The most familiar sacred geometrical forms are the platonic solids which physically describe the volumes enclosed by these patterns. A platonic solid may be defined as the surface delineating a fully enclosed volume, all lengths defining any portion of the volume are equal, as are the values of all interior angles defining the corners. Conceptually, each solid may be thought of as a single unit (cell) of form, repeating until it falls back upon itself with adjacent, matching units (cells), each angle formed by the meeting of the units (cells), and the dimensions of each side of the unit (cell) are equal. At present, there are five solids known that meet this criteria (and correlate with the five elements), they are, in order of increasing complexity as defined by the number of faces: Tetrahedron (4), Cube-Hexahedron (6), Octahedron (8), Dodecahedron (12), and Icosahedron.
The term "platonic" is a reference to the scientist and philosopher Plato, who said, "Geometry is the knowledge of the Eternally Existent," and "rhythm and symmetry are everywhere identical with beauty and excellence." Plato was initiated into the ancient mysteries studied at Heliopolis (Greek "City of the Sun"), a great center of scientific and priestly learning in ancient Egypt. Plato's philosophy is best understood by studying Pythagorean sciences: arithmetic, geometry, music theory, and astronomy. Pythagoras was a mathematician. His major contribution was the Golden Ratio, best symbolized by the Golden Rectangle which, when squared, leaves a Golden Rectangle behind with the same unique ratio. It is important to note that Pythagoras gave credit for his knowledge to Hermes, and was a vegetarian. Connecting a curve through the concentric Golden Rectangles generates the Golden Spiral, which is found microcosmically in the DNA strand and macrocosmically in the Milky Way Galaxy.