Geomancers are interested in sacred geometry because it is the study of the way that spirit integrates into matter  by echoing and amplifying the geometry of nature and planetary movements, we help to align the resonance of body/mind/spirit with the harmonic frequencies of the above and the below. Spaces that use sacred geometrical ratios, enable the participant to resonate or vibrate at the appropriate rate that maximizes the possibility of connection to the One. While there are others, when one looks at sacred enclosures globally, there is a prominent group of five mathematical ratios that are found all over the world from India's temples to underground stone chambers in Vermont, and from Stonehenge to the Great Pyramid. These ratios are:

pi  (π)  3.1416∞ : 1  pi is found in any circle. If the diameter is 1, the circumference is 3.1416 (C =πd ).

Square Root of Two  (√2)  1.414∞

Square Root of Three  (√3)  1.732∞

Square Root of Five  (√5)  2.236∞

phi (Ø)  1.618∞ : 1  phi is the Golden Section of the Greeks. It was said to be the first section in which the One became many.
The square represents the physical. The circle represents the spiritual. All sacred geometers have attempted the impossible: to square the circle (create a square who's perimeter is equal to the circumference of a circle.) Even so, we feel the Great Pyramid and the ratio of Earth to the Moon are two examples that are remarkably close.
No study of Sacred Geometry is complete without a disscussion of rational, irrational, and transcendental numbers. These examples come from a human made structure and from Mother Nature Herself.
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