Sacred Geometry
The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, cosmology. This value system is seen as widespread even in prehistory, a cultural universal of the human condition.
It is considered foundational to building sacred structures such as temples, mosques, megaliths, monuments and churches; sacred spaces such as altars, temenoi and tabernacles; meeting places such as sacred groves, village greens and holy wells and the creation of religious art, iconography and using "divine" proportions. Alternatively, sacred geometry based arts may be ephemeral, such as visualization, sandpainting and medicine wheels.
As worldview
Sacred geometry may be understood as a worldview of pattern recognition, a complex system of religious symbols and structures involving space, time and form.
According to this view the basic patterns of existence are perceived as sacred. By studying the nature of these patterns, forms and relationships and their connections, insight may be gained into the mysteries – the laws and lore of the Universe.
Music
The discovery of the relationship of geometry and mathematics to music within the Classical Period is attributed to Pythagoras, who found that a string stopped halfway along its length produced an octave, while a ratio of 3/2 produced a fifth interval and 4/3 produced a fourth.
Hans Jenny, a physician who pioneered the study of geometric figures formed by wave interactions and named that study cymatics, is often cited in this context. Kepler explored the ratios of the planetary orbits, at first in two dimensions (having spotted that the ratio of the orbits of Jupiter and Saturn approximate to the in-circle and out-circle of an equilateral triangle).
When this did not give him a neat enough outcome, he tried using the Platonic solids. In fact, planetary orbits can be related using two-dimensional geometric figures, but the figures do not occur in a particularly neat order.
Even in his own lifetime (with less accurate data than we now possess) Kepler could see that the fit of the Platonic solids was imperfect, however, other geometric configurations are possible.
Closeup of inner section of the model
Natural forms
Many forms observed in nature can be related to geometry (for sound reasons of resource optimization). These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms.
But some scientists see such phenomena as the logical outcome of natural principles.
Art and architecture
The golden ratio, geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture. For examples of sacred geometry in art and architecture refer:
Labyrinth (an Eulerian path, as distinct from a maze)
Mandala
Flower of Life
Parthenon
Taijitu (Yin-Yang)
Tree of Life
Rose Window
Celtic art such as the Book of Kells
Yantra
Swastika
Dharmacakra
Vesica piscis
Metatron's Cube
Contemporary usage
Approximate and true golden spirals.
A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science. Pantheon Books New York 1983 ISBN 0-394-54812-8
Johnson, Anthony: Solving Stonehenge, the New Key to an Ancient Enigma.