Sacred geometry

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Sacred geometry is the study and use of certain geometric forms, patterns and ratios which are considered sacred or divine, being symbols of archetypal perfection in an imperfect world, and sometimes being representative of "secret knowledge" which can be elucidated only through studying such geometry. In more secular terms, humans may exhibit common psychological responses to certain geometric forms, and sacred geometry studies and exploits these responses (as do the designers of corporate logos and advertising).

Sacred geometry is used in the design of sacred architecture and sacred art, but the same principles, including mathematical ratios, harmonics and proportion, are also found in music, and some extend them further to light and cosmology.

The value system of sacred geometry 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.

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[edit] 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 connecting with these, a believer contemplates the Mysterium Magnum, and the Great Design. 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.

[edit] 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. Pythagoreans believed that this gave music powers of healing, as it could "harmonize" the out-of-balance body, and this belief has been revived in modern times[1]. 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. However, Dr. Jenny did not make healing claims for his work.

Even though Hans Jenny did pioneer cymatics in modern times, the study of geometric relationships to wave interaction (sound) obviously has much older roots (Pythagoras). A work that shows ancient peoples understanding of sacred geometry can be found in Scotland. In the Rosslyn Chapel, Tomas J. Mitchell has found what he calls "frozen music". Apparently, there are 213 cubes with different symbols that are believed to have musical significance. After 27 years of study and research, Mitchell has found the correct pitches and tonality that matches each symbol on each cube, revealing harmonic and melodic progressions. He has fully discovered the "frozen music", which he has named the Rosslyn Motet, and is set to have it performed in the chapel on May 18th, 2007, and June 1st, 2007.

Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596)
Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596)

[edit] Cosmology

See also Kepler conjecture, Mysterium Cosmographicum, Pythagoreanism

At least as late as Johannes Kepler (1571-1630), a belief in the geometric underpinnings of the cosmos persisted among scientists. 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
Closeup of inner section of the model

[edit] Natural forms

Many forms observed in nature can be related to geometry (for sound reasons of resource optimization). For example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. 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.

[edit] 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. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of mandala and yantra. For examples of sacred geometry in art and architecture refer:

[edit] Contemporary usage

Approximate and true golden spirals. The green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a Golden Spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio.
Approximate and true golden spirals. The green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a Golden Spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio.

A contemporary usage of the term sacred geometry describes assertions of a mathematical order to the intrinsic nature of the universe. Scientists see the same geometric and mathematical patterns as arising directly from natural principles.

Some of the most prevalent traditional geometric forms ascribed to sacred geometry include the sine wave, the sphere, the vesica piscis, the 5 platonic solids, the torus (donut), the golden spiral, the tesseract (4-dimensional cube), and the merkaba (2 oppositely oriented and interpenetrating tetrahedrons).

[edit] See also

[edit] Further reading

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