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Sacred geometry is geometry used in the design of sacred architecture and sacred art. The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, and cosmology. This value system has been found even in human prehistory and is considered by some to be a cultural universal of the human condition. Sacred geometry is foundational to the building of 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. Sacred geometry-based arts may also be ephemeral, such as found in sandpainting and medicine wheels.

As worldview

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.

Sacred geometry may be understood as a worldview of pattern recognition and a complex system of religious symbols and structures involving space, time and form. According to this belief, the basic patterns of existence are perceived as sacred. By connecting with these, a person 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.

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.

Cosmology

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

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.

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 scientists generally see such phenomena as the logical outcome of natural principles.

Sunflower
Haxagon in a Snowflake
Cutaway of a Chambered Nautilus
A Spiral Galaxy

A Spiral Galaxy
North polar hexagonal cloud feature in saturn
Naturally formed basalt columns
Bee Honeycomb
A low pressure area shows an approximately logarithmic spiral pattern

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.

Many of the sacred geometry principles of the human body and of ancient architecture have been compiled into the Vitruvian Man drawing by Leonardo Da Vinci, itself based on the much older writings of the roman architect Vitruvius.

Note how all the sacred geometry concepts evolve out of each other. For example, the Flower of Life contains many Vesica Piscis, Metatron's Cube can be overlaid exactly on the Flower of Life, the Vitruvian Man links back to the star tetrahedron that is part of Metatron's Cube, and so on.

For examples of sacred geometry in art and architecture refer:

Labyrinth (an Eulerian path, as distinct from a maze)
Mandala
Parthenon
Tree of Life
Celtic art such as the Book of Kells

Contemporary usage

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.

Among the most prevalent traditional geometric forms ascribed to sacred geometry are the sine wave, the sphere, the vesica piscis, the torus (donut), the 5 platonic solids, the golden spiral, the tesseract (4-dimensional cube), Fractals^[1] and the star tetrahedron (2 oppositely oriented and interpenetrating tetrahedrons) which leads to the merkaba.

Fractals
tesseract
sphere
Wave
Torus
Octahedron
Dodecahedron
Icosahedron

Notes

^ Fractals and Recursive Geometries

External links

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[1] Fractals and Recursive Geometries

[1]

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 {{Refimprove|date=September 2009}}
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 [[File:Pacioli.jpg|thumb|300px|right|[[Luca Pacioli]] teaching Sacred Geometry]]
 '''Sacred geometry''' is [[geometry]] used in the design of [[sacred architecture]] and [[sacred art]]. The basic belief is that geometry and [[math]]ematical ratios, harmonics and proportion are also found in [[music]], [[light]], and [[cosmology]]. This [[value system]] has been found even in human [[prehistory]] and is considered by some to be a [[cultural universal]] of the [[human condition]]. Sacred geometry is foundational to the building of sacred structures such as [[temple]]s, [[mosque]]s, [[megalith]]s, [[monuments]] and [[Church (building)|churches]]; sacred spaces such as [[altar]]s, [[temenos|temenoi]] and [[church tabernacle|tabernacles]]; meeting places such as [[sacred grove]]s, [[village green]]s and [[holy well]]s and the creation of religious art, [[iconography]] and using "divine" proportions. Sacred geometry-based arts may also be ephemeral, such as found in [[sandpainting]] and [[medicine wheel]]s.

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