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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 visualization, sandpainting and medicine wheels.

[edit] As worldview

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.

[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.

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

[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:

• 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

[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.

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), and the star tetrahedron (2 oppositely oriented and interpenetrating tetrahedrons) which leads to the merkaba.

[edit] See also

• Arabesque
• Bindu
• Sri Chakra
• Crop circle
• Bush Barrow
• Ley lines
• Folk mathematics
• Proportion (architecture)
• Platonic solids
• Pythagorean tuning
• Golden ratio
• Golden spiral
• Astrological aspects
• Pythagorean symbols
• Sangaku

[edit] Further reading

• Lesser, George (1957-64). Gothic cathedrals and sacred geometry. London: A. Tiranti. 
• Beginnings: Geomancy, Builders' Rites and Electional Astrology in the European Tradition by Nigel Pennick
• Sacred Geometry: Symbolism and Purpose in Religious Structures by Nigel Pennick
• The Ancient Science of Geomancy: Living in Harmony with the Earth by Nigel Pennick
• The Sacred Art of Geometry: Temples of the Phoenix by Nigel Pennick
• The Oracle of Geomancy by Nigel Pennick
• The Ancient Science of Geomancy: Man in Harmony with the Earth by Nigel Pennick
• George Bain. Celtic Art: The Methods of Construction. Dover, 1973. ISBN 0-486-22923-8.
• Robert Lawlor. Sacred Geometry: Philosophy and practice (Art and Imagination). Thames & Hudson, 1989 (1st edition 1979, 1980, or 1982). ISBN 0-500-81030-3.
• John Michell. City of Revelation. Abacus, 1972. ISBN 0-349-12320-9.
• Michael S. Schneider. A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science. Harper Paperbacks, 1995. ISBN 0-06-092671-6
• Lucy R Lippard: Overlay: Contemporary Art and the Art of Prehistory. Pantheon Books New York 1983 ISBN 0-394-54812-8
• Johnson, Anthony: Solving Stonehenge, the New Key to an Ancient Enigma. Thames & Hudson 2008 ISBN 978-0-500-05155-9
• Steiner, Rudolf; Catherine Creeger (2001). The Fourth Dimension : Sacred Geometry, Alchemy, and Mathematics. Anthroposophic Press. ISBN 0880104724. 
• Critchlow, Keith (1970). Order In Space: A Design Source Book. New York: Viking. 
• Iamblichus; Robin Waterfield, Keith Critchlow, Translated by Robin Waterfield (1988). The Theology of Arithmetic: On the Mystical, Mathematical and Cosmological Symbolism of the First Ten Numbers. Phanes Press. ISBN 0933999720. 
• Critchlow, Keith (1976). Islamic Patterns: An Analytical and Cosmological Approach. Schocken Books. ISBN 0805236279. 
• The Golden Mean, Parabola magazine, v.16, n.4 (1991)
• West, John Anthony, Inaugural Lines: Sacred geometry at St. John the Divine, Parabola magazine, v.8, n.1, Spring 1983
• Bamford, Christopher, Homage to Pythagoras: Rediscovering Sacred Science, Lindisfarne Press, 1994, ISBN 0-940262-63-0
• A. T. Mann, Sacred Architecture, Element Books, 1993, ISBN 1-843333-55-4.

[edit] External links

• Sacred geometry at the Open Directory Project