Sacred geometry

Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temples, mosques, religious monuments, altars, tabernacles; as well as for sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art. In sacred geometry, symbolic and sacred meanings are ascribed to certain geometric shapes and certain geometric proportions, according to Paul Calter:

In the ancient world certain numbers had symbolic meaning, aside from their ordinary use for counting or calculating ... plane figures, the polygons, triangles, squares, hexagons, and so forth, were related to the numbers (three and the triangle, for example), were thought of in a similar way, and in fact, carried even more emotional value than the numbers themselves, because they were visual.

As worldview and cosmology

The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). In modern times the mathematician Carl Friedrich Gauss adapted this quote, saying "God arithmetizes."

At least as late as Johannes Kepler (1571–1630), a belief in the geometric underpinnings of the cosmos persisted among scientists. See also Kepler conjecture, Mysterium Cosmographicum, Pythagoreanism

Closeup of inner section of the Kepler's Platonic solid model of planetary spacing in the Solar system from Mysterium Cosmographicum (1596).

Natural forms

The study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. Many forms observed in nature can be related to geometry, 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. These phenomena can be explained through natural principles.

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  Sunflower

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  Passion Flower

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  Fractals in a Romanesco broccoli

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  Snowflake

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  Hexagon in a Snowflake

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  Cutaway of a Chambered Nautilus

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  North polar hexagonal cloud feature in saturn

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  Naturally formed basalt columns

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  Bee Honeycomb

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  A low pressure area shows an approximately logarithmic spiral pattern

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  The arms of spiral galaxies often have the shape of a logarithmic spiral, here the Whirlpool Galaxy

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.

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

Fringe theory

As is pointed out by Stephen Skinner in his book Sacred geometry: deciphering the code, it is possible to place a geometric diagram over virtually any image of a natural object or human created structure, and find some lines intersecting the image. If the geometric diagram does not intersect major physical points in the image, the result is what Skinner calls "unanchored geometry." Unanchored geometry, and speculation about the meaning of the geometry itself unsupported by any reliable sources, frequently leads the subject of sacred geometry into the area of New Age fringe theory.

Music

Pythagoras is often crediting for discovering that an oscillating string stopped halfway along its length produces an octave relative to the string's fundamental, while a ratio of 2:3 produces a perfect fifth and 3:4 produces a perfect fourth. However the Chinese already had instruments that were thousands of years older, such as the Guqin that also feature these tonal scales. Pythagoreans believed that these harmonic ratios gave music powers of healing which could "harmonize" an out-of-balance body^{[citation needed]}. This belief has been revived in modern times.^{[citation needed]}

See also

• Arabesque
• Bindu
• Sri Chakra
• Crop circle
• Bush Barrow
• Ley lines
• Folk mathematics
• Harmony of the spheres
• Proportion (architecture)
• Platonic solids
• Pythagorean tuning
• Golden ratio
• Golden spiral
• Astrological aspects
• Pythagorean symbols
• Sangaku
• Vitruvian Man
• Labyrinth (an Eulerian path, as distinct from a maze)
• Mandala
• Parthenon
• Tree of Life
• Celtic art such as the Book of Kells

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.
• Bromwell, Henry P. H. (2010). Townley, Kevin. ed. Restorations of Masonic Geometry and Symbolry: Being a Dissertation on the Lost Knowledges of the Lodge. Lovers of the Craft. ISBN 0-9713441-5-9. http://www.kevintownley.com/products/books/restoration-of-masonic-geometry-and-symbolry/. Retrieved Jan. 7, 2012. 
• 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.

External links

• Sacred geometry at the Open Directory Project