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About Sacred Geometry

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Europa
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« on: July 04, 2007, 09:23:13 pm »


Sacred geometry can be described as a belief system attributing a religious or cultural value to many of the fundamental forms of space and time. According to this belief system, the basic patterns of existence are perceived as sacred because in contemplating them one is contemplating the origin of all things. By studying the nature of these forms and their relationship to each other one may gain insight into the scientific, philosophical, psychological, aesthetic, and mystical laws of the universe.

The term sacred geometry is also used for geometry which is employed in the design of sacred architecture or art. The underlying belief is that geometry and mathematical ratios discoverable from geometry also underly music, cosmology, and other observable features of the natural universe. This belief was held from ancient times through the Renaissance and influenced the construction of temples and churches and the creation of religious art.
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Europa
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« Reply #1 on: July 04, 2007, 09:26:38 pm »


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« Last Edit: July 04, 2007, 09:34:25 pm by Europa » Report Spam   Logged
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« Reply #2 on: July 04, 2007, 09:32:32 pm »

Music

The discovery of the relationship of geometry and mathematics to music 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 13 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
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« Reply #3 on: July 04, 2007, 09:35:19 pm »



The Parthenon's facade showing an interpretation of golden rectangles in its proportions.
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« Reply #4 on: July 04, 2007, 09:37:27 pm »



Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1596)
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« Reply #5 on: July 04, 2007, 09:39:30 pm »

Cosmology

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 [2]. 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 [3]. However, other geometric configurations are possible.

The connection between geometry, cosmology, astrology, harmonics, and music is said to be through musica universalis (the "music of the spheres")
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« Reply #6 on: July 04, 2007, 09:40:43 pm »

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. Scientists, on the other hand, see such phenomena as the logical outcome of natural principles.

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« Reply #7 on: July 04, 2007, 09:42:07 pm »



Closeup of inner section of the model
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« Reply #8 on: July 04, 2007, 09:45:01 pm »

Art and architecture

The golden ratio, geometric ratios, and geometric figures were often used in the design of Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Examples include:
   Labyrinth (an Eulerian path, as distinct from a maze)
   Mandala
   Parthenon
   Taijitu (Yin-Yang)
   Tree of Life
   Rose Window
   Celtic art such as the Book of Kells
   Yantra
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« Reply #9 on: July 04, 2007, 09:45:46 pm »

Contemporary usage

A contemporary usage of the term sacred geometry describes New Age and occult assertions of a mathematical order to the intrinsic nature of the universe. Scientists see the same geometric and mathematical patterns arise 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).

Believers in sacred geometry also see religious and spiritual significance in crop circles and in ancient architecture, such as the Great Pyramid of Giza and Stonehenge.

Chris Korda, an infamous software engineer and leader of Church of Euthanasia, designed an open-source software named Whorld that visualizes and generates sacred geometry patterns.

The Flower of Life Research organization uses sacred geometry in meditation techniques based on the teachings of New Age author Drunvalo Melchizedek. These teachings focus primarily on the Flower of Life, the Merkabah, and Metatron's Cube as spiritual allegories. Flower of Life facilitator Simon Prone describes sacred geometry as "meditation for the logical side of our brain"[5].

The MERU Foundation focuses on geometric properties of the Hebrew alphabet and geometric metaphors in the Bible based on the writings of Stanley Tenen.

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« Reply #10 on: July 04, 2007, 09:46:58 pm »



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.
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