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" In sacred geometry, symbolic and sacred meanings are ascribed to certain geometric shapes and certain geometric proportions....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.....

"Pythagoras was an Ionian Greek philosopher who lived during the time of Buddha, around 570-495 BC. He was born on the island of Samos in the North Agean Sea.....Pythagoras founded Pythagoreanism, a religious movement within which education, science and religion were all perfectly unified. His mystery school, which stood on the southern coast of Italy, was called the Pythagorean Italic School..... his esoteric teachings were kept a profound secret.....The discovery of the Golden Ratio, which appears frequently in geometry, is attributed to Pythagoras. The ‘division of a line into extreme and mean ratio’....

Pythagoras found that if a triangle had a right angle (90°) ...... and you made a square on each of the three sides, then ...... the biggest square had the exact same area as the other two squares put together!.....It is called "Pythagoras' Theorem" and can be written in one short equation: a2 + b2 = c2"......http://www.mathsisfun.com/pythagoras.html

"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 (c. 80–15 BC) .

"....the shape of the older Dashly 3 building (2300-1700 BCE) ...oasis situated south of the Āmū Daryā (q.v.), on the desert plain of northern Afghanistan, ancient Bactria.... a shape that is fairly unique and a similar shape found in Yantra........The tantric mandala embodies the Yantra as a design of the sanctum at Mr. Meru in Shambhala....." ...http://www.heritageinstitute.com/zoroastrianism/balkh/dashly.htm

"....in the Kalachakra mandala (a painting on cloth or sand mandala representing the concentric strata of the palace of the meditational deities at the heart of Mount Meru), the Cosmic (or wind tracks) mandala of interlocking circles which represents the paths of the heavenly bodies...."....http://web.ccsu.edu/astronomy/tibetan_cosmological_models.htm

"At the centre of the land of Tagzig (called Shambhala in the Kalachakra) was Olmo Lungring which had at its centre, Yungdrung Gutsek, a four-sided mountain similar to Mount Meru / Sumeru (see above). The mountain is surrounded by temples, cities and parks. To the mountain's south is the Barpo Sogye palace, where Tonpa Shenrab was born. The complex of palaces, rivers and parks with Mount Yungdrung Gutseg in the centre constitutes the inner region (Nang-gling) of Olmo Lungring. The intermediate region (Bar-gling) consists of twelve cities, four of which lie in the four cardinal directions. The third region includes the outer land (mTha'-gling). These three regions are encircled by snow-capped mountains and an ocean.".....http://www.heritageinstitute.com/zoroastrianism/aryans/location.htm

AVESTAN GEOGRAPHY....."The first stumbling-block in the study of Avestan geography is the mixture of mythical and historical elements."......http://www.iranicaonline.org/articles/avestan-geography

"It was Baudhāyana who discovered the Pythagoras theorem. Baudhāyana listed Pythagoras theorem in his book called Baudhāyana Śulbasûtra (c.800 BC). Incidentally, Baudhāyana Śulbasûtra is also one of the oldest books on advanced Mathematics. The actual shloka (verse) in Baudhāyana Śulbasûtra that describes Pythagoras theorem....Baudhāyana used a rope as an example in the above shloka which can be translated as – A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together."....http://mysteriesexplored.wordpress.com/2011/08/31/baudhayana-pythagoras-theorem-world-guru-of-mathematics-part-8/

"Vitruvius (c. 80–15 BC) is often credited as father of architectural acoustics for describing technique of echeas placement in theaters....Vitruvius worked a basilica completed in 19 BC.It was built at Fanum Fortunae, now the modern town of Fano. The Basilica di Fano has disappeared so completely that its very site is a matter of conjecture, although various attempts have been made to visualise it. The early Christian practice of converting Roman basilica (public buildings) into cathedrals implies the basilica may be incorporated into the cathedral located in Fano.".....http://en.wikipedia.org/wiki/Vitruvius

Pythagoras ( c. 570 BC – 495 BC) is often credited 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 culture already featured the same mathematical positions on the Guqin and the tone holes in flutes, so Pythagoras was not the first. Pythagoreans believed that these harmonic ratios gave music powers of healing which could "harmonize" an out-of-balance body.....

"The guqin is a plucked seven-string Chinese musical instrument of the zither family....associated with the ancient Chinese philosopher Confucius. It is sometimes referred to by the Chinese as "the father of Chinese music" or "the instrument of the sages".....http://en.wikipedia.org/wiki/Guqin

"..... the lunar mansions are used in the Kālacakra system as the means of describing longitude. For this purpose the mansions are numbered 0 (Aśvinī) to 26. They are also each subdivided into 60 nāḍī (chu tshod), each of which can be further subdivided into 60 pala (chu srang). Each of these units are further subdivided into six breaths. Further subdivisions are also used, but we can ignore these....This notation is commonly used in western representation of ancient Babylonian mathematics, where the use of base-60, or sexagesimal, arithmetic originated."....http://www.kalacakra.org/calendar/caldesc.htm

"Bonpos cultivate household gods in addition to other deities: Traditionally in Tibet divine presences or deities would be incorporated into the very construction of the house making it in effect a castle (dzongka) against the malevolent forces outside it. The average Tibetan house would have a number of houses or seats (poe-khang) for the male god (pho-lha) that protects the house. Everyday [sic] the man of the house would invoke this god and burn juniper wood and leaves to placate him. In addition the woman of the house would also have a protecting deity (phuk-lha) whose seat could be found within the kitchen usually at the top of the pole that supported the roof."......[http://www.sharpham-trust.org/centre/Tibetan_unit_01.pdf]

"The hogan is a sacred home for the Diné (Navajo) people who practice traditional religion. Every family even if they live most of the time in a newer home -- must have the traditional hogan for ceremonies, and to keep themselves in balance......"......http://navajopeople.org/navajo-hogans.htm

"The Pythagoreans believed that the Universe is composed of four elements – air, fire, water and earth, and that the particles of each of these elements are in the shapes of these four Platonic solids....They also believed that the Earth is surrounded by one solid, which is then surrounded by another solid, and so on....the Earth grid of electro-magnetic lines and vortexes is comprised of smaller grids, each of which is in the shape of a different Platonic solid.....But there is a fifth solid, called the dodecahedron, which has a pentagon on each of its 12 sides. The dodecahedron is by far the most difficult of the solids to construct because the drawing of the pentagon requires an elaborate application of the Theorem of Pythagoras for which he is best known.....But what is most interesting is that the Pythagoreans believed that the element that is in the shape of the dodecahedron is etheric Spirit, the original source of all things that arise in Space and Time. And it is this shape that surrounds Earth and the other four solids combined.".....http://mattovermatter.com/2011/08/pythagoras-sacred-geometry/

"Plasmas, the "4th state of matter", are the dominant form of matter in the universe. As material is heated from solid, to liquid, to gas phase, and then even hotter, it begins to become ionized .... that is, one or more of the electrons on an atom become liberated. A plasma can be described as a collection of ionized particles, which interact collectively by long-range electromagnetic forces associated with their charges and motion.Fortunately for human beings and other living things, plasmas are not routinely encountered on the surface of the Earth."....http://plasma.lanl.gov/

"Pythagoras... the spiritual significance of geometry has been studied for ages, from the ancient Egyptians to the Vedas in early India. These were studied by Pythagoras, who helped immensely in putting sacred geometry "on the map".... Born around 580 BC in Samos, this amazing Greek philosopher, mathematician, and spiritual leader formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy. He founded the Pythagorean brotherhood in Cortona, a mystical school.....He and many of his followers were eventually killed, and his teachings largely destroyed...."...Robert Lawlor, Sacred Geometry: Philosophy and Practice (Thames and Hudson, London, 1982).

Email....okarresearch@gmail.com

John Hopkins.....Northern New Mexico….August 2013

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