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## Sacred Geometry

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**What is Sacred Geometry?**• Sacred Geometry – religious, philosophical, and spiritual beliefs that have surrounded geometry in various cultures throughout history • www.arthistory.sbc.edu/sacredplaces**The Medicine Wheel**• The medicine wheel was an ancient way of creating sacred space and calling forth the healing energies of nature. • It is used for teaching, meditation, prayer, healing, and celebration. • From stories associated with the quadrants of the medicine wheel, Native Americans have taught about their relationship with Nature and the Spirit World, the cycles of life, connection to their past, and the interconnectedness of all things.**The Medicine Wheel**• The circle has been very sacred to the Lakota people, as it represents unity. • The medicine wheel particularly represents unity in all of existence. It contains the four directions, the four seasons, the four stages of life, etc., which are separate but united in the wheel. Literature sources: Black Elk Speaks**Star Quilts**• Star quilts (or wicahpi sina) hold several symbolic representations of life, spirituality, honor, and community for the Lakota. • Eight rhombus pieces are placed with the smaller angle rotated about a central point to form the initial star pattern. From that central star, quilters add other rhombi outward to form a larger eight-pointed star. • The 8-pointed star is known as the “Northern Star.” • Star quilts are a great example of geometry actually informing an important cultural element.**Christian Elements of Sacred Geometry**The Cross Gothic Cathedrals The Rose Window**The Cross**The cross is used as the major emblem for the Christian religion. In geometrical terms the cross, elaborated in the Medieval period, is the form of an unfolded cube.**Gothic Cathedrals**• Use proportions derived from the geometry inherent in the cube or the double-cube. • Windows are the source of intricate geometry.**Tracery**• Tracery is the stonework elements that support the glass in a Gothic window • It is exclusively constructed from circular arcs and straight line segments.**The Rose Window**• The theme of the window is geometry. • Regular n-gons are shown. • Variations of the pentagon show the pentagram and rose.**Ancient Greeks**The Golden Ratio**The Golden Ratio aka ϕ**• ϕ~ 1.6180339887 • Two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one.**ϕ**• A number often encountered when taking the ratios of distances in simple geometric figures such as the rectangle, pentagon, pentagram, decagon and dodecahedron.**Why should I give a ϕ?**• It is EVERYWHERE • The Pyramids (a wonder of the world) • Anatomy • Architecture • Parthenon**Suggested Reading**• The Golden Ratio: The Story of PHI, the World's Most Astonishing Number - Livio • The Golden Section - Walser • Is God a Mathematician? - Livio**Ancient Egyptians**Polygons**Polygons**• Egyptians were one of the first societies to use polygons in the construction of their buildings. Sagarra, city of the dead**Uses of Polygons**• Rectangles and squares survive dry heat • Efficient use of an area**The Gnomon**• The Egyptians used a device, later named a “gnomon” by the Greeks, to keep the ratio of sides of a polygon the same.**Gods and Royalty**• The god Osiris was given credit for the concept of a ratio-retaining rectangle. • The square was a symbol for kingship.**Suggested Reading**• Architecture and Mathematics in Ancient Egypt -Rossi • The Mathematics of Egypt, Mesopotamia, China, India, and Islam – Katz • Mathematics in the Time of the Pharaohs - Gillings**Hindus**Mandalas**Buildings**• Before the Hindus build any building for religious purposes they construct a square establishing due East and West.**Buildings**• The temples are visualized as mandalas, which is the intersection of a circle and a square.**Buildings**• Square – represents earth and the four cardinal directions • Circle – represents heaven since it has not beginning or end • Mandala – represents meeting of heaven and earth Temple Floor plan contains many mandalas**Suggested Reading**• The Hindu Temple: An Introduction of Its Meaning and Form – Michell • Temples of India: Circles of Stone – Marache • 42 Seasonal Mandalas Coloring Book – Hund