In the Masonic tradition, Geometry is a central point as we grow and understand more in our journey toward more "Light." But why do we ask for "Light" in our tradition? When you begin searching through information about Ancient Mysteries, Sacred Geometry comes up repeatedly. You begin to realize that Sacred Geometry is a beacon of amazing "light." Here is an explanation from the author, Janoosh:
The term, "Sacred Geometry," is often used to refer to architectural forms and is also applied to those proportions, shapes, and patterns that reoccur regularly in nature. Ancient people of many cultures observed these endless repetitions of the same numerical relationships and assigned a divine significance to Geometry. The ancient Egyptians, Indians, Maya, Celts, and other cultures constructed their buildings and monuments in accordance with the sacred geometric proportions they had observed. The ancient Greeks - Euclid, Plato, and Pythagoras among them - came to the conclusion, since confirmed by scientific study, that Geometry is inherent to the design of the Universe! Geometric secrets have been passed down through the ages by various mystery schools, and now even appear in the enigmatic form of crop circles,
Behind Geometry lurks the mystery of creation. There is no denying that our entire world is shaped according to set geometric values. These mathematical patterns arrange the cells in our body and define the distances between the stars and the planets. They can be recognized in everything - from atoms, stars, and flowers, to human creations and structures. Our very bodies are excellent examples of this universal geometry. Simple examples of sacred geometric shapes are, among other things, the circle, triangle, square, pentagon, and pentagram. Three-dimensional examples include the sphere and the five Platonic solids: the tetrahedron, hexahedron (cube), octahedron, dodecahedron, and icosahedron. Numerical values of significance are "Pi" and the Golden Ratio or Mean, also known as "Phi" ([pronounced "fee"). What follows is a brief discussion of some of these wonders.
Tetrahedron (4 triangular sides) - Fire
Hexahedron (6 square sides) - Earth
Octahedron (8 triangular sides) - Air
Dodecahedron (12 pentagonal sides) - Universe
Icosahedron (20 triangular sides) - Water
The five Platonic solids, so named because of Plato's extensive exploration of their significance, are only solid shapes whose faces are all identical, even-sided polygons. Plato related four of them to the elements of fire, earth, air, and water, with the 12-sided dodecahedron designating the Zodiac, or the Universe. Perhaps it is to be expected that a scientific theory has recently surfaced positing that the Universe is, in fact, in the shape of a dodecahedron! Plato also theorized that atoms have these five shapes. He was not very far from the truth. Atoms are arranged in the shapes of cubes, octahedra, and dodesahedra in crystalline substances. Water molecules [of which the human body is approx. 80%] can arrange themselves in icosahedral clusters [see Dr. Masaru Emoto's work - http://www.masaru-emoto.net/english/e_ome_home.html]. But human understanding of these shapes - predates - Plato! Megalithic stone sculptures of the five Platonic solids, preceding Plato by at least a thousand years, have been unearthed in Scotland.
"Geometry will draw the soul toward truth, and create the spirit of philosophy." - Plato (c. 427-347 B.C.E.)
The Golden Ratio
The Golden Ratio, or Mean, also called "Phi," is a mathematical proportion that appears everywhere in nature. Classically known as the "extreme and mean ratio," it is derived by dividing a line into two unequal segments, where the proportion of the whole line to the larger segment is the same as the proportion of the larger segment to the smaller segment [the whole and it's own relation to itself in a larger relationship of 3]. This ratio is expressed as a decimal, approx. 1.61803. (Like the more familiar "Pi," this irrational number cannot be expressed as a true fraction, and its decimal places seem to extend into Eternity! The decimal places for "Phi" have been calculated to 1.5 billion places, with no discernible pattern to the digits.) Note that where the value of the whole line is 1, the larger segment is approx. 0.61803. These two numbers are sometimes called the "Golden Section numbers," and have all manner of fascinating mathematical interrelationships that go beyond the scope of this discussion. A basic geometric example of the omnipresence of "Phi" is the simple five-pointed star [a Masonic symbol], made by connecting the points of a Pentagon, which consists of five lines, each intersected line dividing into the - Golden Ratio.
Since ancient times this ratio, 1:0:618..., has been regarded as the ultimate proportion of perfection, harmony, and even Divinity. We find the Golden Ratio in the Egyptian Pyramids, Leonardo da Vinci's "The Last Supper," the Notre Dame Cathedral in Paris, the Parthenon in Athens, and even the structure of musical pieces by Mozart [a Mason] and Beethoven. In nature, the Golden Ratio occurs with great regularity. The chambered nautilus shell is the most famous example. Its spiral is constructed according to the Golden Ratio, as many other spirals that appear in nature. Our body, face, heartbeat, and even our handwriting express this proportion. It is observable all the way down to the cellular level. Even the fluctuations of the stock exchange have been shown to express the Golden Ratio. It should come as no surprise that "Phi" frequently appears in crop circles, and thus in the images in Sacred Geometry.
"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel." - Johannes Kepler (1571-1630 C.E.)