Sacred Geometry - Tutorial and interpretations
Sacred geometry isn't really sacred. It is a term that has been given to various geometrical representations of commonly occurring mathematical relationships in nature, and it is these relationships that pervade through music, cosmology, geometry and even physics. Our ancestors had come to observe and learn of these geometrical instances and it has usually been described and defined in terms of spiritual and divine allusions, often influencing decisions such as the construction of holy buildings and interpretation of events. And it was because of this association with nature and the divine that it came to be known as sacred geometry.
You are undoubtedly familiar with certain aspects of sacred geometry, such as the Golden Ratio, Da Vinci's "Proportions of the Human Body", Fibonacci Spiral, Platonic Solids, the Star of David, fractals and of course the Pyramids. Then there are the lesser known facets, such as toroids, numerical representations in the Zodiac, clocks, the Last Supper and even the derivation of the shapes of the Hebrew Alphabets.
It is the recurring nature and pervasiveness of sacred geometrical concepts that they are often associated with spiritualistic principles, such as the creation of the Universe as I shall show you in this article. Such interpretations are understandably the product of personal convictions and depend upon an individual's view of the universe, but exploring this would go beyond the scope of this article. The point is, there is much to explore in this field as it is a natural component of mathematics. The reason that very little analysis has been performed on this is due to the New Age associations that it has now come to be considered an integral part of, although this is an ignorant misconception that many people like to hold.
In this article, I will show you how to create various sacred geometry objects, specifically the vesica piscis, the Egg of Life, the Flower of Life, the Fruit of Life, the Tree of Life and then using these to derive the five Platonic Solids. Along the way, I shall be associating a Universal Creation story along with the initial progression of the geometry, merely to demonstrate how these simple concepts can give rise to spiritual interpretations, although these do not reflect my personal beliefs.
You can do this yourself if you have a compass to draw circles with and a pencil. Or, if you have a graphics software such as Adobe Photoshop or Corel/Jasc Paintshop Pro. I used Adobe Photoshop owing to the fact that I am a programmer and therefore have lost the knowledge of the usage of a pencil.
To begin with, draw a two-dimensional representation of the three spatial axes, X, Y and Z. In actuality, the sacred geometry derivations occur in the three dimensional space. However, for the sake of simplicity, we represent it in two dimensions as that is the form we are most comfortable with.
In the beginning God created the heaven and the earth. And the earth was without form and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light.
The next step is to complete the projection by connecting and completing itself. Every point connected to every other line in the order shown here.
The Spirit of God starts to connect itself, first forming a rectangle.
And then a pyramid at both ends.
And finally all the lines to make an octahedron.
Now that we have the lines connected, we can make a circle from the octahedron by using the middle point as the center of the circle and any of the vertices of the octahedron as a measurement of the radius. Using these two points, we get a very simple circle.
Sphere
The Spirit beings to rotate, and a sphere is formed.
Notice the two red dots in the image. One is at the center, and one is on the circumference of the circle. These two points now serve as the points from which to create a new circle.
Sphere
A new sphere is created, and this is the first day of the Creation or Genesis.
This creates two interlocking spheres, and this is known as the vesica piscis. Notice the thick blue line running from the intersection points of the circle. The intersection points serve as the center point for the next circle to draw, again using the center of the original circle as radius of the new circle. Similarly, we continue until we have drawn six circles (spheres) around the original.
The Second day of Creation
The Third day of Creation
The Fourth day of Creation
The Fifth day of Creation
The Seed of Life
The Sixth day of Creation. On the Seventh day, God rested. (The Seed of Life)
We now continue with another set of rotations, this time using the intersections of the outer circles with each other. If you're observant, you can already see which point will serve as the radius of the new outer circles we're about to draw.
Another rotation creates six new circles.
Now, by erasing some of the lines from the image, we end up with a two dimensional representation of a three dimensional object. Keep in mind that these are all actually three dimensional objects, and the eighth sphere is directly behind the center sphere.
The Egg of Life
Getting back to the previous rotation we just made, if we use the same principle to create one more rotation of circles around it, we end up with a very important figure. The Flower of Life.
The Flower of Life
The Flower of Life is an important aspect of Sacred Geometry and happens to be a mysteriously ubiquitous symbol across almost all cultures and religions. The oldest Flower of Life symbol has been found in the Temple of Osiris at Abydos in Egypt, in intricate detail. Other Flowers of Life have been found at the Golden Temple in India, Hampi and the Temples at Ajanta in India, Islamic mosques in the Middle East, old Roman sites in Turkey, as well as Spain, the Forbidden city in China, Morocco, Lebanon, Peru, Mexico and Austria.
The Flower of Life is usually depicted by taking the seven main circles and completing the 'petals' overlaying them and its traditional significance has been to represent Creation.
Seven main circles of the Flower of Life
Most common depiction of the Flower of Life
Getting back on the Flower of Life, we can now further add to it by drawing circles of half the radius of each circle, within each of the circles highlighted above.
The Fruit of Life
Notice the darkened circles in the image above. The tree of life is periodic, because you can further draw circles within the half-circles in exactly the same manner as before, and this would create Fruits of Life connected to other Fruits of Life.
We now take the Fruit of Life as represented by the darkened circles above and will now derive the Platonic solids from it. Start at one circle's center, and draw a line to the centers of all other circles.
Connecting the cirles
Do the same thing for each of the centers of the circles and you will finally end up with a seemingly complex set of connections. This is known as the Metatron's Cube.
Metatron's Cube
Metatron's Cube is another sacred symbol and is often used to ward off demons, for luck, for protection and also in alchemy. Metatron's cube contains all five of the Platonic solids. The Platonic solids have been known since antiquity although it was the Greeks who studied it in detail. Plato called them the 'perfect solids', as they were the most aesthetically beautiful and and symmetrical. The criteria for a Platonic solid is that all their edges be equal, that there only be on regular polygonal surface with one angle, and that the points all fit on the surface of a sphere. There are exactly five known Platonic solids: the cube, the tetrahedron, the octahedron, the dodecahedron and the icosahedron. By systematically eliminating some of the lines from the Metatron's Cube, you can derive these solids.
The five Platonic solids
Cube, outlined by the solid black lines. A smaller cube inside is outlined in gray.
Interlocked tetrahedrons (star tetrahedron)
Octahedrons, with the bases touching. A smaller pair of the octahedrons outlined in gray.
Icosahedron
Dodecahedron
And with this, we have seen one of the derivations that the Flower of Life and Fruit of Life can lead to, although there are many others, whose significances vary from immensely appealing to the utterly kooky. Among the ones not mentioned so far, is the Tree of Life. For instance, you can recognize the Star of David in the star tetrahedron. The Tree of Life can be derived from the Seed of Life by the placement of smaller circles at specific intersections of the circles. One may recognize this as the Tree of Life of the Kabbalah faith.
Tree of Life
There are several versions of the Tree of Life. I was sent this version, known as the Gates of Light mapped onto the cube and dodecahedron.
Gates of Life
The Gates of Life (Submitted by Big Bytes)
I have only shown you a glimpse of the applications of sacred geometry, and there is definitely much, much more than this. One only needs to find the time to explore this area and this would be possible if the intransigent notions of the associations of sacred geometry were let go of, for they only mark the ignorance of a potentially educated and open mind.
The dodecahedron and icosahedron actually have their "inner" corner points touching the star tetrahedron that fits in a circle that is = 1/Ø x the circle connecting the corners of the outer cube.
