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This page is a unique sacred geometry workshop to illustrate the role of geometry in the creation of the spiritual and physical universe. Most authors on this subject differ in their understanding and description of this process. After extensive research and contemplation, this workshop offers a unique perspective to this age-old mystery.|
Tools needed: A drawing compass and a straight edge. You can do this simple experiment on any surface, including a stand up desk or adjustable height desk.
Yes, that's all that's needed for the creation of the cosmos! A drawing compass can be as simple as a piece of string with a sharp pencil on one end and a pin on the other. But a good drawing compass will work much better. A good straight edge can be a ruler, but you won't need the measurements on the side. In geometry, we work with units and ratios. You can make one unit, usually the radius of your circle, represent one inch, one meter or one light year. Please yourself, and forget about metric conversions!
Laws needed: Cosmic and human laws are plentiful, but you will only have to know one main geometric law for this workshop:
Pythagorean Theorem: where "a" and "b" are the two shorter sides of a triangle and "c" is the longer side or the hypotenuse, opposite a right angle (90 degrees). By some simple math, we find that c (un-squared) will be equal to the square root of a plus b i.e.
There are many ways of explaining and studying Sacred Geometry. We trust that on this website, this unique method of integrating the creative power of sound into the unfolding geometric process will be helpful to you. So let's get to the essence of Sacred Geometry by contemplating the creation of the cosmos through geometry, or the Geometry Of Divinity (GOD).
The One God or supreme Spirit, as Wholeness, is represented by the circle.
Looking in more detail, God has a dual aspect, a male/female nature as Alpha and Omega, the Divine Us or Elohim, as hinted at in Genesis 1:26: "Let us make man in our image after our likeness." In the East, Brahman (with an n) has the dual polarity of Brahma and his feminine consort Sarasvati, the creators. They are symbolized by the balanced yin/yang action in the Tai Chi.
How did they create us? In their own image and likeness (Genesis 1:26 as quoted above), and by sounding the "soundless sound" (OM, AUM or the Word, as discussed below). Geometrically, this process is done in two stages. The first is by drawing a second circle of the same radius with it's centre anywhere on the circumference of the first.
This creates what is called the "vesica piscis" (fish-shape in the middle) in the West or "mandorla" (almond shape) in the East. The One point, at the centre of the circle, has now become two points, which create a line between them equal to the radius of each circle. We shall assign a length of 1 unit to that radius line.
This line represents a musical string at rest, which is the same as the straight line on an oscilloscope (like the no-heartbeat straight line on a cardiograph).
The second stage is to draw another radius line from the centre of each circle to the top (or bottom) of the vesica pisces. This creates a perfect equilateral triangle. The line, which had no surface area or "substance" or sound, has now given birth to the triangle of defined area, representing the primordial sound.
This is seen as an oscillation on an oscilloscope, or a heartbeat on a cardiograph, like Elohim breathing life into their creation. This primordial sound is the beginning of the entire creation (the REAL "big bang"!). The ancient wisdom from East and West explain sound as the origin of the creative process of the universe:
"In the beginning was the Word, and the Word was with God, and the Word was God." - Bible: John 1:1
"In the beginning was Brahman with whom was the Word. And the Word was Brahman." - Vedas (Written long before the Book of John.)
The ancient source of all esoteric Hindu texts, called the Book of Dzyan, describes creation in a sequence of unfolding sounds, linked to geometric symbols. It starts with a circle, representing Brahman; then the point in the centre called Para Sabda (the Word as the first vibration); then two parallel lines as Pasyanti; then a triangle as Madhyama (patterns of spiritual sound as consciousness); and finally Vaikhari, as sound made manifest as the physical cosmos, represented as a small triangle within a larger segmented triangle. Some of the Greek philosophers like Pythagoras and Plato understood creation to be based on sound and music, and they used geometry as part of their language. Goethe once said: "Geometry is frozen music."
Sound and music do not have to be physical, traveling through the air etc. You can hear a song in your heart or mind with no physical sound. Music exists in the mind of a composer before it gets written and performed. Therefore this triangle, and the sound it represents, is still on the spiritual level, which is why the original sound is called the "soundless sound". The closest approximation to this original soundless sound is the OM or AUM.
From this first triangle, other triangles can be formed by other radii, all having the same size and shape. These represent the offspring of God, as spiritual sons and daughters not yet born into physical embodiment. Their three equal sides represent the divine qualities of love, wisdom and strength, as described on the page Balancing the Trinity Within.
Interestingly, these triangles created by the original primordial sounding of the OM are not only symbolic. There is also a literal aspect to it. The science of Cymatics, described on page 2, depicts the specific geometric patterns created by a certain frequency or chord of sound. When the OM is sounded into a microphone, a pattern of interlaced triangles appears on the oscilloscope screen. This knowledge is not new. In the East, advanced adepts tuned in intuitively to this knowledge. A yantra is a pattern that relates to a specific mantra (spoken prayer), which they meditate on while giving the mantra. The yantra used for the OM bears a striking resemblance to the oscilloscope pattern . So "modern" science is not always so far ahead of the "primitive" people of the past. (In fact, our modern metal vehicles that poison us with carbon monoxide are primitive to those adepts who can bi-locate at will.)
So far the process of creation we have followed is still on the spiritual level. The next step is for its crystallization into the physical. Geometrically, this is done via the square. From the diagram of the single triangle in the vesica pisces , draw two verical parallel radii from the base of the triangle (centre of each circle) to the circumference of the two circles, which will cut them exactly at their tops. (There is a way to draw an exact right angle with just a compass and straight edge, but it's a bit complex to explain now.) Now join the two top points to form a perfect square, with sides of 1 radius. This represents the proverbial base of the pyramid, the foundation for all manifestation on the physical plane. It gives us the 4 points of the compass, the 4 winds, the 4 elements of fire, air, water and earth etc.
The physical plane is the feminine polarity to the spiritual as the masculine. The English word "matter" comes partly from the ancient sanscrit word "mater", meaning mother. Hence Mother Nature and Mother Earth. How does nature grow? Cells multiply by division! They first divide in half. This is done by diagonally dividing the square. This diagonal now becomes the first side of the next square. This is where the Pythagorian Theorem comes in handy. The diagonal is the hypotenuse "c" and the 2 shorter sides of the triangle are both 1 unit. Therefore c = (1 + 1) = 2. Arithmetically, the sqaure root of 2 is equal to 1.4142135.... ad infinitum, which is pretty clumsy to work with, which is one of the advantages of sticking to geometry. It also illustrates that the spiritual realm, represented by geometry, cannot be exactly defined or understood in the physical realm, represented by arithmatic. There are actually just 3 important numbers upon which all of the Platonic Solids and most of sacred geometry are based, and they are all square roots: 2, 3 and 5. The other two will be introduced shortly.
What is interesting is that the area of the second square is exactly double that of the first. It can be seen that the one half of the first square in the diagram above forms a quarter section of the second square. And if you divide the second one diagonally in half, the third square formed by it's diagonal will be double the area of the second, and on and on, doubling each time.
This multiplication by division is one of the two geometric depictions of how nature grows. The other is by the Golden Ratio described on page 1. It is based on 5 and the Fibonacci Series, where each number is the sum of the previous 2 numbers. This is the actual ratio that Mother Nature uses in the growth process.
The next step after constructing the square, as the foundation for all manifestation on the physical plane, is to cover 3-dimensional volume. There are five volumes which are thought to be the most essential because they are the only volumes which have all edges and all interior angles equal, as shown on page 1, and are the expressions in volume of the triangle, the square and the pentagon: 3, 4, 5. Therefore our next step is to construct the pentagon. It can be done from the vesica pisces, which we shall do for the sake of flow, even though there is a more exact method.
First of all, from the initial vesica pisces, draw a vertical line from it's top to it's bottom.
If the width of the vesica pisces is still 1 unit (radius), then the vertical line will be exactly 3. Neat, huh! (3 = 1.73205.....). (The proof of this is a bit too complex to include here.)
Now draw another circle, radius still equal to 1, with its centre at the bottom of the vertical line. Draw dotted lines, as shown in the figure below, from where the bottom circle cuts the outside of the other cirles, through the point where the bottom cirle cuts the vertical line, and continue them to where they cut the tops of the opposite circles. Draw a solid line radius from those points to the centre of their circle. These points will also be the ends of the horizontal line through the vesica pisces. From the top of these 2 new lines, subtend an arc equal to one radius across the extended vertical line through the vesica pisces. Both these arcs will coincide at the same point on the vertical line. Now join this point to the tops of the circles where the previous 2 new lines cut. This will now form a pentagon.
We have found out above how to get 2 and 3. To get 5, the last of the 3 Platonic Solid numbers, draw a line from any corner on the pentagon, to any other corner on the pentagon. It will always equall 5 (or 2.23606...).
Congratulations! You have just gone through the creation of the universe! We have covered the symbolic process of creation, from circle to triangle to square, to physical volume through the Platonic Solids. (There are also other geometric ways of describing the creative process, including starting with the most complex and all-inclusive Platonic Solid, the icosahedron. This is covered on Page 1 in the paragraph The 5 Platonic Solids.)
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