Sacred Geometry

Numbers

Geomancers are interested in sacred geometry because this is the study of the way that spirit integrates into matter - by echoing and amplifying the geometry of nature and planetary movements, we help to align the resonance of body/mind/spirit with the harmonic frequencies of the above and the below.

Geomancers are interested in sacred geometry because it has been found that certain spaces, with particular ratios, enable the participant to resonate or vibrate at the appropriate rate that maximizes the possibility of connection to the One.

A violin ain't built out of a cigar box! It is built with the proper wood with the proper shape and ratios, so that it resonates correctly for the notes/frequencies it is expected to produce. These same principles are applied to sacred spaces to maximize the possibility that whatever is being done there on spiritual levels will succeed.

Definition: Two Dimensions

I've been a student of sacred geometry for over thirty years. While there has been recent interest in three-dimensional sacred geometry based on the Platonic Solids and in sacred sites themselves, most sacred geometrical documents I've read talk in only two dimensions - height and width.

Obviously there is a fourth dimension and others beyond it that are much more complex and sophisticated. But why does the record left to us from geomancers of the past come primarily in two dimensions? Don't just tell me about paper being only two-dimensional! ;-)

Two is closer to the One than three is. It's less complex. I think one of the biggest mistakes Western geomancers have made was to take something that is very simple and make it much more complex. The Chartres Labyrinth strikes me as being an example of this. This stuff is simple. If you really gnow (that is, know both rationally and intuitively) a handful of irrational ratios - pi (∏), phi (Ø) and the square roots of two, three and five, you've basically got it all.

Three-dimensional sacred geometry just builds on this basic handful.

Numbers

One aspect of Sacred Geometry is that it works with irrational numbers. To go to the spiritual, one must go beyond the rational, and it appears that some of these ratios and numbers can lead us there. By being inside a sacred space that has been constructed using one of a handful of these sacred geometrical ratios, the resonance that has been set up can enhance the possibility of your making the spiritual connection you want to make.

So, what are these irrational numbers? (Thanks to Forrest Cahoon for his help with the following mathematical definitions.) Let's begin with the rational.

Rational Numbers

A rational number is a number which can be expressed as the ratio of two integers (whole numbers), such as 1/3 or 37/22. All numbers which, when represented in decimal notation, either stop after a finite number of digits or fall into a repeating pattern, are rational numbers.

Irrational Numbers

An irrational number is one that cannot be represented as a ratio of any two whole-number integers, and consequently it does not fall into a repeating pattern of any sort when written in decimal notation.

All of the Sacred Geometry ratios we will be working with, the square roots of two (1.414), three (1.732) and five (2.238), phi (1.618) and pi (3.1416), are all irrational numbers.

Transcendental Numbers

There are certain kinds of irrational numbers that are called transcendental numbers. Just like irrational numbers, they are defined by what they are not (they aren't rational numbers), yet transcendental numbers are so identified because they are not another sort of number, known as an algebraic number.

Any number which is a solution to a polynomial equation is an algebraic number. A polynomial equation is a sum of one or more terms involving the same variable raised to various powers, for example:

7 (x⁵) + 5 (x³) + x = 137

Any x for which any such equation is true is an algebraic number. Because the square root of two is a solution to the polynomial equation

x² = 2

it is an algebraic number.

A transcendental number requires an infinite number of terms to be defined exactly. That's one way of thinking of God/dess. There are special equations to derive transcendental numbers where the terms get smaller and smaller as you go along, so you can keep adding them together to reach any level of accuracy you need, but the true number cannot be reached exactly. That is the beauty of transcendental numbers!

Pi (, 3.1416...) is such a transcendental number. It is the only one we will be using here with Sacred Geometry. One infinite equation which relates to the value of pi is this: