Sacred Geometry
Nearly every ancient archaeological site predating recorded history, from the Pyramids of Egypt and Mexico, to Stonehenge and beyond, employs mysterious mathematical alignments throughout their design. These archetectural formulas, rarely used today, are considered sacred and have also been found in the way they're arranged relation to each other and, most inexplicably, in the Monuments of Cydonia, and the Face on Mars. Following text and images from: MidAtlantic Geomancy 
The Five Basic Sacred Geometrical Ratios
When one looks at sacred enclosures globally, there is a group of five mathematical ratios
that are found all over the world from Japan's pagodas to Mayan temples
in the Yucatan, and from Stonehenge to the Great Pyramid. These ratios are:
These are all irrational numbers. I have seen pi taken to 1500 decimal places with no discernable pattern to it (is that Chaos?). Let's take a closer look at each of these special numbers, and see how we can find them in the sacred geometry used by geomancers around the world. All five of these numbers gain their meaning only when beaten against the One. They are all ratios of x:1. The One is where it begins. 
Pi  3.1416 : 1  the Circle

Square Root of Two  1.414 : 1  the Square

Square Root of Three  1.732 : 1  Vesica Pisces
The Vesica Pisces is created by two identical intersecting circles, the circumference of one intersecting the center of the other. The vulvashaped space thus created is called the Vesica Pisces.

Square Root of Five  2.236 : 1  the Double Square

Phi  1.618:1  Ø  the Phi Rectangle

Squaring the Circle  The Great Pyramid

Squaring the Circle  The Earth & the Moon
 
Sacred Geometry
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.
Two Dimensions
I've been a student of sacred geometry for over twentyfive years. While there has been recent interest in threedimensional 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 twodimensional! ;) 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. Threedimensional 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 wholenumber 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: Pi / 4 = 1  (1/3) + (1/5)  (1/7) + (1/9)  (1/11) + (1/13)  (1/15) + ...and so on into infinity.

One final point
there is just one trick When working with Sacred Geometry: K I S S
You Got It! KEEP IT SIMPLE STUPID! {Really.}
