The Art of David Rankine          MANDALA

SACRED GEOMETRY

 Sacred Geometry by definition is simply the acknowledgement and recognition that all matter, energy and form is structured upon basic geometric models and ratios. When we create using these same forms and ratios we cannot help but create beauty, whether it be dance, thought, relationship art or music...it will all resonate. Geometric forms are the forms of harmony and for each of us there is complex and also simple geometric hologram of energy.  When we fall into the shape of it, then we are resonating with similar forms all through the Universe...and we are in flow.

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                            (Meanings and Use of Sacred Geometry)        (Applications)

 methods of construction

Any mandala (including a Sri Yantra) is a Sacred Geometric construction. All sacred geometric designs can be drawn using only a compass and straight edge. All these designs begin with a circle, which is created by one point revolving around another (static) point. The circle can represent expression of self or consciousness. The circle is "that which is", whole and complete and as we create more and more complex designs using circles we also simulate how interpenetrating consciousnesses combine to create complex systems.

The series of drawings below illustrate how we start off with the simple dynamic building block (a vesica piscis) created using a straight edge and compass. The combination of interpenetrating circles provides us with all the angles necessary to create any geometric form. 

This method  follows a incremental growth pattern*, from points to line to circles to angles to polygons etc and it always starts off with the same form (the circle) The more complex a design sought after- the greater the number of steps necessary so the actual drawing of these forms becomes a moving meditation - a process of expansion and expression. The act of drawing mirrors the act of consciousness expansion.

                          a vesica piscis                the 90 degree angle         the 30, 60 and 90 degree angles

                           Three circles touching centre points                  The 30 and 60 degree angles created by it.
 

same three circle arrangement informing triangles in increments of 5 degrees
 

  The hexagon created by these angles.

contained within and informed by the hexagon, would be a hexagram - a double-delta (below)

                             

  

                                   Within the hexagon are also three interpenetrating PHI ratio rectangles    

 

The following design uses four interpenetrating circles. This design will also be used later to develop a  matrix which will inform the positioning and size of all the nine triangles of a Sri Yantra

                              four circles             10, 20, 30 and 60 degree angles          the square within
 

The Phi ratio present in the relationship of the width of the design to the face of the square informed by it

PHI = 1.618:1

We will see how PHI is revealed also with the structure of a Sri Yantra.

 

The following design is created by  three inter-penetrating circles in a triangular layout.

Notice that the three circles touch on the centre points of the others. By adding a third circle we increase the number of angles generated by connecting the cross-over points. The angles provided allow us to generate triangles (equilateral and various isosceles), squares and pentagons, not to mention (once again) hexagons generated by double equilateral triangles

 The three circles represent self, other and universe. A equilateral triangle is the form created within the central intersection area . The faces of the triangle represent the dynamic flow of information (communication) between these three states of being while the circles represent the potential - the space held open (through intent) of what can be.
 

three circles intersecting through their centre points

 This arrangement can inform the construction of triangles (60 degrees, 45/90 degrees and 51.5/103 degrees), squares and pentagons

The same drawing showing all the angles generated by connecting intersection points.

notice that the triangle to the right has a 51.5 degrees face which is the same angle of inclination of

the Great Pyramid of Cheops. This pyramid contains within it the PHI ratio (base: height= PHI)
 

The Celtic Cross
Long accepted as a symbol of Celtic Spirituality, the Celtic Cross (a cross with a  circle or square set behind the intersection point) is shown here with it's construction matrix revealed - a process that did not require measurement  (with numbers) but only used a compass and straight edge.
The interpenetration of circles through their centre points have provided all the required right angles and even the proportion of arms to post.  The result is an elegant design, as is the design process- a step by step moving meditation that is more intuitive than logical.
 
 
* Growth pattern. The beautiful  thing about sacred geometric patterns is that they reflect the operation, structure and dynamics of many systems. It could be cell growth or the relationship between energy systems of an interpersonal relationship between two people.

 

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Stand by for Sri Yantra construction methods!