Mandalas and Sacred Geometry - Squaring the Circle and other symbolic mandalas

Of course mandalas can be used as profoundly spiritual routes into meditation so I have been looking for mandalas with an added message or significance.

I feel very relaxed when I am filling in mandalas, whether I have drawn them myself or chosen them to complete, so I have been browsing around the web to look at the spiritual aspect of mandalas.

There is a lifetime's reading out there! And I am still only scratching the surface with Jung and his mandala work , however I keep coming across the idea of a sacred geometry

 which has been felt to underpin everything that exists; including the tree of life, Metatron's cube and squaring the circle

Wikipedia says "Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straight edge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.
In 1882 it was proven to be is a mathematical impossibility.."


However, geometry notwithstanding,  I found this rather natty template on www.charlesgilchrist.com and have been playing with it, using a ruler, protractor and circles template because - as is the way with scissors, rulers, glue etc,  I have mislaid the compass.


I much prefer the metaphorical approach to squaring the circle:-

"From the domed Pantheon of ancient Rome, if not before, architects have fashioned sacred dwellings after conceptions of the universe, utilizing circle and square geometries to depict spirit and matter united. Circular domes evoke the spherical cosmos and the descent of heavenly spirit to the material plane. Squares and cubes delineate the spatial directions of our physical world and portray the lifting up of material perfection to the divine.
Constructing these basic images is elementary. The circle results when a cord is made to revolve around a post. The right angle of a square appears in a 3:4:5 triangle, easily made from a string of twelve equally spaced knots. But "squaring the circle"... drawing circles and squares of equal areas or perimeters by means of a compass or rule... has eluded geometers from early times. (2) The problem cannot be solved with absolute precision, for circles are measured by the incommensurable value pi (π = 3.1415927...), which cannot be accurately expressed in finite whole numbers by which we measure squares. (3) At the symbolic level, however, the quest to obtain circles and squares of equal measure is equivalent to seeking the union of transcendent and finite qualities, or the marriage of heaven and earth. Various pursuits draw from the properties of music, geometry, and even astronomical measures and distances. Each attempt offers new insight into the wonder of mathematical order."
Rachel Fletcher,
Squaring the Circle: Marriage of Heaven and Earth
Nexus Network Journal, Vol. 9, No. 1, 2007 119"




I have also found the comtemplative  labyrinth  at Chartres cathedral and used it as a mandala...

It was used by pilgrims as a path for meditation (and I  see it also comes up in the http://www.charlesgilchrist.com/ site on sacred geometry; I did not notice until I was fact checking just now about the labyrinth so I seem to be sticking well to my theme:))

The Kabbalistic tree of life....

and a temple plan based on the Vasta Purusha Mandala

also interested me as meaningful mandalas  ...