Squaring the Circle

The geoglyphs in Peru known as the Nazca Lines are usually images of animals or eerie humanoid designs but there is one that stands out called the Sun-Star.  I believe this is a design for squaring the circle.

Neither of these pics show the actual design but uses an overlay graphic that obscures the actual image.  This is unfortunate because it seems something is lost or taken from the original.  I could not find a clean picture of it on the web so I made my own and started to do the math.

In the designing I found adding the larger circle to the outside is a decent approximation to the ancient problem of squaring the circle.  (finding a square and circle of the same perimeter or area)  In this case the outer circle is about 92% of the perimeter of the square’s and the square has about 94% of the circles’s area.  So this simple design approximates both the area and perimeter, a very hard thing to achieve.

Squaring the circle is an very ancient problem that has drove intellectuals literally crazy.  It is impossible to construct a perfect solution to this problem but it was not known as impossible until 1882.  It is easy to prove something is possible by just finding a solution but very hard to prove something is impossible.  This takes a logical argument built on sound axioms.

There is a spiritual aspect to this exercise as well.  The circle is mystical and not measurable while the square is very measurable and known.  This is like knowing the infinite (God) with tools built from the finite (human).  Humans attempting to know the mind of God is a perfect analogy to squaring the circle and is why the ancients were so concerned with this problem.  We have now replaced these ideas with science but science itself pursues the same mystical problem of knowing ourselves, the Universe, and our place within it all.  We are the squares trying to match ourselves with the circular universe.

 

Four, beauty of stability

All numbers have a personality and the four’s personality is of balance, stability and knowledge. We use it to build our structures, to layout a coordinate system and to even navigate our way across the earth with our cardinal directions (N,S,E,W). Perpendicular and parallel lines are inherent to the square and even show up when writing the number four. Perpendicular and parallel lines are how we come to know things in the material world and this is why the square is symbolic for knowledge.

Twelve is timeless but quick

 

These designs may look like they take a long time to construct but they do not.  With a few foundation concepts in natural geometry, they are laid out in minutes and most of the time is spent thinking about what to do with the controlling geometry that lays waiting.

 

 

House of Gold divided into Six

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Two circles combined to make what is known as the Vesica Pisces (fish bladder). This is that small seed shape in the midst of the circles and is the most important construction in sacred geometry. It is sometimes called the birth canal of the universe. Then two larger arcs come together to make what I call the House of Gold because it has the golden ratio (1,618…) within the midst of its arced walls. Then taking one of the central distances (line) creates a perfect division of the House of Gold into six parts as the six circles show this. I was very excited to work this simple but lost construction out and bring it back from the dead 3 years ago. Grab a compass and try to construct it.

Germ of Life

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The germ of life is the first full construction that is taught by Justin The Cirler.  This is a magical little construction that naturally falls out with seven simple steps.  This can be done with just rusty compass (compass that does not change size) in seconds.  Ancient peoples would have come discovered this very quickly and would adored if for its organizational properties and simplicity.