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.


Hidden Ireland

This is a hidden section of Britas Bay on the East Irish coast.  Another cold day while the tide chases me up the beach.  No symmetry here just a free flow of organic shapes and curls.  Usually do a bit more geometry I’m trying to expand a bit more since meeting the two Irish sand crews from the last post.


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Logo for the musician group The High Children.

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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.