Crop Circles and More

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Squaring the Torus

  After some articles on Squaring the Circle, I found it to be time for something ‘new’. I was just getting ready to write about the landscape geometry of Wiltshire, when the first crop circle of 2008 came down on April 19.


At first glance the design of the crop circle looks pretty much straight forward, but let me point out some amazing geometrical peculiarities of this formation. We are looking at Squaring the Torus! After all the squaring the circle it appears to be time for the next step.


Let me explain how you can reconstruct the design found on April 19, 2008, at Waden Hill, just outside Avebury.


Start with a hexagon circumscribed by a circle. Now construct a circle with its centre indicated by the left arrow as indicated in the diagram above, and its circumference intersecting the hexagon at the opposite site, indicated by the right arrow. Construct a second circle with the same centre, but with its circumference intersecting the hexagon as shown in the diagram above on the right. This constructing of two concentric circles can de done six times, resulting in the diagram below. You have now constructed the backbone of a torus.


The intersection points of the outer perimeter of the rings can be connected by a circle as shown in the right diagram above. The intersection points of the inner perimeter of the rings can be connected by straight lines, forming a hexagon. The diagram below on the left shows the contructed circle and hexagon.

The hexagon now determines the size of a square, and yes, this square squares the circle. The perimeter of the square is identical to the circumference of the circle with a precision of 99,3%.


The hexagon defines actually three squares. See diagram above on the right. Notice how the torus is interconnected with the red Circle and the blue Squares. In a way we are not only looking at squaring the circle, but also at Squaring the Torus. Truly amazing!


Since the shape of the Great Pyramid of Gizeh is directly related to squaring the circle, you will find the Great Pyramid wherever you will encounter squaring the circle. In the diagram above you see how the Pyramid is related to squaring the circle and through that how it is related to the Torus and thus to the crop circle. The arrows indicate a further relationship between the Pyramid and the torus geometry.
Because of the geometry at hand, six ‘Great Pyramids’ fit in the formation as shown above on the right.


The left diagram above shows how amazingly deep the connection between the Pyramid and the Torus reaches. The connections are so plenty that they far exceed coincidence.



By projecting ‘all’ the Pyramids in the torus formation, you get an incredible powerful drawing. See above on the left. The right diagram shows the drawing with the squares included. Take some time to study this diagram and be amazed by the overwhelming amount of geometrical ‘coincidences’. A better start of the season we could not have wished.
In a future article I will show how all of this can also be found in the Wiltshire landscape!

After the 2007 crop circle season was stretching us to understand the multi layered informational matrix of the circles, the 2008 season takes it right from the start even further. Where will it go? Where does it stop? Does it?

© Bert Janssen, 2008.