



It took an other while before I realised that not only was Squaring the Circle encoded in 'my' 1994 crop circle, it was also encoded in the most basic way one can define Squaring the Circle. An oval, or egg! This oval or egg is secretively hidden away in architecture all over the world and can be found once you have opened your eyes to it. The diagram below on the left is a graphical representation of the crop circle that I discovered near BovenSmilde, the Netherlands, in 1994 and which was the first crop circle I ever walked through. The diagram in the middle shows how simple ‘squaring the circle’ has hidden itself in the formation. Do notice how the square and the small circles are slightly overlapping. The red circle though exactly touches the small circles. It is the square around the central circle and the red circle that touches the small circles, that together form 'squaring the circle'. 



The diagram above on the right shows the next intriguing element of amazing beauty. If the small circles would have been bigger or smaller, ‘squaring the circle’ could still hide itself as long as the small circles were placed at the right spot. Even moving the small circles to a different location, would still enable 'squaring the circle'. Click here to see the different options. The small circles are exactly of the right size to be captured by a set of lines that define the square at the top side and bottom side and at the same time define the circle at the left side and right side. ‘Squaring the Circle’ created and captured at the same moment. Truly fascinating. 



The set of lines actually form a rectangle as shown in the left diagram above. By stretching the central circle, an oval or egg is constructed that exactly fits in the rectangle. This oval or egg is the most basic way of defining ‘Squaring the Circle’. The width of the oval defines the size of the square and the length of the oval defines the diameter of the circle. 



Not long after I had come up with this oval or egg, I was visiting the Cathedral of Aachen in Germany. The central part of the Cathedral, called the Octagon, was build by Charlemagne starting in 792 (8 years before 800) and finishing it in the year 800. The eightfold geometry of the Octagon is reflected in the central floor pattern, as shown above on the right. All these number eights  octagon (8) and the year 800 (8 vertical and oo horizontal)  intrigued me and I expected to find some interesting things. I was in for a shocking surprise. 



Stepping into the building I noticed an oval in the marble floor. I immediately recognised the shape. Squaring the Circle was unmistakenly encoded in the floor. Was this some sort of hint? Was there more to the Cathedral then meets the eye? I decided to further analyse the Octagon. 



My first step was to reconstruct the floor plan of the Octagon. I expected the geometry of the building, like the floor layout, to be pretty much straight forward and I proceeded accordingly. 



Using eightfold geometry I came up was a design of which I was sure was identical to the building. A mind provoking surprise was waiting for me. 

My design did not fit the blueprint of the building. The boxes were not long enough. Or in other words. The design of the Octagon was NOT based on straightforward eightfold geometry. I was baffled. The oval in the marble floor came back into my mind. The oval which was so clearly pointing into the direction of Squaring the Circle. I decided to give it a try... 



I took my design and superimposed ‘Squaring the Circle’ on it. As expected the design had no relationship with squaring the circle. Next I decided to change my design in such way that it would have a relationship with squaring the circle. I elongated the boxes until they would match the superimposed ‘Squaring the Circle’. I compared this new design with the blueprint of the Octagon. I was in for a new shocking surpsrise. 

My new design and the blueprint exactly matched. Amazing! So, the geometry of the Octagon is NOT based on straightforward eightfold geometry. Instead the Octagon is based on ... Squaring the Circle. 



What to make of this? There is Charlemagne, who was crowned Emperor in the year 800, who build the Octagon (the 8building) in Aachen in the year 800. But Charlemagne decided to base the Octagon not on 8fold geometry, but on squaring the circle. And to make sure that people whose eyes are open to it, would see it, he hid a key in the marble floor in the shape of an oval! Is this unique? No. There are more places, famous places, where you can find the same phenomenon. Read on with Secret and Sacred Architecture  part 2 © Bert Janssen, 2009. 

In my book 'the Organizing Principle' you can read more about this fascinating subject.
