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The internal geometry of crop circles
What is it that makes crop circles such a fascinating phenomenon? No doubt the mysterious and inexplicable aspect plays a mayor role here, but is that all? How can it be explained that people get so fascinated merely by looking at them? Even when they don't know a single thing about the crop formations, the symbols seem to stir up interest nevertheless.
The question why this is has kept me occupied for many years now.
There's something about the pictogrammes that has some kind of hypnotising effect on people.
From the very first crop circle formations, people like John Martineau and Wolgang Schindler have worked with geometry. They mostly aimed at the 'outside' of the pictogrammes. Until 1992 many formations indeed could be fit into fivefold geometry. But in 1992 the formations changed, and their geometrical explanations no longer held. Later Gerald Hawkins intensively studied the various elements within the crop circles. He found strong indications for the existence of diatonic ratios in the patterns.
Although all these results are indeed fascinating, they weren't enough for me, to be honest.
There had to be more. A more fundamental basis. And I found it.
Many crop circles are built on simple but enlightening geometry. Geometry that provides us with certain results, certain derivatives, such as the findings of Martineau, Schindler and Hawkins. Geometry that is the basis, the source, the cause of their findings. The internal geometry of crop circles.
The book in which I thoroughly describe these fundaments will be published at short notice. The core however will be further explained here.
It all started with my attempts to reconstruct certain formations on paper by means of a ruler and a pair of compasses. I didn't use the ruler to measure, only to draw straight lines. I was therefore working with mere construction. The results were fascinating:
1. All formations I studied turned out to have exactly the same basic pattern.
2. All elements in a formation (and, as a result, all internal proportions as well) are not coincidental, but strict results from their construction.
3. The necessary construction points (centres of used circles) can never be found in standing crop.
This is how it works.
The above-mentioned basic pattern looks like this:
From this basic pattern many formations can be constructed. In my book I will explain how this basic pattern can be made.
Let's now try to reconstruct a formation, a relatively simple one. Let's try the Harlequin formation of 1997.
Via several simple construction steps we come to this diagram:
This diagram shows an equilateral triangle, constructed in the three circles necessary to make the basic pattern and is the same as we can see in the Harlequin formation. Please notice the circle constructed neatly in the triangle. It's the same circle as those three constructed on the corners. Coincidence?
The inner circle in the formation fits exactly in the equilateral triangle of the basic pattern. Coincidence?
The end result looks like this:
I must admit that this is a relatively simple and obvious formation. The next formation however shows us differently. Starting off with the same basic pattern we can reconstruct the following through mere 15 steps:
It seems a variety of lines and circles, but in reality it is the internal geometry of the following pictogram:
In spite of the complex character of this formation, it can be constructed without trampling the standing crop. The following diagram shows the position of the necessary construction points. As you can see they all lie in the flattened crop.
Some construction points lie exactly on the edge of the standing crop. It all fits just perfectly. If, for instance, the central circle had been just a little bit smaller, the formation could not have been made without damaging the standing crop. 'Luckily', the central circle has the perfect shape. Coincidence?
We see the same principle when looking at the following formation. Starting off from the basic pattern we reconstruct through
And here as well we find the necessary construction points exactly on the edge of the standing crop.
If the inner circle of the standing crop had been just a tiny bit bigger, this formation could not have been constructed without damaging the standing crop. But also this formation has the perfect size. Coincidence?
The formation of Etchilhampton of 1997 leads us even further.
Via many steps we are able to reconstruct the final pattern, which shows the following construction points:
In order to construct this formation, we need several points that lie relatively far from the centre. This could have been a problem, but the ring around the formation brought help. Coincidence?
Inside the formation the outer construction point also lies just in the flattened crop.
Does this mean that we should only be focusing on the construction points?
No. These points are merely one of many indicators that show us that the crop circle formations are formed via an extremely precise geometric pattern. The are made with geometric principles that are so well known to us.
What can we do with this knowledge? What does it tell us?
One of the things is that, since they are all created from the same basic pattern, we can compare them with each other. For instance, we can compare their size, thanks to the basic pattern which enabled us to superimpose the various formations.
Moreover, now that we know their internal geometry, we can make them three-dimensional.
And as we saw before in the basic pattern, every crop circle formation is based on a equilateral triangle, which is a tetrahedron three-dimensionally. By means of the above mentioned geometry, the pictograms can be turned into three-dimensional figures based on mere tetrahedrons!
Every single element inside a formation is related by definition to all other elements inside that formation because of this geometry. Diatonic ratios are a logic result of this. But it goes even further. Every single element of a formation can be related to ever single element of another formation!
So far, we have only looked at sixfold geometry. But what about fivefold geometry that we find, for instance, in the Star of Bethlehem from 1997?
By means of the basic pattern this is how we can come to fivefold geometry:
Via a couple of construction phases we can construct this figure:
which leads us directly to:
Here too we notice that all construction points are neatly inside the formation.
If the inner circle were one inch smaller, we would have had a problem.
What you just saw is only the surface of the fascinating world of the crop circles' inner geometry. What I found out goes a lot further than described on these pages. For instance, it can be proved that Avebury's Web is an amalgamation between five- and sixfold geometry.
Both geometries are interlocking in this extraordinary formation.
Perhaps this perfect geometry is not telling us anything. Perhaps it is just needed to make the pictograms beautifully harmonic, which has a hypnotising effect on people. Perhaps the fact that the construction points are never in the standing crop is done on purpose to show us we're on the right track with this form of geometric analysis.
In my book a broad analysis will be given on many formations. The reader will meet an incredible number of 'coincidences'. Not only concerning the construction points, but also unbelievable intersections, concurrences and ratios inside formations.
And relationships with sound, music, architecture and so called 'sacred geometry'.
Copyright: Bert Janssen, 1997
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