Crop Circle Geometry - size, placing and ratios

There is no coincidence in geometrical constructions. Every element is in size and placing determent by the previous steps. That is the nature of geometrical construction. This means also that if it is possible to reconstruct crop circles using geometrical construction techniques, the different elements within the construction (crop circle) will by nature have special ratios to each other and their placing do follow strict rules! Neither the size of the elements nor their placing is coincidental. So letís try to reconstruct a crop circle and see for yourself the far reaching implications.
Winterbourne Bassett, England 1997
The formation of 1997 at Winterbourne Bassett was a real eye‑opener for me. It demonstrates very clearly how the different elements in the formation are not random. The size and placing of the elements follow strict geometrical rules.
After a few construction steps you get the diagram shown on the left. The blue circle is very important. Take another look at it and notice that the size and placing is not random. They are determent by the previous construction steps. This circle plays an important role later on in the construction.

A circle with its center in the middle of the pattern and its circumference just touching the bigger triangle is constructed. See diagram above on the right.
Now construct three circles of the same size as the previous one, but with their centers on the indicated intersection points.
The three circles just constructed have a fixed size and have a predetermined placing. The big triangle rules the size and the big circle rules the placing.

From here it takes only a few steps more to finish the reconstruction of the 1997 Winterbourne Bassett formation.

What can be learned from the reconstruction of the 1997 Winterbourne Bassett formation? First of all, like I emphasized already several times, we could see that the different elements in the final design are in size and placing all determent by previous steps, determent by geometrical rules. Secondly, and this is at least of equal importance, we can see that several constructed elements cannot be found back in the final design. These elements were strictly necessary for the following steps but were then rubbed out. A good example is the big circle that was necessary to determine the placing of the three outer circles. This big circle cannot be found back in the final design! This is something that can be done easily on paper, but is impossible to perform in crop. You cannot make downed crop stand again!

I also ask you to notice that since the big triangle determines the size of the three outer circles, it is obvious that these three circles have a special ratio to the overall circle. A diatonic ratio. In this case an octave. This is not something special or coincidental. It is the logic of geometry.

Barbury Castle, England 1999
The formation at Winterbourne Bassett was not the only one to show how strict geometrical rules were followed by the different elements in the formation. The 'Crescents' formation of 1999 at Barbury Castle showed the same features. The following diagrams show which rules were followed by the crescents and why there is a diatonic ratio within the crescents. The ratio is 9/4 which is the note D in the second octave.

Starting with the basic pattern it is not difficult to get to the situation as shown in the right diagram. The smaller triangle and the larger triangle form again a diatonic ratio. In this case 16, which is the 5th octave. Let me emphasize again that this is not a coincidence. It is the logical result of the geometrical construction.

The next step is very important. Construct a circle with its centre in the left corner of the large triangle and with its perimeter just touching the side of the small triangle.

Now do the reverse! Construct a circle with its centre in the left corner of the small triangle and with its perimeter just touching the large triangle.

The two circles overlap and form a crescent. This crescent is exactly at the same place and of the same size and shape as the crescent that could be found in the Barbury Castle formation of 1999. Because of the way it is constructed, of the way it follows those strict geometrical rules, it is logical that the crescent has a diatonic ratio in it. The ratio is 9/4. The note D in the second octave.

Here again we see that necessary elements cannot be found back in the final design. The two triangles were absolutely necessary to construct the crescents, but the triangles don't show up in the final design. They disappeared, were rubbed out. You can do that on paper, but not in crop!
See also Barbury Castle ‑ England 1999 in the main-section: Crop Circle Reconstructions.

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