Early Reflections on Crop Circles
These pages contain my early work on crop circle geometry and crop circle reconstructions.
My later work can be found on my website Crop Circles and More

  Geometry | Reconstructions | Crop Circles and More
 

Crop Circle Geometry - construction lines

     
 
If you take a closer look at the lay of the crop in a crop circle you will sometimes find pathways of crop under the general lay. These pathways are on average a foot wide and it often looks as if these pathways represent the general outlay of the formation. They look like 'construction lines' and these construction lines have for obvious reasons a very bad reputation. A lot of people think that these lines are the ultimate proof of human activity. But it is not that simple. I will show you that construction lines found in formations can turn out to be of unexpected value. For this I will use the 1998 Tawsmead Copse formation as an example. I won’t show the whole reconstruction, I will just show those steps necessary to explain what I mean. See Tawsmead Copse - England 1998 in the main-section Crop Circle Reconstructions for all the steps. The formation is based on seven-fold geometry. Look at Construction of  7 fold Geometry in the main-section Crop Circle Reconstructions to see how seven-fold geometry can be constructed.
 
 
Tawsmead Copse, 1998

Starting off with a big heptagram I constructed a smaller heptagram that exactly fits into the bigger one. Beside of that I constructed a heptagon that also exactly fits in the bigger heptagram. See diagram on the left. The right diagram shows how a heptagon is constructed in the smaller heptagram.
 
 

 
 
A few steps later I constructed another heptagram and yet another heptagram. With this the reconstruction of the 1998 Tawsmead Copse formation is virtually ready. Picking the appropriate lines completes the reconstruction. The result looks as follows. It has to be said that the original formation contained numerous small circles. These are left out in the reconstruction.
 
 

 
 
I used the Tawsmead Copse formation as an example because this formation contained very definite pathways that lie under the general lay. The white lines in the diagram on the left represent these pathways or so called construction lines. The diagram on the right shows the same formation but now with all the heptagrams and heptagons necessary to reconstruct the formation. Do notice that one heptagram and one heptagon I needed for the reconstruction could also be found back in the actual crop formation. The rest of the needed heptagrams and heptagons could not be found back!
 
 

 
 
The construction techniques that I used on paper cannot be repeated in the fields without leaving their traces. Look for instance at the large number of seven-fold stars that I needed and that can no longer be found in the end result. It is absolutely impossible to erase those figures in the fields. And yet, the underlying construction lines found in the crop formation indicate that exactly the same construction techniques were used when this formations was created! 

Of course, one might claim that humans actually can mark out those large figures in the fields - like for instance the large seven-fold stars - without leaving a trace. Although this is quite unlikely to be true, let's give them the benefit of the doubt. Just for now... Suppose it is indeed possible to make those constructions without leaving a trace. This means one can make absolutely fascinating formations: formations without underlying construction lines! 
From a human point of view, those are the ultimate formations. In other words, if humans have the possibility to leave out construction lines, they will definitely leave them out. If they can make large seven-fold stars without leaving any construction lines, they will never make smaller seven-fold stars, which do show construction lines! 

Now we have a catch-22 situation. 

  • Either humans can make large seven-fold stars without leaving construction lines, but that means we would not have found any construction lines in the formation at all. However, we did find them! 
  • Or humans cannot make seven-fold stars without leaving construction lines, but that means we should have found the construction lines in the large seven-fold stars as well. However, we didn't. They weren't there! 

Whichever way you look at it, any human claim drops out for good. So what conclusion can we draw now?

  • Construction lines are not the ultimate proof of human activity. On the contrary. Construction lines are a strong indication of non-human involvement.