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 | Photos | Crop Circles and More
 

Crop Circle Geometry - internal geometry

     
 
It all started early 1996 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.
 
 
One of the findings was that the formations I studied turned out to have exactly the same basic pattern. The diagram on the right shows this basic pattern. It is very simple and you most likely have made this pattern many times while you were bored during the mathematic lessons at school. Look at the section Crop Circle Reconstructions - the Basis for all the steps needed to construct this basic pattern. The three constructed lines in the basic pattern are perpendicular to the sides of the equilateral triangle and are dividing these sides exactly in half. It is important to notice that this is not a coincidence, but the result of the used geometrical construction techniques!

 
 
While reconstructing different crop circles you will see that this happens over and over again. You will for example find perfect ratios, diatonic ratios of which you will think it's all-coincidental. But it is not. It is just the simple consequence of the used techniques. In geometry there is no such thing as coincidence. It all follows strict rules. Every new element is determent by previous elements. Taking the 'basic pattern' as starting point, one can reconstruct many crop formations. For instance the formation that appeared near Winterbourne Bassett in 1995. 
 
 
Winterbourne Bassett, England 1995
This formation is a very good example showing clearly how all the different elements in the formation are connected to each other. One element follows logically out of the previous one. There is nothing random about it.
 
 

 
 
First construct the basic pattern. Then construct a circle and three sets of lines as indicated in the diagrams.
 
 

 
 
Now construct two other sets of lines. See diagrams.
 
 

 
 
Construct a big circle as shown in the diagram. Finally construct a small circle using the dimensions at the bottom of the diagram and place this circle in the center.
 
 

 
 
With this the reconstruction is finished. Just rub out the appropriate lines, fill in the center circle and you have the crop formation as it appeared near Winterbourne Bassett.
 
 

 
 
It is of course nice to know that different elements within a crop circle are connected, but it goes a lot further. I urge you to read the sections Size, Placing and Ratios, Construction Points and Construction Lines. In these sections you will see how far reaching this internal geometry is and what the implications are.