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 - external pentagonal geometry

 
Among the first people to study the geometry of crop circles were John Martineau and Wolfgang Schindler. They mainly studied the formations of the early 90s. Both John and Wolfgang concentrated on the outer shape of the patterns trying to find some relationship between the different elements in a pattern. And they sure found it! I highly recommend John Martineau's booklet "Crop Circle Geometry" published by Wooden Books and his book "A Book of Coincidence" which is unfortunately out of print. This book is also published by Wooden Books.
 
 
Where John was working with different sorts of geometry, Wolfgang Schindler concentrated on just pentagonal geometry. In this section I will show you just one of Wolfgang's findings. It is a rather simple example, but it shows perfectly how far their findings reach. The example shown is the formation that appeared in 1990 near Chilcomb Down in England.


Wolfgang Schindler
 
 
Chilcomb Down, England 1990
If we draw a circle, that has it centre point in the left circle of the formation and meets the right circle of the formation, this newly constructed circle precisely touches two tramlines (orange lines) that seemed to have nothing to do with the formation. In this new imaginary circle we can construct a pentagram. This pentagram precisely cuts the centre of the outer box, and exactly crosses one of the edges of the inner boxes. Furthermore, the ring of the formation fits perfectly into the pentagram. 
 
 

 
 
Apart from this, if we construct a circle around the right circle of the formation, this imaginary circle meets the ring of the formation, and just touches one of the edges of the outer boxes. In this imaginary circle we can construct a pentagram. This pentagram precisely crosses one of the edges of the inner boxes, whereas the right circle of the formation perfectly fits into the pentahedron of the pentagram. 
 
 

 
 
On top of that, we can construct a circle that has its centre point in the left circle of the formation and its perimeter in the centre of the right circle of the formation. In this large, imaginary circle we can also construct a pentagram. And this pentagram too meets one of the edges of the outer boxes. And the ring of the formation fits perfectly into the pentahedron of this pentagram.
 
 

 
 
Anyone who knows anything about geometry will know that all of this goes way beyond chance. There is no way that this could be a coincidence. And once again, this is only a simple example. John Martineau and Wolfgang Schindler found many formations that were far more complex.
But it goes further. The shown sophisticated geometry contains an extra dimension. A hidden, internal geometry. Read the next sections to find out more about this internal geometry.