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 - summary and conclusions - see also: Crop Circles and More

The previous sections have made it very clear that a lot of crop circles not just have pretty shapes, but are based on a very strict geometry. This was first noticed by John Martineau and Wolfgang Schindler. Both John and Wolfgang looked mainly at the outer shapes and found many peculiarities. Read the section external pentagonal geometry to see an example of Wolfgang's work.
But there is far more in crop circle shapes then their perimeters do suggest. This is not always directly visible, but it is definitely there. Where John and Wolfgang mainly looked at the outer shapes of the crop circles, I took a look inside and found that a lot of formations were based on an intriguing internal geometry. This geometry was not visible at the outside but it was definitely there. Read especially the sections internal geometry, size, placing and ratios, construction points and construction lines to find out what is so fascinating about this geometry.
All in all the next conclusions can be drawn:
  • The size and placing of the different elements in the studied crop formations are not random but do follow strict geometrical construction rules;
  • Because off the internal geometry some elements will have special (diatonic) ratios to other elements;
  • Some for the construction necessary elements can not be found back in the final design;
  • The necessary construction points could in the studied formations never been found in standing crop;
  • Some formations have elements that are strictly necessary to avoid construction points in standing crop;
  • Construction lines are not the ultimate proof of human activity. On the contrary. Construction lines are a strong indication of non-human involvement.

The above conclusions show how intriguing crop circles can be. Though I have to admit that I didn't study all the formations that ever appeared. I just studied a selection and it is arguable that this selection is a little bias. I therefore urge the reader to do his or her own geometrical studies on formations I left out.

One conclusion can be drawn anyway:

Crop circles are far less straightforward then you would think at first sight. They cannot be done away with as just a simple joke. Their geometry shows that there is far more to it. The different aspects of this geometry of crop circles as shown in the previous sections even suggest that it is impossible for humans to reproduce the shown crop circles in an actual field.

see also:
Crop Circles and More