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
size, placing and ratios,
construction points and
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;
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
- 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;
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.
conclusion can be drawn anyway:
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.
Circles and More