



introduction
Inspired by people like John Martineau, Michael Glickman and Wolfgang Schindler,
I got somewhere round 1995 the idea to try to reconstruct crop formations.
The only tools I use are a ruler and a pair of compasses. I don't use the
ruler to measure, only to draw straight lines and therefore I am working
with mere construction. In this section you can find the results of my
efforts. First you will find reconstructions based on threefold
geometry, then fivefold geometry and finally formations based on
sevenfold geometry. Most diagrams speak for themselves, but in some
occasions you will find additional text explaining what to do or why the
construction is so special.









the Basic Pattern
Almost right from the
start I noticed that the geometry of many formations was
based on the same pattern. The diagram on the right shows this basic
pattern. It is very simple to construct and you most likely have made
this pattern already many times.
Click on the diagram to find out how it
can be constructed. 














Winterbourne Bassett  England 1995
The 1995 formation at Winterbourne Bassett was one of the very first
formations I tried to reconstruct. This formation has fascinated me
right from the moment I
visited it back in 1995. Perhaps the fascination has something to do with
my mathematical background. For me the formation has a strong
link with the famous theorem a2+b2=c2 of Pythagoras, the Greece
mathematician who lived around 450 BC. 














Winterbourne Bassett  England 1997
The formation at
Winterbourne Bassett in 1997, also known as the 'Harlequin', was a real eyeopener for
me. It was during the reconstruction of this formation that I noticed for the
first time how different elements within a crop circle were all
related to each other. How it is logical that you will find diatonic
ratios in crop circles. Read also
Size, Placing and Ratios
within the section
Crop Circle Geometry!















Little Bury Green  England 1996
When Michael Glickman saw
the formation at Little Bury Green in 1996, he made the remark: "Ah,
three bananas in a basket". This was reason enough for me to look
if this formation was indeed just 'three bananas in a basket'. Part of it
looks perhaps just like bananas, but the formation in totally is geometrically
spoken a real beauty.
Click on the image and judge for your self. 














Barbury Castle  England 1997
A formation of such
beauty in oilseed rape screams for a closer inspection. And that is what
I did. I took a closer look and again I found that the
formation could easily be reconstructed and that the basic pattern formed
the basis for this formation as well. If you look at the reconstruction
you will notice that it resembles the reconstruction of the formation at
Little Bury Green.















Barbury Castle  England 1992
Barbury Castle 1992. The
socalled 'Mother of all pictograms'. Of course this pictogram could not
fail in the row of formations I have analised. Notice how this formation
doesn't look 100% perfect. One of the sides of the triangle is crooked and
the spiral looks turned in a strange way. But as with the Liddington Castle
formation, these irregularities again could very well be reconstructed.
Beside of that this formation had one very special construction point.
Read also
Construction Points
in the section
Crop Circle Geometry.















Etchilhampton  England 1997
It is especially the ring
round the formation that makes this crop circle so interesting. While
reconstructing this formation, I noticed that it needed six
construction points that were lying away from the main pattern. It turned
out that these six points were located exactly where the ring was. An
intriguing combination of size, placing and construction points
Read also
Construction Points
in the section
Crop Circle Geometry.















Hackpen Hill  England 1999
Interlocking spirals!
That was the general opinion when this beautiful formation appeared in
1999 at the foot of Hackpen Hill. And indeed, I thought the
same. The question was: 'Which kind of spirals are we looking at?' So I
investigated the formation and found to my own amazement that the
formation was not based on spirals at all! It turned out to be a clever
interaction of semi circles. A real beauty that will be remembered for
years.















Barbury Castle  England 1999
This very interesting
crop circle appeared in 1999 just below Barbury Castle. Interesting to
look at from the outside, but foremost very interesting if you look
inside. The internal geometry of this formation shows how the different
elements of the formation are not random. The size, shape and place of the
crescents could only be the way they were! It is a showcase example of
what I already earlier noticed at the Winterbourne Bassett formation of
1996.
Read also
Size, Placing and Ratios
in the section
Crop Circle Geometry.









I was so impressed by this formation (also because the effect it
had on the crop the following year and the fact that Donald Fletcher filmed
balls of light in this formation) that I made this into my personal logo!












Construction of 5 fold Geometry
Pentagrams and pentagons
intrigue many people. They think the shape of the pentagram has a special
quality, whatever that is. Pentagonal geometry did also appear in crop
circles. First at the outside.
Read
Pentagonal Geometry
in the section
Crop Circle Geometry
for more information.
In later years crop circles
appeared that were fully based on five fold geometry. Here I show how to construct fivefold geometry.















Bishops Cannings  England 1997
The Bishops Cannings
formation of 1997 is a classic example of a formation that is based on
fivefold geometry. This cannot be overlooked, no matter how hard you try.
And although the formation is pretty straightforward it also contains some
beautiful geometrical elements. Take a look and try to find them for
yourself.















Avebury  England 1994
One of the most famous
crop circles ever appeared near Avebury in 1994. Of course the combination
of a monumental crop circle beside a monument like Avebury contributed to
its fame, but the formation on itself was already stunning enough to be in
the top ranks. I couldn't resist studying its internal geometry
and stumbled on something really special. It turned out that the formation
is not solely based on tenfold geometry but is also interlocked with the
threefold geometry of 'the basic pattern'.















Construction of 7 fold Geometry
Using sticks of equal
length it is possible to make a perfect heptagram, but using ruler and
compasses it is impossible! There is no known method. Though there are
several methods that come close. Here I show a method that is
relatively simple and near perfect. If you use the method the traditional
way, that is with a compasses on paper, you won't even notice that it is
not 100% perfect.















Tawsmead Copse  England 1998
It does not often happen
that a crop circle based on sevenfold geometry appears. In 1998 it did at
Tawsmead Copse. And it was a special one. It was beautiful and it was
based on sevenfold geometry. But I found something that
made it real special. In the Crop Circle Geometry
section under
Construction Lines
you can read what this 'something' was. Here you can find all the
construction steps needed and form your own opinion on this 'something'.















Eastfield  England 1998
Although crop circles
based on sevenfold geometry don't appear often, in 1998 there was more
then one. The first one appeared in the Eastfield near Alton Barnes. It
had an intriguing shape and an even more intriguing internal geometry. The
sevenfold formation at Tawsmead Copse appeared a month after the
Eastfield formation, but the geometry of the Eastfield looked like an
extension of the Tawsmead Copse geometry. It looked like the appearance
should have been the other way round.















Construction of 9 fold Geometry
It is impossible to construct 100% precise ninefold geometry using a ruler and compasses,
though there are different methods that come close. The method shown here is perhaps the most simple,
is almost 100% accurate and has oddly enough a six pointed star as starting point!










