



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 used were a ruler and a pair of compasses. I didn't use the ruler to measure, only to draw straight lines and therefore
I worked 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.




the Basic Pattern
Almost right from the start I noticed that the geometry of many formations was based on the same pattern. The following diagram 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 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 in the section Crop Circle Geometry.




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 in 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.




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 yourself.








Liddington Castle  England 1997
In 1997 there were two formations in the same field just below Liddington Castle. One of them was a little 'Julia set' with the most beautiful lay.
Of course the 'Julia set' got a lot of attention, but I concentrated on the other one. If you look closely you will notice that this formation
does not have perfect geometry, at least that's the way it seems. The irregularity can however very well be reconstructed.




Liddington Castle  England 1997
In 1997 there were two formations in the same field just below Liddington Castle. One of them was a little 'Julia set' with the most beautiful lay.
Of course the 'Julia set' got a lot of attention, but I concentrated on the other one.


If you look closely you will notice that this formation
does not have perfect geometry, at least that's the way it seems. The irregularity can however very well be reconstructed.








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 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.








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.




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.




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.




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.








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 External 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.




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 External 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.




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
next to a monument like Avebury contributed to its fame, but the formation itself was already stunning enough to be in the top ranks.
I felt the urge to study 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 connected to the threefold geometry of the Basic Pattern.




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
next to a monument like Avebury contributed to its fame, but the formation itself was already stunning enough to be in the top ranks.
I felt the urge to study 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 connected to 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.




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'.




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
East Field 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 East Field formation, but the geometry of the East Field looked like an extension of the
Tawsmead Copse geometry. It looked like the appearance should have been the other way round.




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
East Field 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 East Field formation.


Though the geometry of the East Field 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.



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.





