Okay here is my final work(above). Below is the original.

Pretty done. The steps 1 to 6 are self explanatory on this avebury crop circle of 3rd july 2006.

Nathaniel.

THE SOLAR SYSTEM CROP CIRCLE - MANMADE

Location: Jackaments Bottom, nr Kemble, Gloucestershire. Reported 13th August 13/08/06 Image Steve Alexander Copyright 2006

If its manmade then we shall refer to it as a hoax for the simple reasons below.

My comments in Jun2007:
The thing about this crop circle is simple.
Everything about it has a feeling of a manmade stuff using local tools.
1. It could probably be that those more energy sensitive can not feel anything when in such a crop circle.
2. The orbits are not that smooth showing that the maker struggled on this one
3. The ratio of the planets in relation to the sun is not there. If that was not the intent then what could the other message have been
4. The makers completely shows that they are earthly. They think the sun has only 9planets revolving around it. The makers are thus too local.
5. Quite a struggle to make it. I wonder what there motives where. To get attention so that their produce can sell?
6. I observe however that the skill they used is quite impressive. They had their notes well made. But none the less not too good according to real crop circle standards.

Overall, this is a local crop circle with not 'special effects'.
For genuine crop circles, this is normally classified as a hoax.

Done.

Nathan. Ddumba
Kampala. Uganda\E.Africa.
Sept’08.
http://geometric-options.blogspot.com/

WAYLAND SMITHY CROPCIRCLE

Location: Once again located at Wayland's Smithy, which is essentially a mass grave from some similar catastrophe in 3000 B.C.

GEOMETRIC CONSTRUCTION/ANALYSIS:
Worked out were steps from 1 to 22. Presented below.













Self explanatory.
Nothing much to add.

Done.

Nathan. Ddumba
Kampala. Uganda\E.Africa.
Sept’08.
http://geometric-options.blogspot.com/

ITALY CROP CIRCLE - april2008

THIS CROP CIRCLE HAPPENING IN ITALY

Apr08 folder.

From crop circle connector website, a relationship is made between the one happened in uk2007 and the one in italy 2008.

They have essentially the same construction principles, the purpose may probably differ.

STEP 1:

The figure above is self explanatory. Likewise the remaining 17circles are drawn with their respective centers. Or rather the circle is rotated 18times at equal angles at a fixed point on the very circle.

The whole set anyway turns into the next figure below.

The red and blue concentric circles are drawn basing on points of intersections of the circles. Quite easy. The red concentric circles are the ones reflected in the crop circle.

Out of this comes the series which ends so easily containing 9 numbers, that including zero…

{0,1,1.9696155, 2.8793853, 3.7016664, 4.4114742, 4.9872416, 5.4114742, 5.6712819}

This is true for a number series(9 in tally) showing the diameters of the concentric circles resulting from intersection of the previous circle rotated 18 times, for a case of an 18 sided arrangement.

STEP 2a:

Involved cutting off the rest of the information-geometry in the blue concentric circles and shading alternately. This forms the UK crop circle of 2007.

In this step, kind of thought of a relationship with the areas of these shaded pieces but it turns out this may involve a complexity of equations...to be done some other time when I am more sure that its not a research direction leading to insignificant facts.

STEP 2b:

The Italy crop circle is either of the two below. It’s most likely the second one due to the angle and circle ration similarity with the real crop circle.

Not different from the UK crop circle only that the inner rings are not included.

FURTHER INSIGHTS INTO OTHER AREAS.

The one I called the easiest of all has brought forth many more geometric options out of it. Namely;

1. To do with geometric expansion.

More issues I had taken for granted are being straightened out one by one. For example, the nature of expansions has to be explained explicitly as the methods of doing it is not one. In one method as employed in the revelatorium on the cubit, the expansion or contraction is endless as it involves adding on more levels on top of the existing ones. Whereas a second expansion involving the use of one particular level ends. This is the kind that would be similar to these two crop circles.

2. To do with Number relationships

Do these numbers have anything in them?

The only problem we may have here is that the numbers are based on a base-ten counting which gives so many endless decimal points…take a case of the PI, the golden number, e.t.c My original thoughts of an 18sided star derived from an 18-sided polygon is a counting to the base 18 and not to the base 10. Oh well, since number 18 is more than number 10, then we have to deal with the numbers as they are. However, when I changed these numbers to be based to the base 3 (it being the least multiple of 18) or to the base 6( it being the substance component of Omega in the Alpha&Omega cube and sphere), this is what turned out [to come later]

3. The concentric blue and red circles

The concentric pattern kind of rings a bell but still fuzzy. Talk of a stone dropped in water.

4. The full complete pattern would look as below.

The red part is the one in crop circles in question above where the blue component is the unrevealed part in the crop circles. It’s eye pleasing, isn’t it?

5. Curvature Aspect

Whenever I look at the second diagram in step 1, I feel a sense of curvature as in a bowl kind of shape coming in. The sense is the one I use in trying to introduce to 3D- component in the figure. For example, a net in curvature. I’ve done this before with a particular shape again arising from crop circle inspires. But this later.

CROP CIRCLE: SWITZERLAND, JUNE 20, 2008

<>
Major interests in crop circles: esp. are those involving a polygon and a circle creating nice geometric art.
It follows three simple processes
1.Trace
2.Understand the concept
3.Reconstruct

CROP CIRCLE: SWITZERLAND, JUNE 20, 2008

From http://www.cropcircleconnector.com/ : KANTON THURGAU - exact location withheld by farmer's request - SWITZERLAND, JUNE 20, 2008
Formations measures approx. 100 meters in diameter. Investigation by KORES (www.kornkreise.ch) pending.

The blueprint of this crop circle was traced so easily. But probably the initial design was not the easy one.

Tracing system:

Tracing it back (see figure below), it was easy to tell that those curves were part of a circle and not a spiral, involving the use of three separate sized circles with the underlying geometry being a pentagram.
The smallest circle appears three times, the immediate once and the largest thrice.
So in terms of usage, Smallest :immediate: Largest = 3:1:3
In terms of size, Smallest to immediate to largest circle = 1:2:4.
[Which reminds me, in concrete construction, British standards, 1:2:4 is a common mixing ratio of Cement:Sand:Aggregates ratio in construction of columns and slabs known to produce a concrete grade 25N/mm2 if using cement class 32.5N with well grades aggregates(sand/stones)]

Noting that the pentagram is normally abused by disoriented spiritualists, this design we could say was out there to reduce some of the negative inception that it has been used for. The pentagram in itself is an important spiritual principle which I would loosely relate to a nice Mercedes benz all but used by robbers to do negative acts of robbery where the benz gets loosely associated with robbers and yet when used for good purposes, the benz would be such useful in doing useful works for creation. Of which when the benz’s positive potential is realized by the ordinary person it can be such a relief thus drawing away the mystery from the negative side. Such is the pentagram. From the positive side of it, this particular crop circle might be a very good initiative to reduce much of the negative karma still attached to the pentagram geometry via the thoughts of the religious zealots to the mass consciousness which has been duped to think of it as a tool for voodooism and cheap occult practices. Otherwise it’s absurd to think of locking a mighty soul in a pentagram and harnessing the spiritual power thereof to feed the souls out of the system of receiving manna from heaven who aim at controlling governments and its population.

Reconstruction:
From the tracing system, we had known how to reconstruct the said geometric art piece.
Start off with the pentagram and carefully arrange these three circles, behold the wonder, it is pure geometric art.

Or in a single step construction:

Easier said that they who did it have the interests of creation at heart. From this viewpoint you have fake or real crop circles though I’ll be quick to point out that particular crop circles do have a Godly love component manifesting itself in form an electromagnetic environment creating interesting experiences from the people nearby or within such crop circles. ‘Good willed mind’ gets you to definitely enjoy such experiences. One person reports that the location of the crop circle may be strategic enough to flush out evil/voodooism in the area.
That was good Crop circle maker.

Done.

Nathan. Ddumba
Kampala. Ug.
Sept’08.

CROP CIRCLE AT Etchilhampton Hill, AUG2006

Crop circle at Etchilhampton Hill, nr Devizes, Wiltshire.
Reported 15th August 2006

[PIC ..]

First impression:
It looks like an elastic sheet, originally a circle, being stretched from four corners. I was hoping to find a relationship between the pulled-in area and stretched-out area. The closest ratio of their areas is 40:7 or simply 5.717219

Construction: Divide the X and Y axis length into 10parts and do a 'primary/elementary school' joining of criss-cross lines...this is what you get(below):

[PIC]

This geometry can also be seen from a three-dimensional format. One way is to view it as a pyramid but with its walls not touching the base (see below)....the square is for construction aid.

[PICS 2NO]

It's a pyramid, from a three-dimensional outlook, but that circle!. Chosen was a 45deg for the sloping edges, I see no principle on the choosing yet, may be the circle would be helpful in that regard. But for now, this is where I end it at.
Meanwhile, this would make a nice building structure based on such principle within the crop circle. Except that modern form of building and interior decoration is not well place to deal with such uniqueness in structure, and so expensive it would be....thinking about designing one such building though..
Meanwhile, I have not fully connected how the circle comes into the picture.
....After contemplating: Well since in the original crop circle, the circle is shaded, it would as well, vaguely stated, represent a sphere in which case, we can modify our three dimensional models to look as follows:

[3PICS]

Hmm...somehow now the sphere comes into play when the selected angle for the edges is 45deg. It touches the most curved part of the curve formed by criss-crossing lines but not very exactly yet. It would thus be tempting to say that the crop circle maker was based the design from a three or multi-dimensional geometric artifact upon which the crop circle was created.

[PIC]

However this may be just a bit of this.
Earlier on another geometric study had been made on yet another crop circle whose artifact is to be described further...possibly connecting both crop circles. Now it would be tempting to think of the maker having used the same artifact in three dimension to create different views in two dimension.
　
　
Nathan.

GEOMETRIC OPTIONS

My first blog on this,
The options include but not limited to;
- Geometry in the cosmos/universe as inspired by the Revelatorium(www.revelatorium.com ) and Cosmic astronomy (www.cosmicastronomy.com) - a must read
- Geometry from crop circles.
- Insightful geometry from which arises all other.

Everything is geometry. Options are much more...to come much later.

[to be edited further]

Nathaniel.D,M.