Crop Circles and the “Prevalence of Polygons”.

An update of the article published on The Crop Circle Connector Website Research Pages In August 2015

The Catherine Wheel. Alfriston. .East Sussex. 1995. From :” Fields of Mystery”, book by Andy Thomas. Photo: by Michael Hubbard.  The design here uses an infinity of concentric squares to precisely define the proportional dimensions of each of the bands. If means were available, the design could be expanded out into the universe or contracted into microscopic dimensions and the proportions would still be true. The geometric analysis, see below, shows that the tips of the four spiral arms are in conformity also. The radii of the tips of the arms is at dimension c2-b2.which is 1.414 x c1 and c1 is 1.414 x c in the base triangle.
My August 2015 article covered seven examples of invisible polygon structures used to fix the proportional band widths in multi-ringed or multi-banded apparently simple crop formations dating back to the 1990s. I have since discovered that there have been many others over a far longer period, which have gone unnoticed because of the general ignorance, including my own, of the possibility of such geometrical structures being hidden in these commonly occurring circular patterns.  This present article presents the results of further of research into all the available archives I could find, including that of ‘The Crop Circle Connector’.  A full list containing text details of some 32 proven examples with their sources, locations and dates of appearance can be found below.  In the Catalogue of illustrations,  I have provided images of  analysis drawings alongside the relevant field image of the individual crop circles. These joint images enable interested readers to carry out their own analysis in each case, using the method explained in the original August 2015 article, or using the information in the ‘Practical Polygons Table’. See below.
The “Catherine Wheel” illustration is a prime demonstration of the way a   hidden polygon structure precisely fixes the multiple band widths.  The principle is common to all of the listed formations, regardless of the  number of polygons each one contains.


Below is a similar Geometrical Analysis for the Longwarren, Chilcombe  formation of 1990. There were a total of six hidden polygons. Five were 7 sided and one 4 sided, the latter not shown here. The basic common triangle is different only in that the angle ‘B’ is 25.7deg., half that of the full chord which is 51.4 deg. for a seven sided polygon.


The following list can be used either to analyse a multi-banded formation in the field or design a polygon structured formation yourself.
 Practical Polygons
Number of      Subtended          Sine Constant       Deg. Angle
Polygon         Angle deg. at       For angle and       of half of
Sides             Circle Centre       Chord Length       Subtended
                                                   Per Unit Dia.        Angle.                                  
      3               120                        0.866025             60
      4               90                          0.707106             45                   Example of Use :-
      5               72                          0.587785             36                    A five sided polygon
      6               60                          0. 500000            30                    of 100 foot diameter 
      7               51.4                       0.433883             25.7                 would have a chord
      8               45                          0.382683             22.5                  length of 100 x Sine
      9               40                          0.342020             20                     Constant 0.587785 =
      10             36                          0.309017             18                     which gives a result:
      11             32.7                       0.281732             16.35                58.7785 feet. This is
      12             30                          0. 258819            15                     the length of one side
      13             27.7                       0. 239315            13.85                of  resultant Pentagon.
      14             25.7                       0.222520             12.85
      15             24                          0.207911             12
      16             22.5                       0.195090             11.25
Where the radius and the chord length are known, the subtended angle at the circle center can be found as follows:- The Sine of the angle is half the chord length divided by the radius of the outer edge of the ring containing the polygon, e.g. where the total chord length is 100 the sine of the angle is 58.7785 x 0.5 divided by 50  =  0.587785 and Sin-1 coverts this to  35.999982 deg. (36 deg.). This is one half of the total chord length subtended angle of 72 deg.   360 divided by 72 = 5, so we now know we have a five sided polygon. This process must be applied to each of the bands in a formation to reveal the full sequence of the structural polygons present.
Multi- Banded Crop Formations Proven to Contain Geometric Polygon Structures. With Locations and Dates from 1960 to Present Day. Archival Sources.
1960 .June.3rd Poplars Farm. Evenlode. Gloucestershire.3 polygons.Source: Data record in “The Secret History of Crop Circles”, book by Terry Wilson
1967 Bowden, Alberta, Canada,2 polygons. Source: Data record in T.Wilson’s Book “The Secret History of Crop Circles.
1987  Winterbourne Stoke.2 polygons. Photo by Busty Taylor. From ”The Crop Circle Enigma” book by Ralph Noyes, also The Crop Circle Connector Archives. This design has appeared five times, see Cheesefoot Head caption below.
1987 July. Cheesefoot Head.2 polygons. From photo in book “Vital Signs by Andy Thomas.This is an identical replica of the formation at  Winterbourne Stoke  (see above.) and which appeared here in 1986 and also in 1989 at the “White Crow “event. Its latest appearance was at the Rollright Stones site, Oxfordshire in July 2015.
1988 June. Longstock. Near Andover. 4 polygons. From The Crop Circle Connector Archives.
1988 Aug. Cheesefoot Head. 4 polygons. Photo by Busty Taylor. From same book by Ralph Noyes. (see above.)  Subject of a BBC TV. Programme. This formation was an identical replica of the Bratton formation of 1987.
1990. Longwarren, Chilcombe Hants. 6 polygons. 5x 7, 1x4. Source : The Crop Circle Connector Archives.
1991 July, Woodford. Northamptonshire. 12 Polygons. 1x9, 1x3, 1x4, 3x9, 1x8, 3x7. 1x6 and 1x5.  From book by Pat Delgado.”Crop Circles Conclusive Evidence”
1992  May.23rd.Cherhill Wilts.2 polygons Source The CCC Archives
1992 May 23rd.Chilbolton Nr.Andover.3 polygons Source: The CCC Archives.
1992 May. Westwood Wilts. 4 polygons. Source:  The CCC Archives.
1994 July South Harting. Photo by Steve Alexander. 4 polygons. Source “ Fields of Mystery”. book by Andy Thomas *
1994  Aug East Dean. West Sussex.3 polygons. Photo by Steve Alexander. From “Fields of Mystery.” by Andy Thomas.
1995  May. Southease. East Sussex. 4 polygons. Photo by  Michael Hubbard and measurements by Andy Thomas.From “Fields of Mystery. Book by Andy Thomas.
1995 May “The Catherine Wheel.”Alfriston. East Sussex.8 Square polygons.Photo by Michael Hubbard. From: book: “Fields of Mystery by Andy Thomas.
 1995  June 39th Felbridge  West Sussex. 6 polygons in two circles of a group of three. From book: “Quest For Contact” by Andy Thomas.
1998 Aug.2nd.Avebury Wilts.Circle with a single triangular polygon. From: The CCC Archives.
1999 July17th Morcott. Leicestershire. Multi band, 6 polygons with spiral. From: The CCC Archives. Photo by P.J. Brookman.
2000 June11th.Beckhampton Nr. Silbury Hill.6 polygons. From The CCC Archives. Photo by Steve Alexander
2001  May 12th. Winchester Old Hill Nr. Warnford. 4 polygons From The CCC Archives.
2001  Aug. 18th. Riplington.West Meon. Hants. 4 polygons. From The CCC Archives
2003  July 19th  Beckhampton. Wilts. 9 polygons. From: The CCC Archives.
2004 June 3rd.  Shillington. Beds.3 polygons. From The CCC Archives.
2005 July 31st. The Ridgeway. Nr. Avebury. 12 Polygons. See illustrations. From The CCC Archives.
2005 Aug.3rd.Collingbourn. Wilts. 8 polygons. Photo by Steve Alexander
2012  June 25th  Cherhill. Wilts. 6 Polygons From The CCC Archives.
2012 Aug.9th..Cheesfoot Head Hants.3 polygons. From: The CCC Archives.
2013 July 6th.The Ridgeway Nr Avebury. 8 cascaded six sided polygons. 
2014 Aug.Gussage St. Andrews. Nr. Sixpenny Handley. Dorset. 5 polygons.
From: The CCC Archives.  Photo by Lucy Pringle.
2015 Sept.15th.Nr. Hoeven Holland. Circle attached to a smaller spiral formation.
2 polygons. From: Robbert van den Broeke’s website. Drone photo by Michel Koenders.
Catalogue of Thirty Three Multi Banded Crop Formations proven to contain hidden polygon structures, with locations and dates from 1960 to present day.


There is no photo available for this formation which appeared at Poplars Farm. Evenlode. Gloucestershire on the 3rd. of June 1960. The dimensions are quoted in “The Secret History of Crop Circles” book, by Terry Wilson. Outer ring 23ft.diameter, Inner ring 16foot diameter. The band widths are stated to be approximately 4 inches wide. There are three polygons: 1x 12 sided. 1x 4 sided and 1x10 sided. These neatly confirm the data and would determine the actual band widths as shown here to scale.
The next illustration is the only other in this catalogue which, because no photo is available, is based entirely on data recorded at the time of the formation’s appearance in Alberta, Canada in 1967.


Bowden. 1967 Alberta Canada.  From Terry Wilson’s book “The Secret History of Crop Circles”. The site records  is that the outer ring was 10 mtr. diameter and the band width was 0.2 mtr. wide.  The drawing above is a true scale representation of these dimensions resulting in the exposure of the 2 hidden polygons. 1x 10 sided and 1x3 sided.                                


  There have been at least 4 appearances of this next simple multi-band formation.  Winterbourne Stoke 1987. two polygons. 1x7 and 1x5, From “The Crop Circle Enigma” by Ralph Noyes. Photo by Busty Taylor.  This formation also replicated identically at Cheesefoot Head Hants. In 1986 and 1987, and  at The White Crow event in 1989 and at the Rollright Stones Oxon in July 2015. Refs. The book ‘Vital Signs’ by Andy Thomas, and  The Crop Circle Connector Archives for 2015.        


Longstock. Nr. Andover. June 1988. 4 polygons.1x9,1x5, 1x7 and 1x4. Source: The CCC Archives. This appears to be similar to the following Bratton formation but the wider fourth band affects a change in polygon values.                             


Bratton.  Castle.  August 1987. 4 polygons. 1x8, 1x5, 1x7, and 1x5. From book by Raph Noyes, “The Crop Circle Enigma”. Photos by Busty Taylor. A replica of this also appeared at Cheesefoot Head in Aug 1988 and it was featured in a BBC TV program shown on Southern TV. During filming, one of the TV Cameras was inexplicably and expensively damaged internally, as reported later.                             


Longwarren. Chilcombe Hants. 1990  6 polygons. A sequence of 5 sided,  plus 1x4. Source: The CCC Archives. The ‘flats’ on bands one and three on the field image could not be produced with a measuring tape anchored at the disc centre. The distortion may be due to a local electrical cable or underground water source.                                 


Woodford. Northants. July 1991. From book by Pat Delgado “ Crop Circles Conclusive Evidence”. There are a total of 12 polygons hidden in the field formation . 1x9, 1x3, 1x4, 3x9, 1x8, 3x7, 1x6 and 1x5.  Compare this with the 2005 Ridgeway Nr. Avebury formation which is a near but not quite replica with twelve polygons also, but with  different polygon values evidenced by obviously different bandwidths. 


Cherhill. Wilts. May 23rd. 1992. 2 Polygons. 1x8 sided and 2x3 sided. Source: The CCC Archives.                                 


Chilbolton Nr. Andover May 23rd. 1992. 3 Polygons. 1x7 sided 1x4 sided and 1x5 sided. Source: The CCC Archives.                                 


Westwoods Lockeridge Wilts. May 1992. 4 Polygons. 1x7 sided, 1x5 sided, 1x9 sided and 1x4 sided. From: The CCC Archives. Photo by Stuart Dike.                                                  


South Harting.  Nr. Chichester. Sussex. July 15th 1994. 4 Polygons: 2x6 sided,2x 5 sided. There is conflict between my  measurements taken from the obviously distorted photo and  the reported field measurements. Bands 1, 2, 3,and 4 are said to be 3 ft. wide. The central flattened disc scales at 24 feet diameter, which conflicts with the recorded site measure of 25 feet. The drawing shows the most logical structural polygon fit. Source “ Fields of Mystery” book by Andy Thomas. 


East Dean. West Sussex. August 8th 1994.  3 Polygons. 2x5 sided and 1x3 sided. Source “Fields of Mystery” Book by Andy Thomas.  Photo by Steve Alexander.                                           


The Catherine Wheel.  Alfriston. West Sussex  May 31st 1995. 9 hidden polygons, all perfect rectangles.  This formation is explained in detail near the beginning of this article.  See the General Geometrical  Analysis included. ­                                  


Southease. Nr. Lewes East Sussex. May 8th. 1995. 4 Polygons. 2x4,1x5 and 1x3. From: “Fields of Mystery”, book by Andy Thomas                                          


Felbridge. Surrey. June 30th.1995.Large Multi-band:.4 Polygons. 2x4 sided and 2x5 sided From: “ Quest for Contact”, book by Andy Thomas.                                       


Felbridge. Surrey.June 30th 1995. Smaller multi-band. 2 polygons x 4 sided. From: “Quest for Contact”, book by Andy Thomas


Avebury. Wilts. August 2nd.1998. One single triangular Polygon which fixes the diameter of the central disc. From: The CCC.Archives.  

Morcott. Leics. July 17th. 1999.  6 Polygons. 1x9 sided 1x6, 1x5, 1x3, 1x9, 1x3. The apparent central multi-rings band ,4 is in fact a a single track Spiral.  The formation diameter was measured at 200 feet. The outermost flattened band was 2.5 feet wide. Photo by P.J. Brookman, In The CCC Archive                                 


  Beckhampton. Nr. Silbury Hill June 11th. 2000. 7 Polygons:  1x12 sided, 1x4, 1x11, 1x5, 1x9, 1x5, and 1x9.  From The CCC Archives. Photo by Steve Alexander.                                            


Winchester Old Hill. Nr. Warnford. May 12th. 2001. 4 Polygons:  1x4 sided, 1x5, 1x4, and 1x5.  From: The CCC Archives.                                   


Riplington. West Meon Hants. August 18th. 2001. 4 Polygons:  2x5, 1x3, and 1x5. From: The CCC. Archives. The double ‘Grape Shot’ seems to be a designer signature often seen near bye extraordinary Crop Formations.                                      


Firs Farm. Beckhampton Wilts. July 19th 2003. 9 Polygons: 1x6 sided, 1x8, 1x4, 1x6, 1x5, 2x6, 1x3, and 1x5.  From: The CCC Archives.                                         


Shillington. Bedforshire June 30th 2004.3 Polygons:  1x 8 sided, 1x6, 1x7,  From The CCC Archives.                               


The Ridgeway.Nr. Avebury Wilts. July 31st. 2005.12 Polygons: 1x9 sided, 1x3, 1x4. These are shown in the drawing above left.  For the other nine see the enlarged centre section drawing below.


The Ridgeway. Nr. Avebury. Wilts. Enlargement of Centre Section showing the nine polygons which determined the widths of the bands seen on the right. The polygons are: 1x9 sided, 1x7,1x9, 1x7, 1x7, 1x6, 1x7,1x6 and one more 1x6. Source: The CCC Archives.                              


  Collingbourn August 3rd. 2005. 8 Polygons. 1x5 sided, 2x6, 2x5, 2x4, 1x5, From: The CCC Archives. Photo by Steve Alexander.


Cherhill. Wilts. June 25th. 2012. 6 Polygons: 1x9 sided, 2x8, 1x4, 2x5. I five pointed Star.which fixes the diameter of the central Disc. From The CCC Archives.                                 


Cheesefoot Head. Nr. Winchester. August 9th 2012. 3 Polygons: 1x10 sided, 1x5 sided and 1x6 sided.  From: The CCC Archives.

The Ridgeway Nr. Avebury. July 6th.2013.  A cascade of 8 six sided polygons. Source: The Crop Circle Connector Archives. There are many photos from different contributors on the archive page for this, grateful thanks to all, but unfortunately all of them have some degree of distortion mainly due to the large diameter of around 180 ft. This distortion made  accurate scaling of the  image dimensions for analysis difficult. The true polygon sequence was revealed only after numerous attempts to make sense of the images to when it finally became very obvious                                          


Gussage  St. Andrews. Nr. Sixpenny Handley.Dorset. August 2014. 5 Polygons in Multi banded central area. 1x6 sided 3x5 sided, and 1x4 sided. Photo by Lucy Pringle. 


Formation in Mustard Seed. Attached to a similar sized spiral Near Hoeven. Holland.
15th September 2015. See Robbert van den Broeke website. 2 Polygons:  1x 6 sided and  1 triangle which fixed the diameter of the central disc. Photo by Michel Koenders. 

In the course of research for this article I analysed five more historical formations which on first sight seemed to hold promise of possible hidden structure as seen in the above illustrations.  None of these exhibited the expected structures. They are pictured below:

The first in the top row appeared at Kiddlington .Oxon in June 1999. There was no photo but the dimensions were reported by Jeremy Kay. Any attempt at relating them to a Polygon structure sequence fail, due to conflicts within the stated measurements.

No.2 top row appeared at Stanton St. Bernard. Wilts in June 2000. It is not possible to construct a polygon sequence proportional to measurements scaled from the aerial photo.

No. 3 top row appeared at Stanton Prior. Bristol and was photographed by Stuart Dike.
A full chord across band 1 subscribes an angle of 80 degrees at the circle centre. This cannot be the side of any polygon. Band 2.does however contain a four sided polygon which neatly fits the diameter of the central disc. This may be a random occurrence and does not qualify the whole formation as one based on hidden structural polygons.
No. 1 in row 2 appeared at Chiseldon in June 1999. It was 200ft.diameter. Photo: Peter Sorenson. Band 1 appears to hold a 12 sided polygon but the actual width would need to have been recorded in the field at the time to prove this. Similar formations with very wide bands usually have a triangular hidden polygon which would accurately circumscribe the central disc. This could not happen here .The proportions are wrong and the disc is too big. This formation does not hold hidden polygon structure.
The last picture, No.2 in row 2. is Peter Sorenson’s photo of the demonstration circle made by Doug Bower, below Milk Hill in 1999. It is not possible to fit any polygons into either of the two bands here, which suggests that the notorious hoaxers had no knowledge of the existence of hidden polygon structures in the many like formations which appeared during their claimed active period.  Perhaps their blatant duplicity and that of their  conspirators is now exposed.
This research has exposed the historical overwhelming preponderance of ‘roundel’like  crop formations holding hidden polygon based structures, rather than being a collection of random sized rings  Far from being a rarity, the structures have been and still are a common basic design feature of most if not all multi-banded crop formations, dating as far back as the ‘Evenlode’ event in June 1960 and over the long period when aerial photography was rarely used, which these days can reveal aspects formerly unsuspected.
 The numbers of sides of the sequenced polygons in a formation can be considered as a unique identification code, or a recipe for that particular formation. Knowledge of a particular code enables identical proportional replication, at any chosen overall dimension in any place in any media. For example The Beckhampton formation of 19th July 2003 had nine polygons with sides numbered : 6,8,4,6,5,6,3,5.  This number sequence, and the number sequences of all other known polygon structured formations is all that is needed to enable precisely accurate replication. It is like using a Pizzeria menu code to order your favourite meal. You need only to additionally, specify the size of the meal you require, and your dinner is served Maybe this automatic coding feature is why the polygon structure principle is used. There are now in the above records quite a few formations which have been duplicated at different times and locations. Having coding records obviously makes duplication or replication at any time a simple operation, especially if computerized.
There is also a ‘puzzle challenge’ element to these hidden structure formations. This has been present from the beginning but the designers seem not to have stressed this before the West Kennet Longbarrow event seen in July 2014. This was the final replicated appearance of five previous formations dating back to 2011. The repeated appearances seemed to reflect insistence for us to pay more attention to this design. Mr Andrew Edwards did just this, and was then able to reveal the sequence of hidden polygons. Reference my previous ‘Hidden Polygons’ article of August the Crop Circle Connector Research Pages.
Finally, I am now forced to realize that the mind or minds responsible for these internally hidden structured crop formations are not human. The technical ability to create and execute the extremely precise  geometric relationships in our fields overnight, in all weathers is beyond us. If groups of talented humans are involved, as so persistently claimed by certain groups and individuals, they have to fully explain many seemingly inexplicable facts:-
Why are the creations generally always faultless, achieved without errors or accidents?  
The multiple rings and bands would entail the need of a central operator with a very firm anchor point for a rope or tape. On completion how does this operative, short of using a helicopter, get out of the formation without leaving tell tale tracks and damage and how could the absolutely necessary precise measurements needed, be guaranteed where the crop has long flexible stalks and a maybe a distorting wind is present?
 Possibly the most difficult question to answer is, how has the secret of the hidden polygon structures with the exception of very few instances, been un-noticed and un-remarked for some 55 years? It is a basic human trait to want discoveries acknowledged. Normal people and aspiring Artists want to make their name known in the world, which is why internet social sites such as Face Book are so popular. To not pursue these things does not accord with our common psychology. We have to conclude that the often claimed talented landscape ‘Artists’ responsible are a fiction.
The usual ‘get out’ used by the hoaxers and fakers to answer these questions is that the real evidence and confession of their deeds would lead to prosecution, but this excuse cannot apply here because of the time scale involved. Authorities would be now unconcerned and expensive investigations would be deemed pointless. The time for such excuses is over.
Jack Sullivan   November 7, 2015.


Mark Fussell & Stuart Dike

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