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.
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.
________I_______________I______________I____________
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.
Conclusions.
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 2015.in 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.
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