The Continuing Power of Hidden Polygons in the Banded Crop Circles of 2017 A research article by Jack Sullivan.
This is essentially an update of my article of
the 7th
of November 2015
published in the Research Pages of the Crop Circle
Connector website.
That article is titled; “Crop Circles and the
Prevalence of Polygons”. It discloses facts and
evidence of the presence of hidden polygon structures
in over thirty examples of banded crop formations
dating back to 1960, examines the geometry involved
and also the benefits to designers of using such
structures.
Their use by the creators of crop formations has
continued.
This year, 2017 there have been eight
significant further examples demonstrating powerful
logical reasons for using polygon based designs. These
reasons may be seen as intended practical gifts to our
human artists who use geometry in their work in
whatsoever field.
Each of these examples is featured with an analysis
below. They are not listed in the order of the date of
their appearance in the field.
Boreham
Wood. Nr. Winchester 1st
of
July 24, 2017
.
This
formation has two outer bands the proportions of which
are determined by two hidden polygons. The outer one
six sided and the secondary one seven sided. The
polygons provide the division points for the seven
petals and also for the central small hexagon. See the
accurate replica drawing below.
This is a remarkable crop circle design since to
accurately replicate it at any desired scale only
three lines are essential. No physical measurements
are needed. The only tools required are simple drawing
instruments as commonly found in a Students Geometry
Set. Compasses, a Protractor to measure the angles and
a straight edged Ruler, or their equivalents dependent
on the scale of your intended replica. See below
Illustration of the two fundamental Stages involved in
producing an accurate Replica of the overall design.
Based on this analysis it, becomes obvious that other
polygon values than the ones used could be
substituted, or additional bands added using different
value angles to form other polygons. These changes
would enable different, may be more elaborate multi
petalled designs for the central area infill. This is
an example
of the enduring power of polygon based geometrical
design.
Battlebury Hill Nr. Winchester
July 1st
2017.
Battlebury Hill Analysis Drawing.
.
At first sight it would appear unlikely that this
formation has hidden polygons as a design basis but it
is actually another clever construction which utilizes
four three sided
polygons to render it capable of quick and
accurate replication to any desired scale without the
need to rely on measurements other than the sixty
degree angles.
The analysis drawing shows the stages of construction
after five identically sized circles 1 to 5 are drawn
initially to any chosen scale, guided by horizontal
and vertical centre lines.
The
triangular polygons govern the dimensions of the
central discs in the four outer circles which in turn
then govern the widths of the two circumferential
bands.
All other minor details can then be added to this
basic construction to match the field image.
Summer Lane
Broad Hinton. Wilts
28th
May 2017
This small multi-banded crop circle suggests at first
glance that hidden polygons are incorporated in the
design. This is indeed the case and the band widths
are governed by 5 hexagon polygons. There is also one
large 3 sided polygon which defines the size of the
central circle. The six large part-circles covering
the bands may have been added after the formation was
discovered because there is no relationship with the
polygons, and the 6 divisions used to position them
are erroneous in that they fail to fit the
circumference.
“To err is human” as the saying goes
.
The Science Space Centre. Nr. Winchester Hants.
This relatively small banded formation has a hidden
cascade of 7 x four sided polygons governing the band
widths, six of which are divided into decorative
quadrants by having only alternating sections of laid
crop. This would seem to be a simple device but it is
difficult to imagine, if humans were involved, how the
precisely defined lay could be achieved without error
and without damaging adjacent standing crop? See the
marked up ‘Connector’ aerial photograph below.
Thorn Hill 2 .
East Kennet
June 26 2017.
The aerial photo by Jane Barford published by ‘The
Crop Circle Connector’ on the web page for this
formation.
has high resolution with only a little distortion and
is accurate enough to allow an initial geometrical
analysis to be directly applied to a
print-out
of her photo. This is clearly a multi banded creation.
The two half band ends are truly circular and
inserting Chord Lines inside them confirms that they
both hold halves of perfect pentagons. See analysis
replica drawing below.
This
is a very long (approx 200ft.) formation and to
produce a perfectly accurate aerial photo would be
very difficult. Thus there is some ovality of the
circles which distorts the applied polygons.
A
true accurately drawn replica analysis using all the
indicated hidden polygons became a necessity. This has
revealed that the formation is a veritable feast of
hidden polygons, all essential to the overall design,
and again as with all the polygon structured designs
found so far, enabling its logical step by step
process of construction to be determined.
No
measurements are required other than precise
installation of the polygon angles. Any replication
will be true to the original design proportions
irrespective of scale.
This latter statement applies to any crop
formation where polygons are the essential but hidden
element of the structure.
Stage by stage construction. All the hidden structures
are shown as broken lines.
To
create a true replica at any desired scale, only three
identically sized circles are required as shown.
Monarchs Way. Nr. Wooton Wawan. Warks. Aug.7 2017.
This relatively small crop formation, approximately 25
metres. diameter appears to have excrescences added by
others post its original creation. I have ignored them
in my analysis as being irrelevant. The Circle itself
with its strange ‘spoked’ wheel centre features,
despite whatever it is intended to convey, has to be
genuine as proven by the two outer bands which owe
their proportions to hidden polygons.
See my true geometric replica below with apologies for
my somewhat crude attempt at depicting the internal
aspects. The two polygons, One Six sided and One Five
sided again enable reproduction of the correct main
proportions at any desired scale.
Bydemill Copse Nr. Hannington Wilts. August 4th 2017.
The Connector aerial photo image above has some
perceptible distortion but non the less it is good
enough to allow its hidden polygon structures to be
clearly depicted.
The design concept is very similar to the Boreham Wood
formation of the 4th
July.
(please see above)
It is of course much more elaborate with
greater complexity but the same geometrical analysis
applies. The polygons determine the widths and
proportions of all the bands and as with other such
structured creations enable perfect replication to any
desired scale without the need for measurements other
than the angles. The three outer bands also as at
Boreham Wood, create accurate division markers for the
multi petalled design of the central area which is
based on the initial 12 sided polygon split into equal
halves to give the 24 divisions required.
The individual petal outlines are described by 24
circular arcs which have their focal points located on
the inner rim of the second narrow band. I have marked
the radii for two of these arcs on the above image to
indicate how the whole set of 24 arcs can be formed by
working from centre points at thirty degree intervals
in clockwise and anti clockwise directions on this
inner rim.
I am sure that this formation and the other polygon
structured formations could be replicated as sand
circles which would be an exercise no more difficult
than producing them on a drawing board, accidental
errors during the process can be easily erased and
correctly redrawn.
However I am unable to believe that any human
team could repeat the process in an arable standing
crop. The marking out of construction lines which are
to be invisible in the finished creation and the
accurate flattening of the laid crop in the time
available without error is a task
beyond us and our present technology.
I would love to be proved wrong, any takers out
there?
Rollright Stones Nr Little
Compton.
Oxon
August 5th
2017.
This is a further example of the basic design concept
as used at Boreham Wood and Bydemill Copse, ( see
above). The outer 9 sided narrow band governs the
proportions of the other circular components and also
determines the size of the large rectangle, the three
large triangles and the 2 x sets of eight smaller
triangles.
The drawing was developed without the use of
any measurements to a randomly selected outer diameter
using only the measured angles as shown. The exercise
confirmed that as with other polygon structured
formations the design concept enables very accurate
replication of the intended image regardless of field
or camera distortions, provided only that existence of
the hidden polygons is recognized.
With my earlier work on these types of banded crop
formations we now have an archive of over forty such
examples dating back to 1960. There are probably many
more historical examples yet to be discovered perhaps
so far unrecognized from other regions of the world.
It is probably a certainty that as long as the
crop circle phenomenon continues there are going to be
many more to enlighten and amaze us in coming seasons.
They will prevail until we openly accept the
truth of the presence of our benevolent visitors among
us.
JS. September 2017
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