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For the schoolchildren of tomorrow

Crop Circle Geometry:

I dedicate this page to Paul Vigay, Genius of the British crop circle world.

Paul, you knew too much.


The Circlemakers have an interest in Astronomy as well as geometry, which may remind us of the traditional role of the mathematicus, before modern science arrived on the scene. A study of this topic will allow us insight into the Intelligence which is creating the formations – always a more interesting question I think, than how they are made! As my book, Crop Circles The Hidden form, has now gone out of print, we here develop its astronomy chapter.

I. The Three Scorpions of '94


All the great scorpion-formations of 1994 had their ‘sting’ missing.

a.       Scorp24May.jpg 24  May 1994, Silbury Hill  This formed ‘on the Full-Moon night of a Lunar eclipse’ i.e the night of 24/25th. There are lunar - eclipse-type themes in this formation. The Moon, in the Scorpio constellation, passed that night over the star Antares, ‘Heart of the Scorpion’.

b.      Scorp8une.jpg8 June at Lopcombe Corner, near Salisbury, two weeks later, at the New Moon: ‘ the small ‘grapeshot’ near the ‘kink’, or ‘bend’, in the tail of this formation corresponds perfectly with the large stars adjacent to the corresponding part of the actual [Scorpio] constellation’. (NB, I’m here drawing heavily from Kris Sherwood’s Scorpius Hour article (1), and using Ed Sherwood’s silhouette images with kind permission).

c.       15 July 1994   Bishop Cannings, near Devizes, Wiltshire: a 640 ft scorpion.

The giant star ‘Antares,’ Heart of the Scorpion, Cor Scorpionis, is strongly emphasised in all three scorpions. The lowest part of the Scorpion in the heavens, ie the ‘sting,’ is not ever visible from England – it’s a summertime constellation, which always remains low on the horizon – and this was as it were ‘chopped off’ from the croppie scorpions, ie they weren’t quite complete.

Scorpio15.7.94.jpgThe Moon passed across the Scorpion constellation during the impact process, shown in two of these glyphs..

II Comet Impact on Jupiter
17 July 1994 - Moulsford

CometintoJupiter.jpginpact23July.jpgImpact.jpgThe comet Shoemaker-Levy 9 crashed into the planet Jupiter from July 16 to July 22, 1994: as it approached it disintegrated due to Jupiter’s huge gravity field, breaking up into 24 particles. ‘Its biggest impact scar left several dark rings with a dot outside of the centre’ (Red Collie’):

23rd July ‘impact’ images:


Insight dawned across the Atlantic: “I was living in California when I made all of the discoveries in the article, and I began making them as the crop circle season of 1994 progressed. I first associated a '94 crop circle with the comet collision when I saw an early so called "String of Pearls" formation comprised of varying sized circles in a straight line. I'd seen aerial footage of that formation and the May 24 Scorpion, with some others as well, on CNN News in late May. It was within a week following the June 8th Scorpion that I knew for certain it was Scorpio and a "conjunction" with the comet collision being referenced, and it confirmed to me it had been in many formations up to that point. I also had found the stars of Scorpio that corresponded to the grapeshot in it at the same time and was amazed. It was then clear to me the progression of the event was being shown in the fields and the symbols were "morphing" as the impacts began. When Moulsford appeared I immediately checked the Skychart and confirmed that the Moon had passed between Scorpio's claws and Jupiter the night it most likely appeared.. In the summer of 1994 as the Shoemaker-Levy 9 Comet was fatally impacting into Jupiter, Jupiter’s orbit positioned it in the sky directly in line and in front of the “claws” of Scorpio.’ Jupiter was then quite near to the Scorpion constellation in the sky. ” (Kris Sherwood, letter to author).

III Galaxy
23 July 1994 - West Stowell, Wilts
  Did this design represented a fourfold conjunction of Mars, Saturn, Jupiter and the Moon, which was going to happen on 6 April, 2000, between the stars of Taurus and Aries? That was claimed by Jack Sullivan:  This grouping was briefly visible after sunset, above the dim constellation of Cetus the Whale. (3) A large solar storm was visible on that day and Andy Thomas witnessed an aurora in the sky on that night: ‘I was lucky enough to witness this effect as a strange shifting curtain of red light above Alton Barnes,’ (quoted in Geoff Stray Beyond 2010, p.177). An earlier ‘galaxy’ formation came on 1st July 1994 at West Kennet in Wiltshire.

b. Seven Sisters  4 August (or 8 August, Sorensen) 1994  Froxfield, Wilts.

Did this represent the Pleiades? Quite how people see ‘seven’ in the Pleiades cluster is always a bit of a mystery. This group of stars has been the focus of far more stories and legends than any other in the heavens.



IV Thirteen Moons
14 August 1994
14 August 1994 The Moon joined Jupiter in the sky on this day: does it depict ‘the Sleeping Dragon’ curling up after all the action is over? Or, maybe it expresses the sequence of 13 orbits of the Moon each year (See below, IX)


V Moons in the Year
Danebury, near Andover - 16 June 1995
There are on average twelve and a third lunar-month cycles each year. Thus, for a lunar calendar, every third year or so an extra 13th mo(o)nth has to be added in, to keep the months and years in synch.


A ‘solution’ to this was given by the Circlemakers, in their charmingly pictorial manner, with twelve half-moons in a circle of the solar year, and a gap signifying the days left over. Next to this was a line of seven rings. What were they for? The Metonic cycle of nineteen years links together the year and month, and has been used for two and a half thousand years to compute the calendar. That twelve of its years have just twelve lunar months in them, then the remaining seven each have a thirteenth month added in. That keeps them in step. We could write ‘Meton’s equation’ as:

Year / Month = 12 7/19

The two sacred numbers twelve and seven thus appear in this formation, a pleasant image of the Metonic Cycle.

VI Inner Solar System
Tichborne, Hampshire - 20 June 1995
Like a dry run for the famous glyph which appeared a week later, this scruffy-looking formation showed the four inner planets, plus a highly eccentric mercury orbit. Did it represent a specific date in the year 2000, when that alignment would happen? ( ) If so, Mercury’s orbit has to be way out. An even more unfocussed ‘inner solar-system’ image appeared on that same day in Bishop’s Sutton, Hampshire, nightmarishly chaotic. Who said the Circlemakers don’t need to practice?



VII.  Asteroid Belt 

26 June, 1995    near Winchester, Hants 

      This classic masterpiece depicted the inner solar system. It showed the planetary orbits as thin rings of standing wheat, about a foot wide. It also depicted planetary orbit radii, eccentricities, perihelion as the orbit-position closest to the Sun, Ceres as the largest asteroid, and heliocentric plantary longitude.


Zodiac.jpg        Yes, Earth is missing … but the positions of the inner planets are shown, together with Mercury’s perihelion position (from ‘helios’ sun and ‘peri,’ near). Around the perimeter was a pretty ring of asteroids. Did the planetary positions define one particular moment - when it formed (as claimed by J.Rasool: Andy Thomas, Vital signs 1998)?


          Let’s start with a diagram of the relevant planets at the time of its formation against a sidereal zodiac, so that the starry constellations are behind these signs. Mercury’ perihelion lies in the stars of Taurus as shown, while Venus was then at two degrees of Taurus. The crop formation doesn’t quite show these as the right way round! But, Venus and Mars are correctly positioned. In the heavens, one sees while facing South the zodiac constellations arched across the sky, such that Taurus is to the right of Aries, and thus the familiar sequence moves round clockwise. That is the way this zodiac circle is here represented.


Planetdist.jpg          The orbits given in this formation of the inner planets plus Ceres, the biggest asteroid, are remarkably ‘true.’ Mercury’s orbit is highly eccentric, whereas Venus’ orbit is almost solarsyst.jpgperfectly circular. Earth’s is fairly circular too, coming about three percent closer to the Sun at our perihelion (in midwinter). Mars’ big eccentricity is also indicated in the diagram. The radii of the circles representing the planets are remarkably accurate, especially if the distance of the asteroid belt is taken into account, as the graph shows.


Asteroid Belt.bmp        This formation contrasted the closely circular orbits of Earth and Venus, with the far more elliptical orbits of Mars and Mercury. It correctly depicted five different relative distances from the Sun, and the degrees of eccentricity of the orbits involved. Finally, it showed fairly well the heliocentric positions of the Sun and three planets around the time of its formation.


During the 1990s astronomers have discovered many new planets in other star-systems, but all with far more eccentric orbits than the planets of our solar system. So, perhaps this formation is telling us that there is, after all - no place like Earth.


A replica of this formation was made as part of the film, ‘A Place to Stay’ with M.W. et al. on 4 August 1998. Some said it depicted the Venus inferior conjunction of 16th January, 2008 (argued by Jack Sullivan, see Geoff Stray Beyond 2012, p.178)

eastmeonEarlyJuly 1995.gif


VIII. Geomagnetic field     mid-July 1995 East Meon, Winchester   

This may show the ionosphere and Van Allen radiation belts that surround Earth.




IX – Sidereal Moon                        29 June 1997 Meon Valley, Hamps  

         The Moon orbits around Earth just over thirteen times each year, in its twenty-seven day ‘sidereal’ cycle. The equation is 365 ÷ 27.3 = 13.4, and the diagram shows this. It moves thirteen times faster than the Sun in the sky, and covers thirteen degrees of the zodiac per day. Thirteen is thus a lunar number and reverberates through folklore in this way – ending up as the unlucky number! The Sleeping Beauty fairytale starts off with a King who has to invite the thirteen wise women to his daughter’s baptism, but only had twelve golden plates …the thirteenth was left out, and so became ‘unlucky.’



X. Lunar month

                          4 July, 1997, New Cheriton, Hants

      The Circlemakers are enchanted by Selene’s sphere and never tire of depicting its phases and meetings with the Sun. One could not count the formations on this theme! A small and little-appreciated formation showed the twenty-nine days of the lunar month, its monthly meeting with the Sun. The average length of the female cycle is also of this length: between twenty-nine and thirty days (and not twenty-eight, as many believe).


         From each side, faint dots cascaded towards the centre, indicating a maximal influence of Luna on the Earth, twice a month. Tides are then highest, at Full and New moons, and perhaps more subtle influences are also at work.


A division of the circle into 29 -  when was the last time anyone did that? Avebury has such a ring of 29 stones, about a hundred metres in diameter, of which eight still remain, inside its great circle. Books on Avebury do not always appreciate that this signified a counting of the 29 days of the lunar month, and likewise nobody seemed to realise that it was the lunar month here depicted.



XI –  The Beltane Wheel       Silbury Hill, May 4th, 1998

          The 'Beltane Wheel' appeared as a powerful solar image, in a yellow field of oilseed rape (whose stems are thick and difficult to bend). It came on the day of Beltane (more or less) in the early morning: thirty-three revolving tongues of fire! Beltane was the traditional fire-festival heralding the start of Summer, as the Sun reached 15° of Taurus (midway between the Vernal Equinox and midsummer


          Its location was precisely due North of Stonehenge - Britain's solar temple. Avebury is quite closely due North of it (about two degrees East of North), but this site was spot-on due North of Stonehenge.


      Every thirty-three years, there appears a close synchrony between day and year. Multiply the length of the year (365.2422 days) by 33, and the remainder is smaller (only eleven minutes) than for any other number. Days and years will roughly coincide every four years, which gives the leap-year adjustment, but exactly they synchronise over this longer period. So thirty-three is a solar number. This is why (Robin Heath has argued), the 'solar hero' Christ was supposed to have lived for that many years. This calendar-principle was discovered by the Persian astronomer Omar Khayam in the 14th century. It is used to the present-day in the Chinese calendar, but not so well appreciated in the West. My graph here shows, how 33 years gives the smallest ‘remainder’ of days.


           Muslim readers may take a different view of the number thirty-three, because of how the lunar months of their calendar move round the solar year. How long do they take to move once round? They take thirty-three years. The feast of Ramadan moves once round the four seasons in thirty-three years. Subtract twelve times 29.53, the lunar month, from the solar year leaving ten and a bit days; dividing which into the year gives thirty-three.


        The lunar year used by Muslims is shorter than our solar year by just this amount. This Beltane6c.JPGMuslims get one extra!


Dividing the perimeter of a circle into 33 is hard enough on a laptop - how was it done in a field at night? Two little circles are centred on each of these 33 points, having a 2:3 ratio between 11c.Beltane.jpgthem. A few are here been reconstructed, showing how their interlocking pattern generated the ‘tongues of fire.’ (According to Martin Noakes) Their centres are on the flattened wheat in-between these tongues of fire. (4) I still have doubts, and would like an overhead photo, to check its accuracy.



XII.   England’s Solar Eclipse of ‘99

* 15 April 1999   Milk Hill near Alton Barnes, Wiltshire

 This solar-lunar eclipse sequences prefigured the total eclipse in August whose path of totality travelled across South-West England. It appeared on the day of a New Moon, so it was exactly four lunar months before the eclipse. Jupiter and Saturn were also fairly close, so you might want to believe that this depicted all four heavenly bodies gathered together.


*   3 May, 1999  Nether Wallop, Hampshire Comment from Andy Thomas: ‘If this doesn’t signify an eclipse then there’s no hope of ever understanding these things!’

XIII Twelvefold Year
Castle Down, Hampshire - 1 July 2000
Lockeridge, Wilts - 22 June 2005
In both these designs, the twelve moons of the year appeared in symmetrical mandala – type compositions. For the mandala-concept, see the illustrations in volume nine of Jung’s Collected Works: painted from dream-images, they are remarkably evocative of the crop-circle design The number twelve signifies integration and wholeness. These two designs separated by five years express a similar theme, it has to be the same Mind that designed them!

As twelve Moons go around the outside, the number four is also emphasised, maybe like the Four Seasons. The problem of how to fit twelve moons/months into the solar year is here expressed in the outer ring. Inside, the pattern is eightfold, and the year has an eightfold structure with its solstices, quarter-days and equinoxes. Then the centres of both designs are fourfold.

XIV The Saros
a. Silbury Hill - July 2004
Solar-lunar ‘embrace’ appears right outside the entrance to the West Kenn ett Longbarrow.

We count 18 rays of the Sun, which must here allude to the Saros (18 years and 11 days) whereby eclipse-patterns of the Sun and Moon exactly recur. As the Crop Circle Connector noted: ‘This formation is wonderfully positioned next to the ancient West Kennet Long Barrow and also very close to the mysterious Silbury Hill. This event presents us with a simple but effective motif of the sun and a crescent moon that adds a new dimension to this remarkable landscape. This indeed merges the past with the present in a very meaningful way.’

VE Transit copy.jpg This formation came one month after thetransit of Venus, across the face of the Sun, on June 8th 2004. Can you see the faint image of Venus, here moving across the face of the Sun?

This formation was exactly due North of Stonehenge. That North-South line has been historically very important for the phenomenon as it has unfolded. Stonehenge surely does have a connection to the 18-year Solar-Lunar ‘saros’ period, insofar as it is believed to have worked in relation to eclipses of the Sun and Moon.

XIV The Saros
MercGlyph.jpg An echo of this theme appeared at the same site four years later, with an 18-fold division of the solar rays. A single, tangent line indicates an 18-fold division, though we only see a part of it. The image looks like a conjunction, and we note that Mercury and Venus were both closely conjunct the Sun on this day.

XV Hermetic Meeting
18 August 2007

We are here reminded of the Mercury ‘glyph’ as used by alchemists and astrologers. There was a remarkable fourfold meeting on this day of the Sun Venus, Mercury and Saturn (Sun and Venus at 25° Leo, Mercury 27° Leo, Saturn 28° Leo). This was just the kind of one that alchemists of old might have chosen for some vital operation! Venus weaves a pentagram in the sky in its meetings with the Sun, which might here be represented. It reminds us of John Dee’s ‘Monas Heiroglyphica’ which he published in 1564.

Web-discussion of this mystery glyph indicated that croppies had not realized that a fourfold conjunction had taken place in the heavens on that day. 


XVI Solar System 2012
Avebury - 15 July, 2008

This design shows all the planets - for the date of 21st December 2012, (some felt it could be two days later, on the 23rd, but the Mercury and Venus positions are surely for the 21st - in line with Saturn). It most clearly depicts Neptune, Uranus, Saturn and Jupiter. The circles are all concentric except for that of Pluto, maybe fainter because it’s no longer a planet (according to astronomers!).

Thus we agree with Mayan calendar expert Geoff Stray: ‘This shows the exact configuration of the planets in the solar system on December 21, 2012, with the exception that Pluto is about 30 degrees off course.’ Its date of appearance was 1620 days before this prophesied end-date, which in the Mayan calendar was found to be ‘6 complete Tzolkin cycles plus 60 days (260 x 6) + 60 = 1620’ (from ‘Mark’ on the Crop Circle Connector). But also, was there some mysterious object shown between Uranus and Saturn?

A couple of years after Pluto was demoted, it is depicted for the first time in a crop circle, crossing over Neptune's orbit.


On the 22nd of July, a week later, a ‘weird circle’ appeared right next to it of comparable size -  maybe indicating the ‘strangeness’ of what many people expect on that 2012 date. Would the world somehow ‘end’ then? Curiously, the ‘Sun’ at the centre of the original design has expanded, from its July 15th size, right out to Venus’ orbit! On the Lucy Pringle link here given, you get to see this ‘final’ image. So, the world was given a week for the 2012 ‘end-date’ to sink in, as shown by a scientific diagram -  before the other half of this composition, depicting the expected ‘strangeness’ of the end-date, was added in.


This formation appeared in two halves a week apart, perhaps contrasting left-brain (logical, factual) and right-brain (childlike fantasy) themes. The Circlemakers’ take on astronomy always has some dream-like component. They seek for symbolic meaning. Never are they just concerned with fact and measure, like a modern astronomer. Also, they seem to be aware of when unusual multiple-planet conjunctions happen in the heavens, though such geocentric events have no interest for a modern astronomer. They express themselves always with grace and beauty, and I sometimes feel they come from our future.  


1.   Libra was traditionally the ‘claws of the Scorpion’ long ago: Kris Sherwood, ‘The Scorpius Hour of 1994’ The Circular Autumn 1977, p18-19.

2.   July 26 1994 Pic with kind permission from Colin Andrews.

3. (SC  Jan ’99p7). For more discussion, see  (also Jeff Stray, Beyond 2012, 2005 p.176)

4.   I’ve here followed Martin Noakes’ construction (SC 78, 1998 ‘Constructing a Wheel of Fire’); but, he said the big circle radius was divided by 6 to get the 33 smaller circles, then he further reduced this by 5/6 to get the smallest: I do not confirm these proportions.