John Sayer

Formation: circle with concentric ring

Crop: wheat

Location: Beltershausen, near Marburg, Germany

Date formed: 15th./16th. June 1995

Dimensions: circle - 38m. diameter, standing ring - 3m. width, 44m. diameter, flattened ring - 2m. width, 48m. diameter, tramlines - 2m. width, 14m. apart

This formation had appeared during the night of 15th./16th. June 1995 in a field of wheat on the edge of the village and close to the road to Marburg, Germany. According to the regional newspaper, the "Oberhessichen Presse", locals interviewed neither heard nor saw anything unusual during the night, although opinions were divided among those who theorised (like so many everywhere!) that it was the result of either a UFO landing in the field or pranksters at work. Both circle and ring were swirled clockwise, and it was recorded in the newspaper that while the crop was recovering within the circle, in the ring it was completely flat.

A 38m. diameter circle was surrounded by a 3m. ring of standing crop and a 2m. wide flattened ring (dimensions of rings derived from photographs). The circle's centre was midway between two sets of tramlines and the entire formation spanned symmetrically four sets of tramlines altogether (fig. 1):

While preparing an illustration for a report I noticed some interesting coincidences about the formation. Already knowing the diameter of the central circle from the newspaper report, and since the photograph published in the "FGK Report" was taken looking straight down the tramlines and was corroborated by the photograph in the "Oberhessichen Presse", I was able to work out to a high degree of accuracy the widths of the rings, the tramlines and the spacing between them. Inspired by the work of John Martineau, but in particular that of Wolfgang Schindler, who drew attention to the significance of tramlines when conducting geometrical analysis, I began idly playing with my plan of the formation - and what I discovered surprised me.

Now, there's nothing significant about two overlapping equilateral triangles circumscribed by a circle, but it does become interesting in the structure of a crop formation when points of intersection of these triangles coincide with tramlines (fig. 2). While it is conceivable that someone could design a crop formation to incorporate various geometrical relationships and then go out and make it (for example, I conducted such a detailed measurement and study of the 1993 Bythorn formation "in situ" that I could, in theory, reproduce it in a field of crop, including the order in which the various parts were laid), to design something which needs tramlines - over which the designer has no control - to give it geometrical importance is something else altogether, in my opinion.

I find it significant that of the eleven analyses presented here, only two have nothing to do with tramlines (figs. 7 & 9). In the cases of the other nine, I have extended the relevant tramlines across the diagram to highlight the point. I am quite prepared for anyone to replicate what I have done and, if necessary, show me to be mistaken, but I have checked these computer-drawn diagrams with pencil, paper, ruler and protractor and am satisfied that they are correct. In a couple of cases, where I was unsure whether my measuring and drawing (including mouse-handling) skills were completely spot on, I am happy that they are accurate above 97.5%, which I think is acceptable, taking a cue from John Martineau's "A Book of Coincidence", when we consider the medium the formation itself was produced in. All the rest, however, are 100% correct.

Without a detailed survey, as I say, I have had to rely on photographs to derive measurements, but the fact that they nevertheless work out so neatly is an interesting coincidence in itself.

The diagrams speak for themselves, but the following notes should clarify them further:

Fig. 2 - Two overlapping equilateral triangles, circumscribed by the inner circumference of the ring, intersect on the inner sides of the innermost tramlines.

Fig. 3 - A square circumscribed by the outer circumference of the ring, drawn at an angle of 45 degrees to the tramlines, coincides with the intersection of the inner sides of the innermost tramlines and the circumference of the circle.

Fig. 4 - A square circumscribed by the outer circumference of the ring, drawn parallel to the tramlines, coincides with the intersection of the outer sides of the innermost tramlines and the circumference of the circle.

Fig. 5 - Two overlapping squares, circumscribed by the inner circumference of the ring, intersect on the inner sides of the innermost tramlines.

Fig. 6 - Two overlapping pentagons, circumscribed by the outer circumference of the ring, intersect on the inner sides of the innermost tramlines.

Fig. 7 - A hexagon drawn around the circle is circumscribed by the inner circumference of the ring.

Fig. 8 - The length of side of a septagon drawn within the circumference of the circle is defined by the distance between the outer sides of two sets of tramlines.

Fig. 9 - An octagon drawn around the inner circumference of the ring is circumscribed by the outer circumference of the ring.

Fig. 10 - The length of side of a nonagon drawn around the inner circumference of the ring is defined by the distance between the outer sides of two sets of tramlines.

Fig. 11 - The length of side of an eleven-sided figure ("undecagon"?) circumscribed by the inner circumference of the ring is defined by the distance between two sets of tramlines.

Fig. 12 - The length of side of a dodecagon drawn around the inner circumference of the ring is defined by the distance between two sets of tramlines.

Further investigation of this event led me to interviewing one of its alleged creators. Yes, in spite of the intriguing geometry involved, it was apparently man-made. In answer to my questions, I learned that no dimensions had been planned and no measurements taken. It was created "intuitively". Now, this provides a further point of interest: if such complex geometrical overlays can be discovered in an "off the cuff" formation, what does this indicate?

My own opinion is that this is all to do with the "natural" balance and harmony we subconsciously recognise in something which is visually pleasing - whether it be part of nature, or a man-made creation such as a sculpture or painting. This notion will be familiar to those who are content to study crop formations simply as "art". To me, finding these geometrical corroborations was interesting and mildly exciting. I do not, however, consider myself to be especially clever for doing so. But I do think that it hints at arrogance to presume that only "nature" or something "other-dimensional" or "cosmic" can incorporate mathematics, geometry or spirituality into a crop circle and that "mere mortals" could not do so. It is even more arrogant to imply that "hoaxers" cannot put into a formation what a researcher can get out of it.

The geometry of innocent flesh on the bone Causes Galileo's math book to get thrown At Delilah who's sitting worthlessly alone But the tears on her cheeks are from laughter...

(Bob Dylan - "Tombstone Blues", from the album "Highway 61 Revisited")

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