An examination of the geometry involved in constructing such an elaborate formation
OS Ref. SU 079700
Date of creation: 22nd July 2000
Date of survey: 29th July 2000 (8.30pm)
We parked the car on what was another magical summer evening in Wiltshire and made our way to the crop formation. Although hardly visible from the A4, the formation was easily spotted from the farm track which passes the field on it's way from Avebury Trusloe to Yatesbury Field.
The formation was some 500 yards into the field and spanned three tramlines, which made it approx 180' diameter. There was no denying that this formation is an impressive creation and a milestone in crop circle design. Resembling a huge magnetic field pattern - if you imagine the orientation of iron filings sprinked on a piece of paper underneath which there is a bar magnet.
From the air, it looks like the formation is a complex series of curves leading out from the two centres. However, ground inspection revealed that the formation was constructed entirely using straight lines and that any 'curving' effect was due to an optical illusion of viewing the formation. My partner Cathy, who is psychic felt immediately that the formation was a hoax - much to the dismay and indignation of the rest of our group. Whilst the ground lay was fairly poor, I put that down the to the fact we couldn't get to the formation for a week and it had been thoroughly visited by tourists and 'croppies'. However, I also detected no electronic malfunctions or equipment failure - often indicative of a genuine formation. None the less, I was less inclined to dismiss the formation as being man-made, simply because of it's impressive design.
I immediately set to working out what geometrical process would be required in order to construct this formation and the following diagrams demonstrate one method by which the design can be plotted. Of course, executing this in the dark of night without getting caught and, more importantly, without making a mistake all go to show what an impressive feat it was to create it - whatever it's ultimate origin.
Following a subsequent discussion with a friend of mine who is a maths and geometry teacher, we discovered that there are at least two different ways of constructing this formation. However, I will concentrate on just one in this explanation, which I think is the simplest to illustrate.
You would initially start with the outer circle of a chosen radius. Indeed, this could be marked out on the ground because the whole formation is surrounded by a larger 'ring' anyway. In the process you would note the centre point (indicated by the dotted lines).
Having constructed the bounding circle, half the radius and move along the horizontal axis line to the centre point (1/4 of the overall diameter), shown in figure 2. This should give you the centre points of the two centres required, from which the radiating lines emit.
Counting from the right most horizontal axis point and moving around half the circumference we can count 29 points (the standing crop 'diamond' shapes). Because both the left and right (start and end) positions are blank, this effectively gives us 30 points in one semi-circle, or 60 points around the whole formation - which makes for a nice convenient 6 degree spacing between points, measured from the centre position (not the smaller circles).
N.B. For simplicity of diagrams I'm basing this explanation on half of the circle, but as you can see, the entire process is merely repeated for the lower half.
Diagram 3a (below) shows what happens if you incorrectly mark the perimeter points by using the half radius point as the centre.
As you can see, the subtle inaccuracy becomes obvious if you make the mistake of marking out the 29 outer points by using the half radius point. If you look carefully, the green lines (radiating from the half radius point) don't correspond with the correct circumference positions defined by the main centre point (the red lines).
Because the centre of origin is nearer one side of the overall circumference, the angle of spread will be wider on the opposite side of the circle than it will be on the near side - similar to the spread of a torch being narrower the closer you are to it.
The next step is to plot straight lines joining each of the half radius points with the 29 perimeter points just marked out (the red lines in fig.3 above). This is shown in figure 4 by the blue lines. Each half radius centre point is joined to every one of the outer 29 points on the circumference. This can either be constructed by zig-zagging between each outer point and each half radius point, or by plotting each line in turn (the first method is probably quicker because it involved less path drawing).
The final step is to actually fill in alternating areas bounded by the intersections of the lines in figure 4. As you can see, the finished design is starting to look familiar.
As I explained earlier, for clarity I've described how to construct the formation based on one half. The remaining half follows exactly the same process as above. Indeed, because the design is symmetrical you could construct the second half whilst you created the paths shown in figure 4 (above) simply by extending the path through the half radius point until it reached the perimeter on the other side of the design.
By flattening the outer 'ring' the formation is complete. As you can now see, the entire formation was constructed using straight lines, but the illusion of curves is quite good.
Whether the circle makers come from elsewhere or are merely humans, I'm sure you'll agree that this is one of the most impressive crop formations so far.