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Enigma Issue 3: Further Research into the Bythorn Formation (1993)

by Paul Vigay | Summer 1994

This formation appeared in Cambridgeshire in 1993 and immediately drew the attention of circle researchers, due to the claims of authorship by a young hoaxer.

Personally I haven't formed an opinion with regards to the origin of this formation. However, in light of some of the controversy concerning it, coupled with various claims from hoaxers and researchers, I was prompted to investigate it in more depth using computer analysis.

As I didn't know what I was looking for, merely hunting for any interesting or strange results, I have included as much calculation as possible so that a starting position for further investigation can be gleened. Also, not knowing if any significant numbers would arise, I have performed all calculations simultaneously in imperial, metric and megalithic yards using the following conversions;

    1 inch              =  25.4000 mm
1 foot = 304.8000 mm
1 yard (36 inches) = 914.4000 mm
1 Megalithic yard = e feet = 2.7183 feet = 828.5323 mm

By scanning a photograph of the formation I was able to calculate a 'computer scale' of measurements by knowing that the NS diameter was 172'9" and the EW diameter was 174'9" (from J.Martineau's survey). On my computer image the EW diameter was 191mm. As 174'9" is equal to 2097", I calculated the following scale;

   2097/191 = 10.9790 inches - therefore, 1mm on my computer image
equals 10.979" on the ground.

Each petal consists of two curves. However, by looking at opposite curves on adjacent petals, I could see that different radii circles were used in their construction*. Using computer graphic overlays I was able to calculate the radii necessary to form the petals (see diagram). I was surprised to find that only two such circles are required to create all ten petals. However the offset between their relative centre points varies quite randomly. Thus we have conclusive proof that the formation cannot have been made using a single radii for all the crescents - as the hoaxer claimed!

By measurement, I found that the two circles have radii of 75mm and 63mm respecitvely on my computer image. Using the scale above, these correspond to actual measurements of;

   75mm  =   823.425"  = 68' 7.425"  = 25.24343 MY
= 20914.995 mm

63mm = 691.677" = 57' 7.677" = 21.20448 MY
= 17568.5958 mm

Surprisingly, given the number of decimal places, the ratio of the smaller circle is EXACTLY 84% the diameter of the larger one. The ratio of the smaller circle to the whole formation is 32.98412% and the ratio of the bigger circle to the whole formation is 39.266810%

I then moved on to measure the distance between relevant centre points of the circles forming the petal arcs. These gave the following values (sorted in order of value) and ratios to each other;

      21.9580" =  557.7332mm      % age of previous value
21.9580" = 557.7332mm 100.0000
32.9370" = 836.5998mm 66.6666 (recurring)
43.9160" = 1115.4664mm 75.0000
60.3845" = 1533.7663mm 72.7272 (recurring)
98.8110" = 2509.7994mm 61.1111 (recurring)
109.7900" = 2788.6660mm 90.0000
109.7900" = 2788.6660mm 100.0000

[image e003b1.gif]

As you can see, the ratios give quite interesting results (although nothing meaningful) in that they are all exact values or fractions of 99. For example

               66.6666 equals 66 and 66/99,
72.7272 equals 72 and 72/99,
and lastly, 61.1111 equals 61 and 11/99.

If anyone finds any of these values significant, I would welcome any feedback from this analysis.

[image e003b2.gif] Click on the image to download a 116k JPEG image.

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