Geometry of the
Northdown, Wiltshire formation
found May 6, 2002

Perspective corrected view of the photo by Steve Alexander

It looks like an ellipse, but apparently it's not. The largest element in this formation looks actually quite irregular. However, at least the arc inside the flattened crescent and the one curving down from it towards the lower right seem to be circular. In the following study we'll see that also the lower left side of this ring might be part of a circle, because the diameter "makes sence".

In the diagram above, all the circles defining this pattern are marked on the perspective corrected photo. You can notice at this point that the smallest one (G) is not a perfect match.

The relative sizes of these circles are (from A to G):

100, 70, 59, 41, 17, 14 and 12.

What is interesting here is that these figures are part of a sequence, where the ratio of all the circles is 0,837 - the square root of 0,7:

100, 84, 70, 59, 49, 41, 34, 29, 24, 20, 17, 14, 12.

What significance does 0,7 have then? Well, 0,7071 is the square root of 0,5 AND it is the ratio betweem two circles defined by a square as displayed in the image on left.

The same sequence, when using sqr of 0,7071; 0,841, is (in integers):

99, 83, 70, 59, 50, 42, 35, 29, 25, 21, 18, 15, 12.

Starting with 99, you can see the difference is nowhere more than 1 integer unit, which does not have much significance here, since it's not possible to get very exact measurements in rape field pattern.

In any case, the sizes of the circles defining this formation follow a sequence of numbers, bound by a fixed aspect ratio.

With the ratio of 0,841 we can conclude the following: Proceeding two steps in the sequence produces the square-circle ratio described above. Proceeding four steps produces 0,5 ratio (twice smaller).

In other words, in the finished pattern there is the square relationship between two circle pairs; A-B and C-D (E-G is not perfect). However, the 0,5 ratio is not present at all.