Geometry of
The
Newmarket Hill spinner, Sussex
crop circle reported May 25, 2003
How do I choose which formations to study (I certainly don't have
time to look at them all with this intensity)? In this case, I browsed
through the images of this summer's formations in chronological order
and picked the first one that looked somewhat interesting.
This one I also visited in early June. On the spot I was actually
not particularly impressed. It just didn't feel anyhow inspiring.
Perhaps this was an additional motivation - to check whether the geometry
would turn out "uninspirational" as well. It didn't... The
formation is very strongly based on the octagram shape (8-pointed
star), as I will point out with the following diagrams. Notice that
a new element is always drawn in white, in order to make the demonsration
clearer.
At
first we two circles (B1 and B2) touching the central circle (A),
their sizes defined by an octagram around the central circle.
A large circle (a) can be drawn over the entire setup.
Next,
we position a second octagram over circle 'a' in the way displayed
here. This octagram defines circle 'b' - which also happens to be
twice as large in diameter as circle 'A'.
Then
two copies of the new circle (c1 and c2) are positioned over it (b),
so that they run through the centres of 'B1' and 'B2'. They also intersect
the large circle and the second octagram at the points marked with
'x'.
Two
new circles are positioned over the intersections of the octagram
and the recently added circles 'c1' and 'c2'. They touch the edges
of circle 'B1' and 'B2'.
This
phase is also done twice, but for clarity I've zoomed into the upper
portion.
The two additional circles (D1 and E1) are also placed over 'c2'.
Their sizes can be determined in two ways. First way (white): E1 is
half of C1. When it's located at a point defined by an extension of
the first octagram, D1 fits between.
Second way (purple): When C1 is placed inside B1, D1 fits inside
the remaining space. Again, E1 is half of C1.
Finally,
copies of E1 (and E2) are placed at the end of the arcs. Their location
is the only thing that remains unexplained, since they don't quite
reach the large circle.
Based on the aerial photo, these small circles are not placed symmetrically,
which makes it even more difficult to define their place in the otherwise
complete geometry.
At
first we two circles (B1 and B2) touching the central circle (A),
their sizes defined by an octagram around the central circle.
Next,
we position a second octagram over circle 'a' in the way displayed
here. This octagram defines circle 'b' - which also happens to be
twice as large in diameter as circle 'A'.
Then
two copies of the new circle (c1 and c2) are positioned over it (b),
so that they run through the centres of 'B1' and 'B2'. They also intersect
the large circle and the second octagram at the points marked with
'x'.
Two
new circles are positioned over the intersections of the octagram
and the recently added circles 'c1' and 'c2'. They touch the edges
of circle 'B1' and 'B2'.
This
phase is also done twice, but for clarity I've zoomed into the upper
portion.
Finally,
copies of E1 (and E2) are placed at the end of the arcs. Their location
is the only thing that remains unexplained, since they don't quite
reach the large circle.
