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In general, for N generating points in a circle,
the number of ways to connect all the points with lines of equal length
is equal to N/2 if N is even or (N - 1)/2 if N is odd. This means that
in the example, there are (47 - 1)/2 = 23 possible layers.
CIRCULAR, ELLIPTICAL, and STARBURST DESIGNS:
As shown previously, it is the arrangement of generating
points which determines the shape of each design. In this section, we will
show how these points are accurately located for each of the basic patterns
shown and how the resulting points are threaded.
DESIGNING a CIRCULAR TEMPLATE:
Needed for laying out a precise template are a sharp pencil,
paper, a ruler, some string, a hammer, nail, a flat board, and a compass.
With these tools anyone can geometrically construct the set of generating
points for circular, elliptical and starbburst geometric thread designs.
Let's look at the simplest case and consider the steps
for drawing a circular template:
1. Cut a piece of paper square to the desired size
or background. Locate the center of the square by drawing diagonal lines
connecting opposite corners. The two diagonals intersect at the center
point, which will eventually be the center of the circular design.
2. Draw a circle using a small nail driven into
the center point and a piece of string to the radius of the desired circle.
3. Subdivide the circle into a prime number of
equal parts.
A prime number has no divisors
other than one and itself, like 11, 41, 67, and 101. With a prime number
of generating points, each layer in the design can be made with one continuous
strand of thread, tied off neatly only where the ends meet.
See Appendix
A for more on prime numbers.
As outlined above, constructing
a circular template if fairly simple. You should take care, however, in
completing each step. The accuracy, for instance, of finding the center
point and drawing a circle will determine how well the finished design
is centered.
Red circle with omitted layers |
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