Lill's
Method with non-Right Angled Polygonal Paths
In Lill's Method the paths are drawn turning through 90 degrees at
each vertex. But a similar method works just as well turning through
any fixed angle f. The construction of
blue and red paths is as before, and the final points coincide only
for angles q corresponding to roots of the
polynomial. In the general case, the root is given by
-sin(q)/sin(f-q). This reduces to -tan(q) when f = p/2.
The animations below demonstrate Lill's Method with paths
whose edges meet at a 75 degree angle. The window on the left has
embedded start and stop points. The one on the right plays
through without interruption. You can also use the control bar
below each image to start and stop the animation.