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.

Embedded
Start and Stop Points |
No Start and
Stop Points |