Lill's Method with Right Angled Polygonal Paths

The animations below demonstrate Lill's Method with right angled paths. 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.

Notice that below each graph are text boxes showing values for the angle, variable t, and p(t). The angle is measured between the red and blue paths at the origin.

For any angle, the red path is drawn as follows. The first leg is drawn at the prescribed angle from the origin to the second leg of the blue path (or the line containing that leg). Each successive red leg is perpendicular to its predecessor, and continues to the next blue leg (or the line containing that leg). The animation shows how the red path evolves as the angle increases. Whenever the endpoints of the red and blue paths coincide, that corresponds to a root of the given polynomial.

Embedded Start and Stop Points
No Start and Stop Points