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