trough@ihuxa.UUCP (Chris Scussel) (12/01/83)
Morley's theorem state that the intersections of the (correct) pairs of a triangle's angle trisectors are the vertices of an equilateral triangle. The bisectors meet at a point (one of the many "special" points of a triangle). Now consider an x-sector: a line that "cuts off" the proportion x of the angle (e.g., a bisector has x=1/2, a trisector has x=1/3). Now consider what happens as x varies. Note that when x=0 the x-sectors are collinear, but intersection points are still well defined (as limits). What other values of x are interesting besides 0, 1/2, and 1/3? What about extending the domain of x beyond [0,1/2]? Comments? Chris Scussel Bell Labs Naperville, Ill.