[net.math] Generalizations of Morley's Theorem

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.