posted 20 years ago
Recently appeared in one regional newspaper.
Draw a rectangle ABCD with length 'x' and width 'y'.From point A ,draw an angle bisector line AE(bisecting angle BAD) ,intersecting BC at E.From point E,draw a line perpendicular to AE,intersecting CD/AD at F.Continue this procedure until you meet in one of the corners of the rectangle.Question is:
1)Is this procedure infinite(i.e.unable to meet at one of the corners) or finite? For what ratios of x/y this procedure is finite?
2)How many of such lines AE,EF.. can be drawn before meeting one of the corners?Answer in terms of x and y.
[ October 27, 2003: Message edited by: Capablanca Kepler ]