The applet below shows your left shoe. How can you put a shoelace into the shoe in such a way to minimize the total length of the shoelaces? The only rule is that you have to start at the top left hole, always alternate between left and right, use all holes, and end at the top right hole. What happens if you change the number of holes, the distance dx between left and right, and dy, the distance between consecutive holes on either side?
Erich Prisner, August 2003