The Mercedes Knot Problem

Have you ever coiled a long extension cord in order to store it (e.g. after you have finished vacuum-cleaning or mowing the lawn)? After you unwind it, you may notice that it is twisted many times (see Figure 1).

Figure 1 : Twisting of an electric cord.

Problem: Why do the extension cords usually get twisted?

Can you imagine that your solution could help you to build the submarine's periscope , i.e., an instrument by which an observer obtains an otherwise obstructed view, and by which it is possible to look around while not moving the head? A mathematical problem closely related to this phenomenon can be found in the article: The Mercedes knot problem, American Math. Monthly 103 (November 1996) 756-770 (Hasse Prize), and here are also transparencies (you can print them 8 per page) of my talk. You can find there also a few interesting puzzles, relations to quantum mechanics, effects of enzymes on a circular DNA, and the model of the quaternion group. More about knot theory can be found at http://www.theory.csc.uvic.ca/~mmania/knots/intro.htm.

Do you need a hint for the above problem?

All postscript (ps) files can be viewed using Ghostscript and GSview, which are available for most computers and browsers.