University of Arizona
Institute for Mathematics and Education

February 19, 2008

Ropin' in the Mathematics

presented by Dr. Ji Li and Ginny Bohme.

The activity Ropin' in the Mathematics was based on a lecture given by John Horton Conway, who is a mathematician noted for his work in the theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. Tom Davis, a scientist who works closely with San Francisco Bay Area Mathematics Circles and Teachers’ Circles, adapted Conway’s notes to create the activity used.


Participants used three “dance moves” using two lengths of rope:
  • Twist
  • Rotate
  • Display
    Repeated steps were used to tangle the ropes. The challenge was to untangle them using only the three kinds of moves available. We worked as a group to design the “untangle” moves by visually seeing the results of each conjectured step. We then used mathematical methods to design “untangle” moves and were delighted to see them work.

    • rope start twist
    The starting position is
    two parallel ropes.    		 The rope is displayed after
    one twist move.
    display knot
    We tested if a twist followed by a rotate was equivalent to a twist.After gaining experience with "untangling", we worked on
    messier knots to practice.


    This activity has roots in topology, which is not a topic typically covered in school mathematics.
    Some of the AIMS Standards addressed include:
    1.2.3 Recognize the application of the properties of the real number system: commutative, associative, identity, and inverse.
    3.3.1 Write an algebraic expression to represent a situation.
    5.1.2 Evaluate the quality and accuracy of an answer based on given information and procedures used.
    5.2.2 Solve a non-routine problem by selecting and using a strategy.