“Tied up in Knots”
This lesson is designed to introduce students to the mathematical definition of a knot and knot equivalence.
6 and up
Using the Powerpoint, the instructor gives a talk about knots: their history and usefulness, the mathematical definition of a knot, and knot equivalence. Students use pieces of rope to investigate whether the trefoil and the unknot are equivalent.
After the Powerpoint:
Have students tie a shoelace knot (just as if they were tying their shoes). What is this knot equivalent to?
Time permitting, groups of students can form a “human knot” by standing in a circle and grabbing hands. The object is to see if they can reduce the knot to a circle (the unknot) or a recognizable knot without releasing their hands.
Powerpoint of the lesson, rope (approx. 1 ½ feet long) for each student.
The answers are:
1. On Slide 6, knot 1 is equivalent to knot 2.
2. On Slide 8, the trefoil and the unknot are distinct—you cannot get the unknot from the trefoil without breaking apart the knot.
2. The shoelace knot (the one most people tie) is equivalent to the trefoil.
3. Human knots may vary.
More about knots:
Why Knot?: An Introduction to the Mathematical Theory of Knots By Colin Adams.